auto_pipeline_slicing_dp_ipynb-copy.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/explcre/pipeDejavu/blob/main/auto_pipeline_slicing_dp_ipynb-copy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!nvidia-smi"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "odJN1gvqnzWh",
        "outputId": "a319dc56-0cc6-4fcf-93cf-39e95af67996"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/bin/bash: nvidia-smi: command not found\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "\n",
        "# Define a simple input tensor with 7 elements\n",
        "x = torch.tensor([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], requires_grad=True)\n",
        "\n",
        "# Apply the max operation on the input tensor\n",
        "max_value, max_idx = torch.max(x,dim=0)\n",
        "\n",
        "# Define the loss function as the max value\n",
        "loss = max_value\n",
        "\n",
        "# Compute the gradients\n",
        "loss.backward()\n",
        "\n",
        "# Print the gradients with respect to the input tensor\n",
        "print(\"Gradients: \", x.grad)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C84lnwV3YjXK",
        "outputId": "0663090e-13bf-44d3-9cf2-39b9228c0420"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradients:  tensor([0., 0., 0., 0., 0., 0., 1.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "def knapsack(items, capacity):\n",
        "    n = len(items)\n",
        "    dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]\n",
        "\n",
        "    for i in range(1, n + 1):\n",
        "        weight, value = items[i - 1]\n",
        "        for w in range(capacity + 1):\n",
        "            if weight <= w:\n",
        "                dp[i][w] = max(dp[i - 1][w], dp[i - 1][w - weight] + value)\n",
        "            else:\n",
        "                dp[i][w] = dp[i - 1][w]\n",
        "\n",
        "    selected_items = []\n",
        "    i, w = n, capacity\n",
        "    while i > 0 and w > 0:\n",
        "        weight, value = items[i - 1]\n",
        "        if dp[i][w] != dp[i - 1][w]:\n",
        "            selected_items.append(i - 1)\n",
        "            w -= weight\n",
        "        i -= 1\n",
        "\n",
        "    return dp[n][capacity], selected_items\n",
        "\n",
        "# Example usage:\n",
        "items = [(2, 3), (3, 4), (4, 5), (5, 6)]  # (weight, value)\n",
        "capacity = 5\n",
        "start=time.time()\n",
        "max_value, selected_items = knapsack(items, capacity)\n",
        "end=time.time()\n",
        "print(max_value, selected_items)\n",
        "print(\"time=\",end-start)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5L6vbkE50S5O",
        "outputId": "8e537c84-b50d-4cb1-9567-38371762cb50"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7 [1, 0]\n",
            "time= 0.00019359588623046875\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "\n",
        "def soft_knapsack(items, capacity, iterations=5000, learning_rate=0.01):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.Adam([item_selection], lr=learning_rate)\n",
        "\n",
        "    for _ in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "    final_selection = torch.sigmoid(item_selection) > 0.5\n",
        "    selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "    max_value = torch.sum(final_selection * values).item()\n",
        "\n",
        "    return max_value, selected_items\n",
        "\n",
        "# Example usage:\n",
        "items = [(2, 3), (3, 4), (4, 5), (5, 6)]  # (weight, value)\n",
        "capacity = 5\n",
        "start=time.time()\n",
        "max_value, selected_items = soft_knapsack(items, capacity)\n",
        "end=time.time()\n",
        "print(max_value, selected_items)\n",
        "print(\"time=\",end-start)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-onagjca0Wnd",
        "outputId": "55642e5d-7314-437c-8b79-c0621d5adfdb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7.0 [0, 1]\n",
            "time= 3.351736068725586\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def soft_knapsack(items, capacity, iterations=5000, learning_rate=0.01, temperature=0.5):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    for _ in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "    final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "    selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "    max_value = torch.sum(final_selection * values).item()\n",
        "\n",
        "    return max_value, selected_items"
      ],
      "metadata": {
        "id": "7pxjDrjH6CW0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def soft_knapsack(items, capacity, iterations=5000, learning_rate=0.01, temperature=0.5):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Print intermediate results\n",
        "        if (i + 1) % 500 == 0:\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\n",
        "\n",
        "    final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "    selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "    max_value = torch.sum(final_selection * values).item()\n",
        "\n",
        "    return max_value, selected_items"
      ],
      "metadata": {
        "id": "Ef3fBuLy6fQ5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import namedtuple\n",
        "\n",
        "Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\"])\n",
        "\n",
        "def soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Update best solutions\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "        max_value = torch.sum(final_selection * values).item()\n",
        "        current_solution = Solution(max_value, selected_items, final_selection)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "        elif max_value > best_solutions[-1].value:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "\n",
        "    return best_solutions"
      ],
      "metadata": {
        "id": "QtR1gr6_7jFT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import namedtuple\n",
        "\n",
        "Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\"])\n",
        "\n",
        "def soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Update best solutions\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "        max_value = torch.sum(final_selection * values).item()\n",
        "        current_solution = Solution(max_value, selected_items, final_selection)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "        elif max_value > best_solutions[-1].value:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "\n",
        "        # Print intermediate results\n",
        "        if (i + 1) % print_every == 0:\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\n",
        "            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\n",
        "\n",
        "    max_value = best_solutions[0].value\n",
        "    selected_items = best_solutions[0].items\n",
        "    return max_value, selected_items, best_solutions\n",
        "\n",
        "# Time and run the differentiable knapsack solution\n",
        "start_time = time.time()\n",
        "max_value_diff, selected_items_diff, best_solutions = soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500)\n",
        "end_time = time.time()\n",
        "\n",
        "print(f\"Differentiable Knapsack: max_value={max_value_diff}, selected_items={selected_items_diff}, time={end_time - start_time:.2f}s\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kvVbbex48qz9",
        "outputId": "b972635f-c478-4e86-9fdd-3ec5d77df1ab"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 500: loss=56169.26, total_value=1222.51, total_weight=1239.57\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 1000: loss=-1010.93, total_value=1011.20, total_weight=1000.52\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 1500: loss=-1957.79, total_value=1958.61, total_weight=1000.90\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 2000: loss=-4612.74, total_value=4612.74, total_weight=996.17\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 2500: loss=-5562.35, total_value=5567.02, total_weight=1002.16\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 3000: loss=-5711.57, total_value=5716.15, total_weight=1002.14\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 3500: loss=-5733.84, total_value=5737.21, total_weight=1001.84\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 4000: loss=-5737.65, total_value=5740.53, total_weight=1001.70\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 4500: loss=-5738.83, total_value=5741.48, total_weight=1001.63\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Iteration 5000: loss=-5739.24, total_value=5741.77, total_weight=1001.59\n",
            "Best solution so far: value=22315.0, items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499]\n",
            "Differentiable Knapsack: max_value=22315.0, selected_items=[0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 278, 280, 281, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 340, 341, 342, 344, 345, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 458, 459, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499], time=8.15s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import namedtuple\n",
        "\n",
        "Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\"])\n",
        "def soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        loss = -(total_value - capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Update best solutions only if the solution is valid (total_weight <= capacity)\n",
        "        if total_weight <= capacity:\n",
        "            final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "            selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "            max_value = torch.sum(final_selection * values).item()\n",
        "            current_solution = Solution(max_value, selected_items, final_selection)\n",
        "\n",
        "            if len(best_solutions) < n_best:\n",
        "                best_solutions.append(current_solution)\n",
        "                best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "            elif max_value > best_solutions[-1].value:\n",
        "                best_solutions.pop()\n",
        "                best_solutions.append(current_solution)\n",
        "                best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "\n",
        "        # Print intermediate results\n",
        "        if (i + 1) % print_every == 0:\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\n",
        "            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\n",
        "\n",
        "    max_value = best_solutions[0].value\n",
        "    selected_items = best_solutions[0].items\n",
        "    return max_value, selected_items, best_solutions\n"
      ],
      "metadata": {
        "id": "U7pW_XWH-8CS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import namedtuple\n",
        "\n",
        "Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\"])\n",
        "\n",
        "def soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500, penalty_factor=1e7):\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        # Multiply capacity_penalty by a large constant\n",
        "        loss = -(total_value - penalty_factor * capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Update best solutions\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "        max_value = torch.sum(final_selection * values).item()\n",
        "        current_solution = Solution(max_value, selected_items, final_selection)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "        elif max_value > best_solutions[-1].value:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "\n",
        "        # Print intermediate results\n",
        "        if (i + 1) % print_every == 0:\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\n",
        "            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\n",
        "\n",
        "    max_value = best_solutions[0].value\n",
        "    selected_items = best_solutions[0].items\n",
        "    return max_value, selected_items, best_solutions\n"
      ],
      "metadata": {
        "id": "CT2ePOF6ARNO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def knapsack(items, capacity, print_every=500):\n",
        "    n = len(items)\n",
        "    dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]\n",
        "\n",
        "    best_solutions_dp = []\n",
        "\n",
        "    for i in range(1, n + 1):\n",
        "        weight, value = items[i - 1]\n",
        "        for w in range(capacity + 1):\n",
        "            if weight <= w:\n",
        "                dp[i][w] = max(dp[i - 1][w], dp[i - 1][w - weight] + value)\n",
        "            else:\n",
        "                dp[i][w] = dp[i - 1][w]\n",
        "\n",
        "        if i % print_every == 0:\n",
        "            best_solutions_dp.append(dp[i][-1])\n",
        "            print(f\"Iteration {i}: Best solution so far for DP: value={dp[i][-1]}\")\n",
        "\n",
        "    selected_items = []\n",
        "    i, w = n, capacity\n",
        "    while i > 0 and w > 0:\n",
        "        weight, value = items[i - 1]\n",
        "        if dp[i][w] != dp[i - 1][w]:\n",
        "            selected_items.append(i - 1)\n",
        "            w -= weight\n",
        "        i -= 1\n",
        "\n",
        "    return dp[n][capacity], selected_items, best_solutions_dp\n"
      ],
      "metadata": {
        "id": "FTZ754y2SdXU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def knapsack(items, capacity, print_every=500,timer_every=10):\n",
        "    n = len(items)\n",
        "    dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]\n",
        "\n",
        "    best_solutions_dp = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for i in range(1, n + 1):\n",
        "        weight, value = items[i - 1]\n",
        "        for w in range(capacity + 1):\n",
        "            if weight <= w:\n",
        "                dp[i][w] = max(dp[i - 1][w], dp[i - 1][w - weight] + value)\n",
        "            else:\n",
        "                dp[i][w] = dp[i - 1][w]\n",
        "            \n",
        "        if i % timer_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solutions_dp.append((elapsed_time, dp[i][-1]))\n",
        "        if i % print_every == 0:\n",
        "            \n",
        "            print(f\"Iteration {i}: Best solution so far for DP: value={dp[i][-1]}, elapsed_time={elapsed_time:.2f}s\")\n",
        "\n",
        "    selected_items = []\n",
        "    i, w = n, capacity\n",
        "    while i > 0 and w > 0:\n",
        "        weight, value = items[i - 1]\n",
        "        if dp[i][w] != dp[i - 1][w]:\n",
        "            selected_items.append(i - 1)\n",
        "            w -= weight\n",
        "        i -= 1\n",
        "\n",
        "    return dp[n][capacity], selected_items, best_solutions_dp,n\n"
      ],
      "metadata": {
        "id": "nXTFNToSWbKr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import namedtuple\n",
        "\n",
        "#Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\"])\n",
        "\n",
        "Solution = namedtuple(\"Solution\", [\"value\", \"items\", \"selection\", \"elapsed_time\"])\n",
        "\n",
        "def soft_knapsack(items, capacity, n_best=10000, iterations=10000, learning_rate=100, temperature=0.5, print_every=500, penalty_factor=1e7,capacity_epsilon=0.1):\n",
        "    capacity_episilon=capacity*1.95\n",
        "    #penalty_factor=0\n",
        "    n_best=iterations\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    ##added as follows\n",
        "    item_selection_divided = (item_selection.detach()+0.5) / temperature\n",
        "    item_selection_divided.requires_grad_()\n",
        "    ##added as above\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature-0.5)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity-capacity_epsilon, min=0) ** 2\n",
        "\n",
        "        # Multiply capacity_penalty by a large constant\n",
        "        loss = -(total_value - penalty_factor * capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) >= 0.5\n",
        "        selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "        max_value = torch.sum(final_selection * values).item()\n",
        "        if max_value <= capacity:\n",
        "          # Update best solutions\n",
        "          '''\n",
        "          final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "          selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "          max_value = torch.sum(final_selection * values).item()\n",
        "          '''\n",
        "          current_solution = Solution(max_value, selected_items, final_selection,time.time() - start_time)\n",
        "          #best_solution = best_solutions[0]\n",
        "          if len(best_solutions) <= n_best:\n",
        "              best_solutions.append(current_solution)\n",
        "              best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "          elif max_value > best_solutions[-1].value:\n",
        "              best_solutions.pop()\n",
        "              best_solutions.append(current_solution)\n",
        "              best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "              # Print intermediate results\n",
        "        if (i + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\n",
        "\n",
        "    max_value = best_solutions[0].value\n",
        "    selected_items = best_solutions[0].items\n",
        "\n",
        "    best_solutions_diff = sorted([(s.elapsed_time, s.value) for s in best_solutions], key=lambda x: x[0])\n",
        "    #best_solutions_diff = [(s.elapsed_time, s.value) for s in best_solutions]\n",
        "\n",
        "    return max_value, selected_items, best_solutions_diff\n",
        "\n",
        "\n",
        "'''\n",
        "def soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500, penalty_factor=1e7):\n",
        "    start_time = time.time()\n",
        "    n = len(items)\n",
        "    weights, values = zip(*items)\n",
        "    weights = torch.tensor(weights, dtype=torch.float)\n",
        "    values = torch.tensor(values, dtype=torch.float)\n",
        "\n",
        "    item_selection = torch.rand(n, requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    for i in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        total_weight = torch.sum(soft_selection * weights)\n",
        "        total_value = torch.sum(soft_selection * values)\n",
        "        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\n",
        "\n",
        "        # Multiply capacity_penalty by a large constant\n",
        "        loss = -(total_value - penalty_factor * capacity_penalty)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        # Update best solutions\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        selected_items = [i for i, selected in enumerate(final_selection) if selected]\n",
        "        max_value = torch.sum(final_selection * values).item()\n",
        "        current_solution = Solution(max_value, selected_items, final_selection, time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "        elif max_value > best_solutions[-1].value:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x.value, reverse=True)\n",
        "\n",
        "        # Print intermediate results\n",
        "        if (i + 1) % print_every == 0:\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\n",
        "            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\n",
        "\n",
        "    max_value = best_solutions[0].value\n",
        "    selected_items = best_solutions[0].items\n",
        "    best_solutions_diff = [(s.elapsed_time, s.value) for s in best_solutions]\n",
        "\n",
        "    return max_value, selected_items, best_solutions_diff\n",
        "'''"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 214
        },
        "id": "lXGejWTBWnEr",
        "outputId": "f7a7f839-146e-4b4f-f8fb-6639497231e6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'\\ndef soft_knapsack(items, capacity, n_best=5, iterations=5000, learning_rate=0.01, temperature=0.5, print_every=500, penalty_factor=1e7):\\n    start_time = time.time()\\n    n = len(items)\\n    weights, values = zip(*items)\\n    weights = torch.tensor(weights, dtype=torch.float)\\n    values = torch.tensor(values, dtype=torch.float)\\n\\n    item_selection = torch.rand(n, requires_grad=True)\\n    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\\n\\n    best_solutions = []\\n\\n    for i in range(iterations):\\n        optimizer.zero_grad()\\n        soft_selection = torch.sigmoid(item_selection / temperature)\\n        total_weight = torch.sum(soft_selection * weights)\\n        total_value = torch.sum(soft_selection * values)\\n        capacity_penalty = torch.clamp(total_weight - capacity, min=0) ** 2\\n\\n        # Multiply capacity_penalty by a large constant\\n        loss = -(total_value - penalty_factor * capacity_penalty)\\n        loss.backward()\\n        optimizer.step()\\n\\n        # Clamp item_selection values between -5 and 5\\n        item_selection.data.clamp_(-5, 5)\\n\\n        # Update best solutions\\n        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\\n        selected_items = [i for i, selected in enumerate(final_selection) if selected]\\n        max_value = torch.sum(final_selection * values).item()\\n        current_solution = Solution(max_value, selected_items, final_selection, time.time() - start_time)\\n\\n        if len(best_solutions) < n_best:\\n            best_solutions.append(current_solution)\\n            best_solutions.sort(key=lambda x: x.value, reverse=True)\\n        elif max_value > best_solutions[-1].value:\\n            best_solutions.pop()\\n            best_solutions.append(current_solution)\\n            best_solutions.sort(key=lambda x: x.value, reverse=True)\\n\\n        # Print intermediate results\\n        if (i + 1) % print_every == 0:\\n            best_solution = best_solutions[0]\\n            print(f\"Iteration {i+1}: loss={loss.item():.2f}, total_value={total_value.item():.2f}, total_weight={total_weight.item():.2f}\")\\n            print(f\"Best solution so far: value={best_solution.value}, items={best_solution.items}\")\\n\\n    max_value = best_solutions[0].value\\n    selected_items = best_solutions[0].items\\n    best_solutions_diff = [(s.elapsed_time, s.value) for s in best_solutions]\\n\\n    return max_value, selected_items, best_solutions_diff\\n'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "sHXnHoDAWnFk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import random\n",
        "\n",
        "def generate_test_case(n, weight_range, value_range, capacity):\n",
        "    items = [(random.randint(*weight_range), random.randint(*value_range)) for _ in range(n)]\n",
        "    return items, capacity"
      ],
      "metadata": {
        "id": "vuN3YriTSpAl"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import torch\n",
        "import torch.optim as optim\n",
        "from collections import namedtuple\n",
        "import matplotlib.pyplot as plt\n",
        "# Generate a large test case with a large capacity\n",
        "n = 1000\n",
        "weight_range = (1, 1000)\n",
        "value_range = (1, 100)\n",
        "capacity = 100000\n",
        "\n",
        "# Test and visualization\n",
        "items, capacity = generate_test_case(n, weight_range, value_range, capacity)\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_dp, selected_items_dp, best_solutions_dp,final_num_epoch = knapsack(items, capacity)\n",
        "end_time = time.time()\n",
        "elapsed_time_dp = end_time - start_time\n",
        "\n",
        "print(f\"DP Final Iteration {final_num_epoch}: Best solution for DP: value={max_value_dp}, elapsed_time={elapsed_time_dp:.2f}s\")\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_diff, selected_items_diff, best_solutions_diff = soft_knapsack(items, capacity,iterations=15000,learning_rate=10)\n",
        "end_time = time.time()\n",
        "elapsed_time_diff = end_time - start_time\n",
        "\n",
        "\n",
        "# Plot the best searched solution so far vs elapsed time for both methods\n",
        "dp_time, dp_values = zip(*best_solutions_dp)\n",
        "diff_time, diff_values = zip(*best_solutions_diff)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QgQh5xb4Xedb",
        "outputId": "6e4611d5-c05b-4dbe-923f-94d7e894781b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 500: Best solution so far for DP: value=17852, elapsed_time=20.58s\n",
            "Iteration 1000: Best solution so far for DP: value=25692, elapsed_time=41.97s\n",
            "DP Final Iteration 1000: Best solution for DP: value=25692, elapsed_time=47.56s\n",
            "Iteration 500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=1.28s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 1000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=2.48s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 1500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=3.82s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 2000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=5.16s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 2500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=6.80s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 3000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=8.26s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 3500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=10.58s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 4000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=12.13s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 4500: loss=-1.42, total_value=1.42, total_weight=13.95, elapsed_time=13.51s\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 5000: loss=-389.43, total_value=389.43, total_weight=37.08, elapsed_time=15.05s\n",
            "Best solution so far: value=388.0, items=[48, 128, 232, 528, 852, 938]\n",
            "Iteration 5500: loss=-3869.73, total_value=3869.73, total_weight=2191.14, elapsed_time=16.49s\n",
            "Best solution so far: value=3868.0, items=[27, 48, 69, 102, 123, 124, 128, 155, 174, 230, 232, 240, 271, 273, 282, 290, 325, 333, 360, 365, 412, 421, 424, 441, 481, 501, 512, 528, 532, 546, 556, 636, 649, 670, 734, 740, 767, 771, 783, 787, 795, 836, 840, 852, 869, 872, 882, 883, 909, 914, 918, 920, 923, 925, 938, 950, 968]\n",
            "Iteration 6000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=18.07s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 6500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=19.56s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 7000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=21.48s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 7500: loss=-1.42, total_value=1.42, total_weight=13.95, elapsed_time=23.87s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 8000: loss=-250.45, total_value=250.45, total_weight=26.04, elapsed_time=25.54s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 8500: loss=-2677.75, total_value=2677.75, total_weight=984.48, elapsed_time=27.16s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 9000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=28.89s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 9500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=30.58s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 10000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=32.40s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 10500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=34.57s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 11000: loss=-1.43, total_value=1.43, total_weight=13.96, elapsed_time=36.96s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 11500: loss=-957.79, total_value=957.79, total_weight=153.35, elapsed_time=38.81s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 12000: loss=-9686.54, total_value=9686.54, total_weight=16148.89, elapsed_time=40.60s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 12500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=42.54s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 13000: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=44.39s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 13500: loss=-1.41, total_value=1.41, total_weight=13.94, elapsed_time=48.60s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 14000: loss=-1.42, total_value=1.42, total_weight=13.96, elapsed_time=50.73s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 14500: loss=-389.49, total_value=389.49, total_weight=37.22, elapsed_time=52.77s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n",
            "Iteration 15000: loss=-5807.28, total_value=5807.28, total_weight=4965.20, elapsed_time=54.74s\n",
            "Best solution so far: value=25352.0, items=[7, 8, 9, 21, 22, 27, 31, 33, 34, 38, 40, 46, 47, 48, 51, 54, 56, 57, 59, 60, 63, 64, 66, 68, 69, 77, 83, 89, 93, 99, 100, 101, 102, 106, 108, 111, 114, 115, 119, 121, 123, 124, 125, 127, 128, 130, 133, 135, 136, 137, 138, 140, 141, 155, 161, 165, 171, 174, 177, 179, 180, 181, 182, 183, 185, 186, 191, 192, 196, 200, 202, 204, 212, 216, 217, 222, 223, 225, 228, 229, 230, 231, 232, 235, 240, 245, 254, 255, 256, 262, 267, 268, 271, 272, 273, 281, 282, 285, 287, 290, 298, 299, 304, 305, 308, 310, 312, 316, 320, 321, 323, 324, 325, 329, 333, 335, 337, 342, 345, 355, 356, 358, 360, 362, 365, 366, 369, 373, 374, 376, 382, 383, 384, 387, 390, 393, 395, 399, 400, 401, 402, 405, 406, 410, 411, 412, 416, 419, 420, 421, 422, 424, 435, 438, 440, 441, 442, 444, 445, 447, 449, 461, 464, 465, 473, 477, 478, 481, 482, 484, 489, 490, 491, 492, 495, 498, 501, 505, 506, 510, 512, 515, 517, 518, 524, 526, 528, 532, 533, 535, 537, 544, 546, 549, 550, 552, 556, 558, 560, 564, 566, 571, 572, 574, 577, 578, 582, 584, 588, 590, 592, 593, 600, 605, 607, 608, 610, 612, 615, 617, 618, 620, 627, 628, 633, 636, 637, 638, 645, 649, 654, 655, 657, 658, 662, 664, 666, 667, 670, 673, 675, 676, 678, 679, 688, 689, 692, 693, 694, 696, 699, 700, 703, 707, 710, 712, 715, 716, 722, 733, 734, 735, 736, 740, 741, 743, 750, 751, 753, 756, 758, 760, 762, 764, 767, 770, 771, 773, 776, 779, 780, 781, 783, 784, 787, 788, 790, 791, 793, 795, 802, 803, 805, 807, 812, 819, 820, 823, 831, 833, 836, 837, 838, 840, 841, 842, 843, 846, 847, 848, 849, 851, 852, 853, 855, 856, 857, 860, 862, 869, 872, 873, 879, 880, 881, 882, 883, 889, 890, 892, 893, 899, 901, 902, 903, 904, 909, 912, 914, 915, 917, 918, 919, 920, 923, 925, 926, 930, 934, 936, 938, 941, 942, 947, 948, 949, 950, 951, 955, 958, 959, 963, 967, 968, 970, 972, 974, 978, 980, 983, 987, 989, 995, 998, 999]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(dp_time, dp_values, label=\"Dynamic Programming\")\n",
        "plt.plot(diff_time, diff_values, label=\"Differentiable Knapsack\")\n",
        "plt.xlabel(\"Elapsed Time (s)\")\n",
        "plt.ylabel(\"Best Searched Solution So Far\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "FmeBDUGIYa4I",
        "outputId": "bbaf68bd-c4c9-4ccb-9d25-c3679ded8809"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Create a non-decreasing sequence of best values with respect to time\n",
        "diff_history_best_values = []\n",
        "max_value_so_far = -1\n",
        "for value in diff_values:\n",
        "    if value > max_value_so_far:\n",
        "        max_value_so_far = value\n",
        "    diff_history_best_values.append(max_value_so_far)\n",
        "\n",
        "# Plot the results\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(dp_time, dp_values, label=\"DP\", marker=\"o\")\n",
        "plt.plot(diff_time, diff_history_best_values, label=\"Differentiable\", marker=\"x\")\n",
        "plt.xlabel(\"Elapsed time (s)\")\n",
        "plt.ylabel(\"Best value\")\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()\n",
        "\n",
        "'''\n",
        "plt.plot(dp_time, dp_values, label=\"Dynamic Programming\")\n",
        "plt.plot(diff_time, diff_values, label=\"Differentiable Knapsack\")\n",
        "plt.xlabel(\"Elapsed Time (s)\")\n",
        "plt.ylabel(\"Best Searched Solution So Far\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "'''"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "id": "OT-VNkG_lIC_",
        "outputId": "72eb88e2-ea2a-45a1-c118-32bcaa2d55c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'\\nplt.plot(dp_time, dp_values, label=\"Dynamic Programming\")\\nplt.plot(diff_time, diff_values, label=\"Differentiable Knapsack\")\\nplt.xlabel(\"Elapsed Time (s)\")\\nplt.ylabel(\"Best Searched Solution So Far\")\\nplt.legend()\\nplt.show()\\n'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import torch\n",
        "import torch.optim as optim\n",
        "from collections import namedtuple\n",
        "import matplotlib.pyplot as plt\n",
        "# Generate a large test case with a large capacity\n",
        "n = 1000\n",
        "weight_range = (1, 1000)\n",
        "value_range = (1, 100)\n",
        "capacity = 100000\n",
        "\n",
        "# Test and visualization\n",
        "items, capacity = generate_test_case(n, weight_range, value_range, capacity)\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_dp, selected_items_dp, best_solutions_dp = knapsack(items, capacity)\n",
        "end_time = time.time()\n",
        "elapsed_time_dp = end_time - start_time\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_diff, selected_items_diff, best_solutions_diff = soft_knapsack(items, capacity, iterations=10000, learning_rate=100)\n",
        "end_time = time.time()\n",
        "elapsed_time_diff = end_time - start_time\n",
        "\n",
        "# Prepare data for visualization\n",
        "x_dp = np.linspace(0, elapsed_time_dp, len(best_solutions_dp))\n",
        "x_diff = np.linspace(0, elapsed_time_diff, len(best_solutions_diff))\n",
        "\n",
        "# Plot the results\n",
        "plt.plot(x_dp, best_solutions_dp, label=\"Dynamic Programming\")\n",
        "plt.plot(x_diff, [sol.value for sol in best_solutions_diff], label=\"Differentiable Search\")\n",
        "plt.xlabel(\"Elapsed Time (s)\")\n",
        "plt.ylabel(\"Best Searched Value\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "GGJmgfN2ShdM",
        "outputId": "51884789-99d0-4723-cd40-1abf4e3e6dd5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-86-a345c8f7a323>\u001b[0m in \u001b[0;36m<cell line: 11>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0mstart_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mmax_value_dp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mselected_items_dp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbest_solutions_dp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mknapsack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcapacity\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0mend_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0melapsed_time_dp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mend_time\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mstart_time\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-83-c0deeee75ba8>\u001b[0m in \u001b[0;36mknapsack\u001b[0;34m(items, capacity, print_every)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mw\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcapacity\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m                 \u001b[0mdp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mweight\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m                 \u001b[0mdp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "'''\n",
        "n = 5000\n",
        "weight_range = (1, 100)\n",
        "value_range = (1, 100)\n",
        "capacity = 1000\n",
        "'''\n",
        "\n",
        "\n",
        "# Generate a large test case with a large capacity\n",
        "n = 1000\n",
        "weight_range = (1, 1000)\n",
        "value_range = (1, 100)\n",
        "capacity = 100000\n",
        "items, capacity = generate_test_case(n, weight_range, value_range, capacity)\n",
        "\n",
        "\n",
        "\n",
        "# Save the test case to a file\n",
        "with open(\"test_case_large.txt\", \"w\") as f:\n",
        "    f.write(f\"{n} {capacity}\\n\")\n",
        "    for value, weight in zip(values, weights):\n",
        "        f.write(f\"{value} {weight}\\n\")\n",
        "\n",
        "\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_dp, selected_items_dp = knapsack(items, capacity)\n",
        "end_time = time.time()\n",
        "\n",
        "total_weight_dp = sum(items[i][0] for i in selected_items_dp)\n",
        "print(f\"Dynamic Programming: max_value={max_value_dp}, selected items: {selected_items_dp}, total_weight={total_weight_dp}, length of selected items={len(selected_items_dp)}, time={end_time - start_time:.2f}s\")\n",
        "\n",
        "start_time = time.time()\n",
        "max_value_diff, selected_items_diff, best_solutions = soft_knapsack(items, capacity, iterations=10000, learning_rate=100)\n",
        "end_time = time.time()\n",
        "\n",
        "for i, best_solution in enumerate(best_solutions):\n",
        "    total_weight_best = sum(items[i][0] for i in best_solution.items)\n",
        "    print(f\"{i}-th Best solution: value={best_solution.value}, items={best_solution.items}, total_weight={total_weight_best}, length of selected items={len(best_solution.items)},\")\n",
        "\n",
        "total_weight_diff = sum(items[i][0] for i in selected_items_diff)\n",
        "print(f\"Differentiable Knapsack: max_value={max_value_diff}, selected items: {selected_items_diff}, total_weight={total_weight_diff}, length of selected items={len(selected_items_diff)}, time={end_time - start_time:.2f}s\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7vSL4BKh4rZR",
        "outputId": "fb4e591a-a49b-4e8f-aefd-84b2387d17fa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Dynamic Programming: max_value=26491, selected items: [999, 998, 990, 981, 977, 974, 970, 966, 965, 963, 960, 958, 957, 955, 954, 949, 946, 945, 943, 942, 941, 939, 937, 929, 927, 926, 925, 923, 922, 919, 918, 917, 916, 913, 912, 911, 910, 908, 904, 902, 899, 898, 892, 891, 886, 877, 876, 875, 874, 873, 871, 870, 867, 866, 864, 863, 860, 858, 855, 854, 852, 851, 848, 846, 843, 842, 840, 839, 838, 837, 835, 830, 828, 826, 824, 823, 822, 816, 809, 801, 798, 797, 796, 791, 789, 787, 784, 783, 778, 777, 769, 768, 763, 762, 761, 754, 751, 749, 748, 747, 743, 738, 737, 736, 734, 730, 727, 725, 724, 722, 719, 717, 714, 711, 709, 708, 706, 704, 703, 695, 694, 693, 689, 688, 687, 681, 680, 669, 666, 665, 663, 662, 661, 660, 659, 656, 653, 652, 650, 649, 647, 645, 644, 643, 640, 638, 636, 635, 634, 633, 629, 628, 622, 618, 616, 615, 613, 610, 606, 605, 604, 603, 601, 599, 597, 594, 590, 589, 587, 585, 583, 580, 579, 572, 570, 567, 566, 564, 563, 562, 560, 557, 554, 543, 539, 537, 534, 533, 531, 529, 528, 524, 523, 520, 516, 513, 511, 509, 506, 502, 500, 498, 497, 494, 486, 484, 482, 481, 480, 479, 478, 477, 473, 470, 468, 462, 461, 460, 455, 453, 452, 450, 449, 445, 443, 441, 439, 438, 435, 431, 428, 426, 423, 421, 419, 418, 406, 402, 400, 399, 398, 391, 390, 385, 384, 382, 377, 374, 373, 371, 370, 368, 366, 365, 364, 363, 362, 361, 359, 357, 352, 351, 348, 345, 344, 343, 341, 339, 335, 332, 329, 328, 326, 325, 323, 318, 316, 312, 310, 307, 304, 300, 297, 296, 294, 293, 289, 288, 287, 283, 282, 281, 280, 276, 273, 264, 261, 260, 259, 258, 252, 250, 248, 245, 241, 240, 237, 234, 230, 229, 228, 226, 224, 222, 220, 219, 218, 211, 206, 200, 194, 193, 190, 187, 186, 185, 183, 175, 174, 172, 162, 160, 157, 156, 155, 154, 152, 150, 147, 144, 140, 138, 136, 135, 132, 131, 129, 128, 120, 118, 114, 113, 109, 104, 102, 101, 100, 96, 94, 92, 89, 87, 86, 85, 82, 81, 77, 72, 69, 68, 65, 63, 61, 59, 56, 52, 46, 42, 37, 36, 35, 33, 32, 30, 27, 23, 20, 16, 15, 12, 11, 10, 8, 7, 4], total_weight=99994, length of selected items=395, time=51.15s\n",
            "Iteration 500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 1000: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 1500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 2000: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 2500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 3000: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 3500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=0.0, items=[]\n",
            "Iteration 4000: loss=-95.35, total_value=95.35, total_weight=23.71\n",
            "Best solution so far: value=93.0, items=[15]\n",
            "Iteration 4500: loss=-499.48, total_value=499.48, total_weight=55.00\n",
            "Best solution so far: value=497.0, items=[15, 316, 384, 597, 687, 816, 923]\n",
            "Iteration 5000: loss=-6105.84, total_value=6105.84, total_weight=5434.46\n",
            "Best solution so far: value=6102.0, items=[15, 16, 20, 23, 30, 102, 109, 113, 118, 131, 135, 138, 140, 144, 160, 174, 219, 220, 222, 230, 260, 293, 307, 316, 318, 326, 343, 351, 357, 368, 384, 385, 390, 400, 418, 439, 450, 461, 473, 484, 498, 502, 513, 516, 557, 563, 566, 567, 589, 590, 597, 634, 650, 656, 660, 662, 669, 687, 708, 722, 747, 754, 761, 777, 784, 787, 816, 824, 828, 839, 843, 846, 851, 852, 854, 863, 899, 902, 904, 917, 923, 937, 939, 945, 946, 955, 965, 977, 990]\n",
            "Iteration 5500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 6000: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 6500: loss=-2.35, total_value=2.35, total_weight=22.69\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 7000: loss=-388.39, total_value=388.39, total_weight=37.82\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 7500: loss=-3778.56, total_value=3778.56, total_weight=1906.60\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 8000: loss=-23281.26, total_value=23281.26, total_weight=83679.91\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 8500: loss=-2.33, total_value=2.33, total_weight=22.68\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 9000: loss=-2.34, total_value=2.34, total_weight=22.69\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 9500: loss=-186.43, total_value=186.43, total_weight=24.76\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "Iteration 10000: loss=-2219.91, total_value=2219.91, total_weight=610.95\n",
            "Best solution so far: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999]\n",
            "0-th Best solution: value=25575.0, items=[4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=101203, length of selected items=385,\n",
            "1-th Best solution: value=25431.0, items=[4, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=99718, length of selected items=382,\n",
            "2-th Best solution: value=25431.0, items=[4, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=99718, length of selected items=382,\n",
            "3-th Best solution: value=25350.0, items=[4, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=99314, length of selected items=381,\n",
            "4-th Best solution: value=25283.0, items=[4, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=98917, length of selected items=380,\n",
            "Differentiable Knapsack: max_value=25575.0, selected items: [4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 20, 23, 30, 32, 33, 35, 36, 37, 42, 48, 52, 56, 57, 59, 61, 63, 65, 68, 69, 72, 81, 82, 85, 86, 87, 92, 94, 96, 102, 104, 109, 113, 114, 118, 125, 127, 129, 131, 134, 135, 136, 138, 140, 144, 147, 152, 153, 155, 156, 158, 160, 162, 174, 183, 185, 186, 187, 190, 191, 193, 194, 200, 206, 218, 219, 220, 222, 224, 226, 229, 230, 234, 237, 241, 248, 251, 252, 259, 260, 261, 264, 273, 275, 276, 281, 282, 283, 287, 288, 289, 291, 293, 294, 296, 297, 300, 304, 307, 309, 310, 312, 316, 318, 325, 326, 328, 329, 332, 335, 339, 341, 343, 344, 347, 348, 351, 357, 359, 361, 363, 364, 365, 368, 369, 370, 371, 373, 379, 382, 384, 385, 390, 391, 397, 398, 399, 400, 402, 406, 408, 418, 419, 421, 423, 426, 428, 435, 438, 439, 443, 445, 450, 453, 455, 460, 461, 462, 466, 468, 470, 471, 473, 477, 478, 479, 480, 481, 482, 484, 485, 486, 490, 494, 497, 498, 500, 502, 511, 513, 516, 520, 521, 522, 523, 524, 526, 528, 529, 533, 534, 537, 539, 543, 554, 556, 557, 560, 562, 563, 564, 566, 567, 570, 571, 572, 580, 583, 585, 586, 589, 590, 594, 597, 599, 601, 602, 603, 604, 606, 610, 613, 616, 618, 622, 628, 629, 633, 634, 636, 643, 645, 646, 647, 649, 650, 652, 653, 656, 659, 660, 662, 665, 666, 669, 680, 681, 686, 687, 688, 689, 693, 694, 695, 703, 704, 706, 708, 709, 711, 712, 714, 717, 722, 724, 725, 727, 734, 736, 738, 742, 743, 747, 748, 749, 751, 752, 754, 761, 762, 763, 768, 774, 775, 777, 778, 783, 784, 787, 789, 791, 796, 797, 798, 801, 809, 810, 812, 816, 817, 822, 823, 824, 826, 828, 830, 831, 835, 838, 839, 840, 841, 842, 843, 845, 846, 851, 852, 854, 855, 858, 860, 863, 864, 867, 868, 870, 871, 874, 875, 876, 886, 891, 892, 898, 899, 902, 904, 908, 911, 912, 913, 917, 918, 922, 923, 925, 926, 927, 929, 937, 939, 941, 942, 945, 946, 947, 949, 953, 954, 955, 957, 958, 960, 963, 965, 966, 970, 974, 977, 978, 981, 990, 993, 998, 999], total_weight=101203, length of selected items=385, time=30.86s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install numba\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WsjpejO9d2am",
        "outputId": "1a3ca3fa-2dc4-4850-d3b0-d4030caaa7af"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: numba in /usr/local/lib/python3.10/dist-packages (0.56.4)\n",
            "Requirement already satisfied: setuptools in /usr/local/lib/python3.10/dist-packages (from numba) (67.7.2)\n",
            "Requirement already satisfied: numpy<1.24,>=1.18 in /usr/local/lib/python3.10/dist-packages (from numba) (1.22.4)\n",
            "Requirement already satisfied: llvmlite<0.40,>=0.39.0dev0 in /usr/local/lib/python3.10/dist-packages (from numba) (0.39.1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install cupy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nzzwEIlId5zy",
        "outputId": "8221a8d3-864d-45f9-b931-6c0c63301799"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting cupy\n",
            "  Using cached cupy-12.0.0.tar.gz (2.0 MB)\n",
            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: numpy<1.27,>=1.20 in /usr/local/lib/python3.10/dist-packages (from cupy) (1.22.4)\n",
            "Requirement already satisfied: fastrlock>=0.5 in /usr/local/lib/python3.10/dist-packages (from cupy) (0.8.1)\n",
            "Building wheels for collected packages: cupy\n",
            "  Building wheel for cupy (setup.py) ... \u001b[?25l\u001b[?25hcanceled\n",
            "\u001b[31mERROR: Operation cancelled by user\u001b[0m\u001b[31m\n",
            "\u001b[0mTraceback (most recent call last):\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/base_command.py\", line 160, in exc_logging_wrapper\n",
            "    status = run_func(*args)\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/req_command.py\", line 241, in wrapper\n",
            "    return func(self, options, args)\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/commands/install.py\", line 463, in run\n",
            "    _, build_failures = build(\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/wheel_builder.py\", line 347, in build\n",
            "    wheel_file = _build_one(\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/wheel_builder.py\", line 221, in _build_one\n",
            "    wheel_path = _build_one_inside_env(\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/wheel_builder.py\", line 268, in _build_one_inside_env\n",
            "    wheel_path = build_wheel_legacy(\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/operations/build/wheel_legacy.py\", line 83, in build_wheel_legacy\n",
            "    output = call_subprocess(\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/utils/subprocess.py\", line 166, in call_subprocess\n",
            "    line: str = proc.stdout.readline()\n",
            "KeyboardInterrupt\n",
            "\n",
            "During handling of the above exception, another exception occurred:\n",
            "\n",
            "Traceback (most recent call last):\n",
            "  File \"/usr/local/bin/pip3\", line 8, in <module>\n",
            "    sys.exit(main())\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/main.py\", line 70, in main\n",
            "    return command.main(cmd_args)\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/base_command.py\", line 101, in main\n",
            "    return self._main(args)\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/base_command.py\", line 214, in _main\n",
            "    return run(options, args)\n",
            "  File \"/usr/local/lib/python3.10/dist-packages/pip/_internal/cli/base_command.py\", line 197, in exc_logging_wrapper\n",
            "    logger.critical(\"Operation cancelled by user\")\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1524, in critical\n",
            "    self._log(CRITICAL, msg, args, **kwargs)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1624, in _log\n",
            "    self.handle(record)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1634, in handle\n",
            "    self.callHandlers(record)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1696, in callHandlers\n",
            "    hdlr.handle(record)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 968, in handle\n",
            "    self.emit(record)\n",
            "  File \"/usr/lib/python3.10/logging/handlers.py\", line 75, in emit\n",
            "    logging.FileHandler.emit(self, record)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1218, in emit\n",
            "    StreamHandler.emit(self, record)\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1104, in emit\n",
            "    self.flush()\n",
            "  File \"/usr/lib/python3.10/logging/__init__.py\", line 1084, in flush\n",
            "    self.stream.flush()\n",
            "KeyboardInterrupt\n",
            "^C\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "1MdvGw37LQRH"
      },
      "outputs": [],
      "source": [
        "import copy\n",
        "import itertools\n",
        "import time\n",
        "import math\n",
        "import numpy as np\n",
        "#import cupy as cp\n",
        "from numba import jit, prange"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!nvidia-smi"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3xbpjSBHVQ3t",
        "outputId": "8ad28114-ab63-4fe9-8bde-fc77dcafa0b0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sun May  7 03:19:53 2023       \n",
            "+-----------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 525.85.12    Driver Version: 525.85.12    CUDA Version: 12.0     |\n",
            "|-------------------------------+----------------------+----------------------+\n",
            "| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                               |                      |               MIG M. |\n",
            "|===============================+======================+======================|\n",
            "|   0  Tesla T4            Off  | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   41C    P8     9W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
            "|                               |                      |                  N/A |\n",
            "+-------------------------------+----------------------+----------------------+\n",
            "                                                                               \n",
            "+-----------------------------------------------------------------------------+\n",
            "| Processes:                                                                  |\n",
            "|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |\n",
            "|        ID   ID                                                   Usage      |\n",
            "|=============================================================================|\n",
            "|  No running processes found                                                 |\n",
            "+-----------------------------------------------------------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mbCfjNagLQRK"
      },
      "outputs": [],
      "source": [
        "# simplification\n",
        "def f(L, maxl, cost, k, B):\n",
        "    if k == 1:\n",
        "        return ([L], B*max(0, L-maxl))\n",
        "    if k == L:\n",
        "        cost_ = max(1, maxl) * B\n",
        "        for i in range(k-1):\n",
        "         #   cost_ += cost[i][i]\n",
        "            cost_ += cost[i]\n",
        "        return ([1] * L, cost_)\n",
        "    \n",
        "    cost_best = float(\"inf\")\n",
        "    S_best = []\n",
        "    for i in reversed(range(k, L)):\n",
        "        S, cost_ = f(i, max(L-i, maxl), cost, k-1, B)\n",
        "        cost_ += max(0, L-i-maxl)*B\n",
        "        cost_ += cost[i-1]\n",
        "        if cost_ < cost_best:\n",
        "            cost_best = cost_\n",
        "            S.append(L-i)\n",
        "            S_best = S\n",
        "    return S_best, cost_best"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ffYWtK1eLQRL",
        "outputId": "a7b791fb-7c54-4c1c-f7bb-f457bb923673"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([2, 1, 2, 2, 2, 1, 1, 1], 15)"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "L = 12\n",
        "k = 8\n",
        "cost = [2,1,1,3] * 12\n",
        "f(L, 0, cost, k, 3)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.optim as optim\n",
        "import numpy as np\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, n_best=5, iterations=10000, learning_rate=10, temperature=0.5, print_every=500, penalty_factor=1e4,selection_penalty_factor = 1e4):\n",
        "    n_best=iterations\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "    \n",
        "    for i in range(1, L+1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(sum(cost_e[ptr:ptr+i]))\n",
        "            ptr += 1\n",
        "    \n",
        "    possible = sorted(list(set(possible)))\n",
        "\n",
        "    item_selection = torch.rand((L, k), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "\n",
        "        # Calculate the cost of each soft selection\n",
        "        cost_matrix = torch.zeros(L, k)\n",
        "        for i in range(L):\n",
        "            for j in range(k):\n",
        "                cur_sum = torch.sum(soft_selection[:i+1, j])\n",
        "                cost_matrix[i, j] = (B-1) * torch.relu(cur_sum - possible[j])\n",
        "                if j > 0:\n",
        "                    #cost_matrix[i, j] += torch.sum(cost_c[:i+1, j-1] * soft_selection[:i+1, j-1])\n",
        "                    #cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float) * soft_selection[:i+1, j-1])\n",
        "                    #cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float) * soft_selection[:i+1, j])\n",
        "                    #cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float) * soft_selection[:i+1, j-1].T)\n",
        "                    #cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float) * soft_selection[:i+1, j-1].permute(1, 0))\n",
        "                    cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float).unsqueeze(1) * soft_selection[:i+1, j-1])\n",
        "\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_matrix)\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_selection, dim=0) - 1.0)) ** 2\n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_selection, dim=0)))\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost  + selection_penalty_factor * selection_penalty + penalty_factor * capacity_penalty\n",
        "        # Define the loss function\n",
        "        #loss = total_cost + penalty_factor * capacity_penalty\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        current_solution = (final_selection, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n",
        "'''\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, n_best=5, iterations=10000, learning_rate=10, temperature=0.5, print_every=500, penalty_factor=1e4, selection_penalty_factor=1e4):\n",
        "    n_best=iterations\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "    \n",
        "    for i in range(1, L+1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(sum(cost_e[ptr:ptr+i]))\n",
        "            ptr += 1\n",
        "    \n",
        "    possible = sorted(list(set(possible)))\n",
        "    print(\"Possible:\", possible)\n",
        "\n",
        "    item_selection = torch.rand((L, k), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "        print(\"Soft selection:\\n\", soft_selection)\n",
        "\n",
        "        # Calculate the cost of each soft selection\n",
        "        cost_matrix = torch.zeros(L, k)\n",
        "        for i in range(L):\n",
        "            for j in range(k):\n",
        "                cur_sum = torch.sum(soft_selection[:i+1, j])\n",
        "                cost_matrix[i, j] = (B-1) * torch.relu(cur_sum - possible[j])\n",
        "                if j > 0:\n",
        "                    cost_matrix[i, j] += torch.sum(torch.tensor(cost_c[:i+1, j-1], dtype=torch.float).unsqueeze(1) * soft_selection[:i+1, j-1])\n",
        "        print(\"Cost matrix:\\n\", cost_matrix)\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_matrix)\n",
        "        print(\"Total cost:\", total_cost.item())\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_selection, dim=0) - 1.0)) ** 2\n",
        "        print(\"Capacity penalty:\", capacity_penalty.item())\n",
        "        \n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_selection, dim=0)))\n",
        "        print(\"Selection penalty:\", selection_penalty.item())\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost + penalty_factor * capacity_penalty + selection_penalty_factor * selection_penalty\n",
        "        print(\"Loss:\", loss.item())\n",
        "\n",
        "        loss.backward()\n",
        "        print(\"Gradients:\", item_selection.grad)\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        current_solution = (final_selection, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n",
        "'''\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, n_best=5, iterations=10000, learning_rate=10, temperature=0.5, print_every=500, penalty_factor=1e4, selection_penalty_factor=1e4):\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "    \n",
        "    for i in range(1, L+1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(sum(cost_e[ptr:ptr+i]))\n",
        "            ptr += 1\n",
        "    \n",
        "    possible = sorted(list(set(possible)))\n",
        "\n",
        "    # Replace the item_selection tensor with a trace-like structure\n",
        "    trace = torch.rand((L, k, len(possible)), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([trace], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_trace = torch.sigmoid(trace / temperature)\n",
        "\n",
        "        # Replace the cost_matrix with a cost_trace to better reflect the original code's structure\n",
        "        cost_trace = torch.zeros(L, k, len(possible))\n",
        "        for i in range(L):\n",
        "            for j in range(k):\n",
        "                for m in range(len(possible)):\n",
        "                    if i+1 <= j:  # invalid\n",
        "                        pass\n",
        "                    else:\n",
        "                        if j == 0:  # base case: 0 cut\n",
        "                            cur_sum = torch.sum(soft_trace[:i+1, j, m])\n",
        "                            cost_trace[i, j, m] = (B-1) * torch.relu(cur_sum - possible[m])\n",
        "                        else:\n",
        "                            cost_best = torch.tensor(float(\"inf\"))\n",
        "                            for cut in range(j-1, i):\n",
        "                                cur_sum = torch.sum(soft_trace[cut+1:i+1, j, m])\n",
        "                                cost_ = (B-1) * torch.relu(cur_sum - possible[m]) + torch.sum(cost_c[cut][j-1] * soft_trace[cut, j-1, m])\n",
        "                                cost_best = torch.min(cost_best, cost_)\n",
        "\n",
        "                            cost_trace[i, j, m] = cost_best\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_trace[-1, -1, :])\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_trace, dim=0) - 1.0)) ** 2\n",
        "        print(\"Capacity penalty:\", capacity_penalty.item())\n",
        "        \n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_trace, dim=0)))\n",
        "        print(\"Selection penalty:\", selection_penalty.item())\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost + penalty_factor * capacity_penalty + selection_penalty_factor * selection_penalty\n",
        "        print(\"Loss:\", loss.item())\n",
        "\n",
        "        loss.backward()\n",
        "        print(\"Gradients:\", trace.grad)\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp trace values between -5 and 5\n",
        "        trace.data.clamp_(-5, 5)\n",
        "\n",
        "        final_trace = torch.sigmoid(trace / temperature) > 0.5\n",
        "        current_solution = (final_trace, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n",
        "'''\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, iterations=10000, learning_rate=0.1, temperature=0.5, print_every=500, penalty_factor=1e4, selection_penalty_factor=1e4, n_best=1):\n",
        "    n_best=iterations\n",
        "    # Create a tensor of shape (L, k) to represent the selection of cuts\n",
        "    item_selection = torch.rand((L, k), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "\n",
        "        # Calculate the cost of each soft selection\n",
        "        cost_matrix = torch.zeros((L, k))\n",
        "        for i in range(L):\n",
        "            for j in range(k):\n",
        "                cost_matrix[i, j] = torch.dot(torch.tensor(cost_e, dtype=torch.float), soft_selection[:, j]) * (B - 1)\n",
        "                if j > 0:\n",
        "                    cost_matrix[i, j] += torch.dot(torch.tensor(cost_c[j - 1], dtype=torch.float), soft_selection[:, j - 1])\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_matrix)\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_selection, dim=0) - 1.0)) ** 2\n",
        "        \n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_selection, dim=0)))\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost + penalty_factor * capacity_penalty + selection_penalty_factor * selection_penalty\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        current_solution = (final_selection, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n",
        "'''\n",
        "\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, iterations=10000, learning_rate=0.1, temperature=0.5, print_every=500, penalty_factor=1e4, selection_penalty_factor=1e4, n_best=1):\n",
        "    # Create a tensor of shape (L, k) to represent the selection of cuts\n",
        "    item_selection = torch.rand((L, k), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "\n",
        "        # Calculate the cost of each soft selection\n",
        "        cost_matrix = torch.zeros((L, k))\n",
        "        for j in range(k):\n",
        "            cost_matrix[:, j] = torch.matmul(torch.tensor(cost_e, dtype=torch.float), soft_selection[:, j]) * (B - 1)\n",
        "            if j > 0:\n",
        "                cost_matrix[:, j] += torch.matmul(torch.tensor(cost_c[j - 1], dtype=torch.float), soft_selection[:, j - 1])\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_matrix)\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_selection, dim=0) - 1.0)) ** 2\n",
        "        \n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_selection, dim=0)))\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost + penalty_factor * capacity_penalty + selection_penalty_factor * selection_penalty\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        current_solution = (final_selection, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n",
        "'''\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B, iterations=10000, learning_rate=0.1, temperature=0.5, print_every=500, penalty_factor=1e4, selection_penalty_factor=1e4, n_best=1):\n",
        "    n_best=iterations\n",
        "    # Create a tensor of shape (L, k) to represent the selection of cuts\n",
        "    item_selection = torch.rand((L, k), requires_grad=True)\n",
        "    optimizer = optim.RMSprop([item_selection], lr=learning_rate)\n",
        "\n",
        "    best_solutions = []\n",
        "\n",
        "    start_time = time.time()\n",
        "    for iteration in range(iterations):\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        # Apply sigmoid and get soft selections\n",
        "        soft_selection = torch.sigmoid(item_selection / temperature)\n",
        "\n",
        "        # Calculate the cost of each soft selection for execution\n",
        "        cost_execution = torch.zeros((L, k))\n",
        "        for j in range(k):\n",
        "            cost_execution[:, j] = torch.matmul(torch.tensor(cost_e, dtype=torch.float), soft_selection[:, j]) * (B - 1)\n",
        "\n",
        "        # Calculate the cost of each soft selection for communication\n",
        "        cost_communication = torch.zeros((L, k-1))\n",
        "        for j in range(k-1):\n",
        "            cost_communication[:, j] = torch.matmul(torch.tensor(cost_c[j], dtype=torch.float), soft_selection[:, j])\n",
        "\n",
        "        # Calculate the total cost\n",
        "        total_cost = torch.sum(cost_execution) + torch.sum(cost_communication)\n",
        "        \n",
        "        # Add penalties for capacity constraints\n",
        "        capacity_penalty = torch.sum(torch.relu(torch.sum(soft_selection, dim=0) - 1.0)) ** 2\n",
        "        \n",
        "        # Calculate the selection penalty\n",
        "        selection_penalty = torch.sum(torch.relu(1.0 - torch.sum(soft_selection, dim=0)))\n",
        "\n",
        "        # Define the loss function\n",
        "        loss = total_cost + penalty_factor * capacity_penalty + selection_penalty_factor * selection_penalty\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Clamp item_selection values between -5 and 5\n",
        "        item_selection.data.clamp_(-5, 5)\n",
        "\n",
        "        final_selection = torch.sigmoid(item_selection / temperature) > 0.5\n",
        "        current_solution = (final_selection, total_cost.item(), time.time() - start_time)\n",
        "\n",
        "        if len(best_solutions) < n_best:\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "        elif total_cost.item() < best_solutions[-1][1]:\n",
        "            best_solutions.pop()\n",
        "            best_solutions.append(current_solution)\n",
        "            best_solutions.sort(key=lambda x: x[1])\n",
        "\n",
        "        if (iteration + 1) % print_every == 0:\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solution = best_solutions[0]\n",
        "            print(f\"Iteration {iteration + 1}: loss={loss.item():.2f}, total_cost={total_cost.item():.2f}, elapsed_time={elapsed_time:.2f}s\")\n",
        "            print(f\"Best solution so far: cost={best_solution[1]}, selection={best_solution[0]}\")\n",
        "\n",
        "    best_solution = best_solutions[0]\n",
        "    return best_solution[0], best_solution[1], best_solutions\n"
      ],
      "metadata": {
        "id": "uLGuxMSzBgy8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install jit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RHoInsuSCGTG",
        "outputId": "38159bf2-7837-466a-90d0-46d2b379eddb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting jit\n",
            "  Downloading JIT-0.2.7.tar.gz (229 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m229.2/229.2 kB\u001b[0m \u001b[31m21.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Building wheels for collected packages: jit\n",
            "  Building wheel for jit (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for jit: filename=JIT-0.2.7-py3-none-any.whl size=251891 sha256=aa3d2477746b8a889bb13c05418b3b1c4c936eab4f216e43473ebb40844f467f\n",
            "  Stored in directory: /root/.cache/pip/wheels/bb/79/b2/37f19beaa2dd882ae3f379c7e88135b63cbfb7424547971393\n",
            "Successfully built jit\n",
            "Installing collected packages: jit\n",
            "Successfully installed jit-0.2.7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "aSgUxlfPLQRL"
      },
      "outputs": [],
      "source": [
        "from numba import jit\n",
        "#@jit(nopython=True)\n",
        "def pipe_dp(L, cost_e, cost_c, k, B):\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "    \n",
        "    for i in range(1, L+1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(sum(cost_e[ptr:ptr+i]))\n",
        "            ptr += 1\n",
        "    \n",
        "    possible = sorted(list(set(possible)))\n",
        "    # print(possible)\n",
        "    # trace will be a 3D list\n",
        "    trace = []\n",
        "    for i in range(L):\n",
        "        outer = []\n",
        "        for j in range(k):\n",
        "            inner = []\n",
        "            for m in range(len(possible)):\n",
        "                inner.append(([],np.infty))\n",
        "            outer.append(inner)\n",
        "        trace.append(outer)\n",
        "    \n",
        "    # i: layer id, starting from 0\n",
        "    # j: number of cut (=GPU-1)\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(len(possible)):\n",
        "                if i+1 <= j: # invalid\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0: # base case: 0 cut\n",
        "                        cur_sum = sum(cost_e[:i+1])\n",
        "                        assert cur_sum in possible\n",
        "                        trace[i][j][m] = ([i+1], (B-1) * max(0, cur_sum - possible[m]))\n",
        "                    else:\n",
        "                        cost_best = np.infty\n",
        "                        S_best = []\n",
        "                        for cut in range(j-1, i):\n",
        "                            cur_sum = sum(cost_e[cut+1:i+1])\n",
        "                            assert cur_sum in possible\n",
        "                            S, cost_ = trace[cut][j-1][possible.index(max(cur_sum, possible[m]))]\n",
        "                            #print(S, cost_)\n",
        "                            cost_ += (B-1) * max(0, cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut][j-1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_ = copy.deepcopy(S)\n",
        "                                S_.append(i-cut)\n",
        "                                S_best = S_\n",
        "                        trace[i][j][m] = (S_best, cost_best)\n",
        "                        \n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            pass\n",
        "            #print(i, j, trace[i][j])\n",
        "    return trace[L-1][k-1][0]\n",
        "\n",
        "\n",
        "@jit(nopython=True)\n",
        "def pipe_dp_v2(L, cost_e, cost_c, k, B):\n",
        "    possible = np.zeros(L + 1, dtype=np.int64)\n",
        "\n",
        "    for i in range(1, L + 1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible[ptr + i - 1] = sum(cost_e[ptr:ptr + i])\n",
        "            ptr += 1\n",
        "\n",
        "    possible = np.unique(possible)\n",
        "\n",
        "    trace = np.empty((L, k, possible.shape[0]), dtype=np.object_)\n",
        "\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(possible.shape[0]):\n",
        "                if i + 1 <= j:\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0:\n",
        "                        cur_sum = sum(cost_e[:i + 1])\n",
        "                        trace[i, j, m] = (np.array([i + 1], dtype=np.int64), (B - 1) * max(0, cur_sum - possible[m]))\n",
        "                    else:\n",
        "                        cost_best = np.inf\n",
        "                        S_best = np.empty(0, dtype=np.int64)\n",
        "                        for cut in range(j - 1, i):\n",
        "                            cur_sum = sum(cost_e[cut + 1:i + 1])\n",
        "                            S, cost_ = trace[cut, j - 1, np.where(possible == max(cur_sum, possible[m]))[0][0]]\n",
        "                            cost_ += (B - 1) * max(0, cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut, j - 1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_ = S.copy()\n",
        "                                S_best = np.append(S_, i - cut)\n",
        "                        trace[i, j, m] = (S_best, cost_best)\n",
        "\n",
        "    return trace[L - 1, k - 1, 0]\n",
        "\n",
        "\n",
        "@jit(nopython=True)\n",
        "def pipe_dp_v3(L, cost_e, cost_c, k, B):\n",
        "    possible = np.zeros(L + 1, dtype=np.int64)\n",
        "\n",
        "    for i in range(1, L + 1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible[ptr + i - 1] = sum(cost_e[ptr:ptr + i])\n",
        "            ptr += 1\n",
        "\n",
        "    possible = np.unique(possible)\n",
        "\n",
        "    trace = np.empty((L, k, possible.shape[0]), dtype=np.object_)\n",
        "\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(possible.shape[0]):\n",
        "                if i + 1 <= j:\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0:\n",
        "                        cur_sum = sum(cost_e[:i + 1])\n",
        "                        trace[i, j, m] = (np.array([i + 1], dtype=np.int64), (B - 1) * max(0, cur_sum - possible[m]))\n",
        "                    else:\n",
        "                        cost_best = np.inf\n",
        "                        S_best = np.empty(0, dtype=np.int64)\n",
        "                        for cut in range(j - 1, i):\n",
        "                            cur_sum = sum(cost_e[cut + 1:i + 1])\n",
        "                            S, cost_ = trace[cut, j - 1, np.where(possible == max(cur_sum, possible[m]))[0][0]]\n",
        "                            cost_ += (B - 1) * max(0, cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut, j - 1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_ = S.copy()\n",
        "                                S_best = np.append(S_, i - cut)\n",
        "                        trace[i, j, m] = (S_best, cost_best)\n",
        "\n",
        "    return trace[L - 1, k - 1, 0]\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "@jit(nopython=True)\n",
        "def pipe_dp_v4(L, cost_e, cost_c, k, B):\n",
        "    possible = np.zeros(L + 1, dtype=np.int64)\n",
        "\n",
        "    for i in range(1, L + 1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible[ptr + i - 1] = sum(cost_e[ptr:ptr + i])\n",
        "            ptr += 1\n",
        "\n",
        "    possible = np.unique(possible)\n",
        "\n",
        "    trace_S = np.empty((L, k, possible.shape[0]), dtype=np.int64)\n",
        "    trace_cost = np.full((L, k, possible.shape[0]), np.inf)\n",
        "\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(possible.shape[0]):\n",
        "                if i + 1 <= j:\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0:\n",
        "                        cur_sum = sum(cost_e[:i + 1])\n",
        "                        trace_S[i, j, m] = i + 1\n",
        "                        trace_cost[i, j, m] = (B - 1) * max(0, cur_sum - possible[m])\n",
        "                    else:\n",
        "                        cost_best = np.inf\n",
        "                        S_best = -1\n",
        "                        for cut in range(j - 1, i):\n",
        "                            cur_sum = sum(cost_e[cut + 1:i + 1])\n",
        "                            S, cost_ = trace_S[cut, j - 1, np.where(possible == max(cur_sum, possible[m]))[0][0]], trace_cost[cut, j - 1, np.where(possible == max(cur_sum, possible[m]))[0][0]]\n",
        "                            cost_ += (B - 1) * max(0, cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut, j - 1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_best = S\n",
        "                        trace_S[i, j, m] = S_best\n",
        "                        trace_cost[i, j, m] = cost_best\n",
        "\n",
        "    return trace_S[L - 1, k - 1], trace_cost[L - 1, k - 1]\n",
        "\n",
        "\n",
        "\n",
        "#@jit(nopython=True)\n",
        "def brute_force(L, cost_e, cost_c, k, B):\n",
        "    best_S = []\n",
        "    best_cost = np.infty\n",
        "    ptr_done = [0] * (k-1)\n",
        "    possible = list(itertools.combinations(range(L-1), k-1))\n",
        "    for p in possible:\n",
        "        p = list(p)\n",
        "        p.append(L-1)\n",
        "        lens = [sum(cost_e[:p[0]+1])]\n",
        "        s = [p[0]+1]\n",
        "        for i in range(len(p)-1):\n",
        "            lens.append(sum(cost_e[p[i]+1:p[i+1]+1]))\n",
        "            s.append(p[i+1]-p[i])     \n",
        "        max_l = max(lens)\n",
        "        cost = (B-1) * max_l\n",
        "        for i in range(k-1):\n",
        "            cost += cost_c[p[i]][i]\n",
        "        if cost < best_cost:\n",
        "            best_cost = cost\n",
        "            best_S = s\n",
        "    return best_S, best_cost\n",
        "\n",
        "#@jit(nopython=True)\n",
        "def uniform_split(L, cost_e, cost_c, k, B):\n",
        "    per_stage = L // k\n",
        "    \n",
        "    s = [per_stage] * (k-1)\n",
        "    s.append(L-sum(s))\n",
        "    p = [s[0]-1]\n",
        "    for i in range(1, k):\n",
        "        p.append(p[i-1] + s[i])\n",
        "    lens = [sum(cost_e[:p[0]+1])]\n",
        "    for i in range(len(s)-1):\n",
        "        lens.append(sum(cost_e[p[i]+1:p[i+1]+1]))\n",
        "    max_l = max(lens)\n",
        "    cost = (B-1) * max_l\n",
        "    for i in range(k-1):\n",
        "        cost += cost_c[p[i]][i]\n",
        "    return s, cost"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import itertools\n",
        "import numpy as np\n",
        "\n",
        "def brute_force_differentiable(L, cost_e, cost_c, k, B, epochs=1000, learning_rate=1e-2, print_every=50):\n",
        "    start_time = time.time()\n",
        "\n",
        "    # Generate all possible combinations\n",
        "    possible = list(itertools.combinations(range(L-1), k-1))\n",
        "    \n",
        "    # Initialize the probability distribution for the combinations\n",
        "    combination_probs = torch.nn.functional.softmax(torch.randn(len(possible)), dim=0)\n",
        "    combination_probs.requires_grad = True\n",
        "    \n",
        "    optimizer = torch.optim.Adam([combination_probs], lr=learning_rate)\n",
        "\n",
        "    best_solution = None\n",
        "    best_cost = float('inf')\n",
        "    best_solutions_history = []\n",
        "\n",
        "    for epoch in range(epochs):\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        # Calculate the cost for each combination\n",
        "        costs = []\n",
        "        for p in possible:\n",
        "            p = list(p)\n",
        "            p.append(L-1)\n",
        "            lens = [sum(cost_e[:p[0]+1])]\n",
        "            s = [p[0]+1]\n",
        "            for i in range(len(p)-1):\n",
        "                lens.append(sum(cost_e[p[i]+1:p[i+1]+1]))\n",
        "                s.append(p[i+1]-p[i])     \n",
        "            max_l = max(lens)\n",
        "            cost = (B-1) * max_l\n",
        "            for i in range(k-1):\n",
        "                cost += cost_c[p[i]][i]\n",
        "            costs.append(cost)\n",
        "        \n",
        "        # Convert costs to a tensor\n",
        "        costs_tensor = torch.tensor(costs, dtype=torch.float32)\n",
        "        \n",
        "        # Compute the expected value of the combination costs\n",
        "        expected_cost = torch.dot(combination_probs, costs_tensor)\n",
        "        expected_cost.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Check and update the best solution\n",
        "        current_best_index = torch.argmin(costs_tensor).item()\n",
        "        current_best_cost = costs_tensor[current_best_index].item()\n",
        "        if current_best_cost < best_cost:\n",
        "            best_cost = current_best_cost\n",
        "            best_solution = possible[current_best_index]\n",
        "            elapsed_time = time.time() - start_time\n",
        "            best_solutions_history.append((elapsed_time, best_cost))\n",
        "\n",
        "        # Print the best solution so far every print_every epochs\n",
        "        if (epoch + 1) % print_every == 0:\n",
        "            print(f'Epoch {epoch + 1}: Best solution so far: {best_solution}, cost: {best_cost}')\n",
        "\n",
        "    return best_solution, best_cost, best_solutions_history\n",
        "\n",
        "\n",
        "# Example usage\n",
        "L = 4\n",
        "k = 2\n",
        "B = 3\n",
        "cost_e = np.array([1, 3, 2, 5])\n",
        "#cost_e = [1,3,2,5]\n",
        "cost_c = np.ones((L-1, k-1)) * 2\n",
        "\n",
        "\n",
        "best_solution, best_cost, best_solutions_history = brute_force_differentiable(L, cost_e, cost_c, k, B,epochs=100)\n",
        "print(f'Final best solution: {best_solution}, cost: {best_cost}')\n",
        "\n",
        "# Plot the results\n",
        "brute_force_time, brute_force_values = zip(*best_solutions_history)\n",
        "\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(brute_force_time, brute_force_values, label=\"Brute Force Differentiable\", marker=\"x\")\n",
        "plt.xlabel(\"Elapsed time (s)\")\n",
        "plt.ylabel(\"Best solution so far\")\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 519
        },
        "id": "SuII2Ka5chnL",
        "outputId": "8775e92f-d53c-4f95-93c3-fa9e783b901a"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 50: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 100: Best solution so far: (2,), cost: 14.0\n",
            "Final best solution: (2,), cost: 14.0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import time\n",
        "\n",
        "def plot_pipe_dp_vs_differentiable(pipe_dp, brute_force_differentiable, L, cost_e, cost_c, k, B):\n",
        "    start_time = time.time()\n",
        "    dp_solution = pipe_dp(L, cost_e, cost_c, k, B)\n",
        "    end_time = time.time()\n",
        "    elapsed_time_dp = end_time - start_time\n",
        "    best_solutions_dp = [(elapsed_time_dp, dp_solution[1])]\n",
        "\n",
        "    start_time = time.time()\n",
        "    best_solutions_diff,total_cost_diff=brute_force_differentiable(L, cost_e, cost_c, k, B, epochs=300, learning_rate=1e-2, print_every=50)\n",
        "    #max_value_diff, total_cost_diff, best_solutions_diff = pipe_dp_differentiable(L, cost_e, cost_c, k, B,iterations=100, learning_rate=1e17, temperature=0.1, print_every=500)\n",
        "    end_time = time.time()\n",
        "    elapsed_time_diff = end_time - start_time\n",
        "    print(f\"best_solutions_diff{best_solutions_diff}, total_cost_diff={total_cost_diff}\")\n",
        "    '''\n",
        "    #diff_time, diff_costs = zip(*[(s[2], s[1]) for s in best_solutions_diff])#commented\n",
        "\n",
        "    # Create history_best_costs\n",
        "    history_best_costs = [diff_costs[0]]\n",
        "    for cost in diff_costs[1:]:\n",
        "        if cost < history_best_costs[-1]:\n",
        "            history_best_costs.append(cost)\n",
        "        else:\n",
        "            history_best_costs.append(history_best_costs[-1])\n",
        "\n",
        "    # Plot results\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.plot([t for t, _ in best_solutions_dp], [c for _, c in best_solutions_dp], label='DP', marker='o')\n",
        "    plt.plot(diff_time, history_best_costs, label='Differentiable', marker='s')\n",
        "    plt.xlabel('Elapsed Time (s)')\n",
        "    plt.ylabel('Best Solution So Far')\n",
        "    plt.legend()\n",
        "    plt.grid()\n",
        "    plt.show()\n",
        "    '''\n"
      ],
      "metadata": {
        "id": "3KCGDocnBrFS"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SBDBuHKRLQRM",
        "outputId": "19f1e35b-c447-4eb8-bb25-a401eb453619"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([3, 1], 14.0)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "L = 4\n",
        "k = 2\n",
        "B = 3\n",
        "cost_e = np.array([1, 3, 2, 5])\n",
        "#cost_e = [1,3,2,5]\n",
        "cost_c = np.ones((L-1, k-1)) * 2\n",
        "pipe_dp(L, cost_e, cost_c, k, B)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_pipe_dp_vs_differentiable(pipe_dp, brute_force_differentiable, L, cost_e, cost_c, k, B)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eWiOhtqhCsGi",
        "outputId": "7f2a0c27-8f43-4810-d743-d1d442d117a9"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 50: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 100: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 150: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 200: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 250: Best solution so far: (2,), cost: 14.0\n",
            "Epoch 300: Best solution so far: (2,), cost: 14.0\n",
            "best_solutions_diff(2,), total_cost_diff=14.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "def replace_nan(tensor, value=1e-6):\n",
        "    return torch.where(torch.isnan(tensor), torch.full_like(tensor, value), tensor)\n",
        "\n",
        "\n",
        "def softargmax2d(input, beta=100):\n",
        "    *_, h, w = input.shape\n",
        "    \n",
        "    input = input.reshape(*_, h * w)\n",
        "    input = replace_nan(input)  # Add this line\n",
        "    input = nn.functional.softmax(beta * input, dim=-1)\n",
        "\n",
        "    indices_c, indices_r = np.meshgrid(\n",
        "        np.linspace(0, 1, w),\n",
        "        np.linspace(0, 1, h),\n",
        "        indexing='xy'\n",
        "    )\n",
        "\n",
        "    indices_r = torch.tensor(np.reshape(indices_r, (-1, h * w)))\n",
        "    indices_c = torch.tensor(np.reshape(indices_c, (-1, h * w)))\n",
        "\n",
        "    result_r = torch.sum((h - 1) * input * indices_r, dim=-1)\n",
        "    result_c = torch.sum((w - 1) * input * indices_c, dim=-1)\n",
        "\n",
        "    result = torch.stack([result_r, result_c], dim=-1)\n",
        "\n",
        "    return result"
      ],
      "metadata": {
        "id": "MqyGXyMLkzjf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import numpy as np\n",
        "import copy\n",
        "\n",
        "\n",
        "\n",
        "def pipe_dp_differentiable(L, cost_e, cost_c, k, B,position):\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "\n",
        "    for i in range(1, L + 1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(sum(cost_e[ptr:ptr + i]))\n",
        "            ptr += 1\n",
        "\n",
        "    possible = sorted(list(set(possible)))\n",
        "\n",
        "    # trace will be a 3D list\n",
        "    trace = []\n",
        "    for i in range(L):\n",
        "        outer = []\n",
        "        for j in range(k):\n",
        "            inner = []\n",
        "            for m in range(len(possible)):\n",
        "                inner.append(([], torch.tensor(float('inf'))))\n",
        "            outer.append(inner)\n",
        "        trace.append(outer)\n",
        "\n",
        "    # i: layer id, starting from 0\n",
        "    # j: number of cut (=GPU-1)\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(len(possible)):\n",
        "                if i + 1 <= j:  # invalid\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0:  # base case: 0 cut\n",
        "                        cur_sum = sum(cost_e[:i + 1])\n",
        "                        trace[i][j][m] = ([i + 1], (B - 1) * max(0, cur_sum - possible[m]))\n",
        "                    else:\n",
        "                        cost_best = torch.tensor(float('inf'))\n",
        "                        S_best = []\n",
        "                        for cut in range(j - 1, i):\n",
        "                            cur_sum = sum(cost_e[cut + 1:i + 1])\n",
        "                            S, cost_ = trace[cut][j - 1][possible.index(max(cur_sum, possible[m]))]\n",
        "                            cost_ += (B - 1) * max(0, cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut][j - 1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_ = copy.deepcopy(S)\n",
        "                                S_.append(i - cut)\n",
        "                                S_best = S_\n",
        "                        trace[i][j][m] = (S_best, cost_best)\n",
        "\n",
        "    # Replace the non-differentiable control-flow statements with softargmax2d\n",
        "    \n",
        "    \n",
        "    cost_matrix = torch.zeros((L, k, len(possible)))\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(len(possible)):\n",
        "                cost_matrix[i, j, m] = trace[i][j][m][1]\n",
        "    softargmax_result = softargmax2d(cost_matrix)\n",
        "    softargmax_result=replace_nan(softargmax_result)\n",
        "    \n",
        "    '''\n",
        "    if cost_matrix is None:\n",
        "        cost_matrix = torch.zeros((L, k, len(possible)))\n",
        "        for i in range(L):\n",
        "            for j in range(k):\n",
        "                for m in range(len(possible)):\n",
        "                    cost_matrix[i, j, m] = trace[i][j][m][1]\n",
        "\n",
        "    softargmax_result = softargmax2d(cost_matrix)\n",
        "    softargmax_result = replace_nan(softargmax_result)\n",
        "    '''\n",
        "    \n",
        "    # Compute the loss using the softargmax_result\n",
        "    i = int(softargmax_result[0, 0].item())\n",
        "    j = int(softargmax_result[0, 1].item())\n",
        "    m = possible.index(max(sum(cost_e[i + 1:j + 1]), possible[j]))\n",
        "    #loss = trace[i][j][m][1]\n",
        "    loss = trace[i][j][m][1] + position[i, j, m]\n",
        "\n",
        "    return softargmax_result, loss,i,j\n",
        "\n",
        "\n",
        "def pipe_dp_differentiable_original(L, cost_e, cost_c, k, B):\n",
        "    cost_e = torch.tensor(cost_e, requires_grad=True, dtype=torch.float32)\n",
        "    cost_c = torch.tensor(cost_c, requires_grad=True, dtype=torch.float32)\n",
        "\n",
        "    # Generate all possible max length\n",
        "    possible = [0]\n",
        "    for i in range(1, L+1):\n",
        "        ptr = 0\n",
        "        while ptr + i <= L:\n",
        "            possible.append(torch.sum(cost_e[ptr:ptr+i]).item())\n",
        "            ptr += 1\n",
        "    possible = sorted(list(set(possible)))\n",
        "    possible = torch.tensor(possible, dtype=torch.float32)\n",
        "\n",
        "    trace = []\n",
        "    for i in range(L):\n",
        "        outer = []\n",
        "        for j in range(k):\n",
        "            inner = []\n",
        "            for m in range(len(possible)):\n",
        "                inner.append(([], torch.tensor(np.inf, dtype=torch.float32)))\n",
        "            outer.append(inner)\n",
        "        trace.append(outer)\n",
        "\n",
        "    for i in range(L):\n",
        "        for j in range(k):\n",
        "            for m in range(len(possible)):\n",
        "                if i+1 <= j: # invalid\n",
        "                    pass\n",
        "                else:\n",
        "                    if j == 0: # base case: 0 cut\n",
        "                        cur_sum = torch.sum(cost_e[:i+1])\n",
        "                        assert cur_sum.item() in possible\n",
        "                        trace[i][j][m] = ([i+1], (B-1) * torch.relu(cur_sum - possible[m]))\n",
        "                    else:\n",
        "                        cost_best = torch.tensor(np.inf, dtype=torch.float32)\n",
        "                        S_best = []\n",
        "                        for cut in range(j-1, i):\n",
        "                            cur_sum = torch.sum(cost_e[cut+1:i+1])\n",
        "                            assert cur_sum.item() in possible\n",
        "                            S, cost_ = trace[cut][j-1][torch.where(possible == torch.max(cur_sum, possible[m]))[0]]\n",
        "                            cost_ += (B-1) * torch.relu(cur_sum - possible[m])\n",
        "                            cost_ += cost_c[cut][j-1]\n",
        "                            if cost_ < cost_best:\n",
        "                                cost_best = cost_\n",
        "                                S_ = copy.deepcopy(S)\n",
        "                                S_.append(i-cut)\n",
        "                                S_best = S_\n",
        "                        trace[i][j][m] = (S_best, cost_best)\n",
        "\n",
        "    result_S, loss = trace[L-1][k-1][0]\n",
        "    return result_S, loss\n",
        "\n"
      ],
      "metadata": {
        "id": "ycspvgOrbgDJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import torch.optim as optim\n",
        "\n",
        "# Parameters\n",
        "L = 4\n",
        "k = 2\n",
        "cost_e = np.array([1, 3, 2, 5])\n",
        "cost_c = np.ones((L - 1, k - 1)) * 2\n",
        "B = 3\n",
        "\n",
        "# Convert to tensors\n",
        "cost_e_tensor = torch.tensor(cost_e, dtype=torch.float32)\n",
        "cost_c_tensor = torch.tensor(cost_c, dtype=torch.float32)\n",
        "\n",
        "# Generate all possible max length\n",
        "possible = [0]\n",
        "for i in range(1, L + 1):\n",
        "    ptr = 0\n",
        "    while ptr + i <= L:\n",
        "        possible.append(sum(cost_e[ptr:ptr + i]))\n",
        "        ptr += 1\n",
        "possible = sorted(list(set(possible)))\n",
        "\n",
        "# Initialize position tensor\n",
        "position = torch.zeros((L, k, len(possible)), requires_grad=True)\n",
        "\n",
        "# Training parameters\n",
        "epochs = 5000\n",
        "lr = 1e-2\n",
        "optimizer = optim.SGD([position], lr=lr)\n",
        "\n",
        "# Training loop\n",
        "for epoch in range(epochs):\n",
        "    # Zero the gradients\n",
        "    optimizer.zero_grad()\n",
        "    \n",
        "    # Run the modified pipe_dp_differentiable function with the position tensor\n",
        "    result_S, loss, i, j = pipe_dp_differentiable(L, cost_e_tensor, cost_c_tensor, k, B, position=position)\n",
        "\n",
        "    # Perform backpropagation\n",
        "    loss.backward()\n",
        "    \n",
        "    # Update the position tensor using gradient descent\n",
        "    optimizer.step()\n",
        "\n",
        "    # Find the index of the maximum value in the result_S tensor along the possible dimension\n",
        "    max_idx = torch.argmax(result_S[i, j])\n",
        "\n",
        "    # Update position tensor with the maximum value at i, j indices\n",
        "    with torch.no_grad():\n",
        "        position[i, j, :] = 0\n",
        "        position[i, j, max_idx] = result_S[i, j, max_idx]\n",
        "\n",
        "    # Print the results\n",
        "    if epoch % 50 == 0:\n",
        "        print(f'Epoch {epoch}: Loss = {loss.item()}, Final Result S: {result_S}', \"i=\", i, \"j=\", j)\n",
        "\n",
        "print(f'Final Result S: {result_S}', \"i=\", i, \"j=\", j)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 243
        },
        "id": "EMihGoIRlyC4",
        "outputId": "5f5abe0e-657e-4066-e762-c7005da54195"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "IndexError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-12-b5874afae49c>\u001b[0m in \u001b[0;36m<cell line: 32>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     49\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     50\u001b[0m         \u001b[0mposition\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 51\u001b[0;31m         \u001b[0mposition\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_idx\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mresult_S\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_idx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m     \u001b[0;31m# Print the results\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mIndexError\u001b[0m: too many indices for tensor of dimension 2"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oi49SwGOLQRN"
      },
      "outputs": [],
      "source": [
        "test_list = [(12, 4), (24, 4), (24,8), (24, 12), (36, 8)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nuFDg9SsLQRN",
        "outputId": "ecfc2e26-ba46-4d58-90cd-3117c7abad35"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "homo dp L=12 k=4 is [3, 3, 3, 3], minimum cost 12.0. Took time 0.011282682418823242\n",
            "homo bf L=12 k=4 is [3, 3, 3, 3], minimum cost 12.0. Took time 0.001417398452758789\n",
            "homo us L=12 k=4 is [3, 3, 3, 3], minimum cost 12.0. Took time 3.0279159545898438e-05\n",
            "homo dp L=24 k=4 is [6, 6, 6, 6], minimum cost 18.0. Took time 0.10501551628112793\n",
            "homo bf L=24 k=4 is [6, 6, 6, 6], minimum cost 18.0. Took time 0.021759510040283203\n",
            "homo us L=24 k=4 is [6, 6, 6, 6], minimum cost 18.0. Took time 2.288818359375e-05\n",
            "homo dp L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.19997739791870117\n",
            "homo bf L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 3.9657673835754395\n",
            "homo us L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 5.221366882324219e-05\n",
            "homo dp L=24 k=12 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 26.0. Took time 0.29858970642089844\n",
            "homo bf L=24 k=12 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 26.0. Took time 30.561776638031006\n",
            "homo us L=24 k=12 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 26.0. Took time 6.246566772460938e-05\n",
            "homo dp L=36 k=8 is [1, 5, 5, 5, 5, 5, 5, 5], minimum cost 24.0. Took time 0.7829232215881348\n",
            "homo bf L=36 k=8 is [1, 5, 5, 5, 5, 5, 5, 5], minimum cost 24.0. Took time 115.16702842712402\n",
            "homo us L=36 k=8 is [4, 4, 4, 4, 4, 4, 4, 8], minimum cost 30.0. Took time 5.984306335449219e-05\n"
          ]
        }
      ],
      "source": [
        "# homogeneous test\n",
        "for L, k in test_list:\n",
        "    cost_e = np.ones(L)\n",
        "    cost_c = np.ones((L-1, k-1)) * 2\n",
        "    time_s = time.time()\n",
        "    res = pipe_dp(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"homo dp L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")\n",
        "    time_s = time.time()\n",
        "    res = brute_force(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"homo bf L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")\n",
        "    time_s = time.time()\n",
        "    res = uniform_split(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"homo us L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MnA1NWzALQRO",
        "outputId": "bb4eab19-8f80-4b6c-e3cd-cbd35e489484"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "hete dp L=12 k=4 is [3, 3, 3, 3], minimum cost 70. Took time 0.05019879341125488\n",
            "hete bf L=12 k=4 is [3, 3, 3, 3], minimum cost 70. Took time 0.0013661384582519531\n",
            "hete us L=12 k=4 is [3, 3, 3, 3], minimum cost 70. Took time 1.9788742065429688e-05\n",
            "hete dp L=24 k=4 is [6, 6, 6, 6], minimum cost 115. Took time 0.7052814960479736\n",
            "hete bf L=24 k=4 is [6, 6, 6, 6], minimum cost 115. Took time 0.016564130783081055\n",
            "hete us L=24 k=4 is [6, 6, 6, 6], minimum cost 115. Took time 2.193450927734375e-05\n",
            "hete dp L=24 k=8 is [3, 4, 3, 2, 3, 3, 3, 3], minimum cost 95. Took time 1.4543581008911133\n",
            "hete bf L=24 k=8 is [3, 4, 3, 2, 3, 3, 3, 3], minimum cost 95. Took time 3.7701711654663086\n",
            "hete us L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 97. Took time 4.601478576660156e-05\n",
            "hete dp L=24 k=12 is [1, 2, 3, 2, 1, 2, 1, 3, 2, 3, 2, 2], minimum cost 104. Took time 1.8105647563934326\n",
            "hete bf L=24 k=12 is [1, 2, 3, 2, 1, 2, 1, 3, 2, 3, 2, 2], minimum cost 104. Took time 28.778594970703125\n",
            "hete us L=24 k=12 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 109. Took time 5.888938903808594e-05\n",
            "hete dp L=36 k=8 is [3, 5, 4, 5, 5, 6, 4, 4], minimum cost 117. Took time 7.158376693725586\n",
            "hete bf L=36 k=8 is [3, 5, 4, 5, 5, 6, 4, 4], minimum cost 117. Took time 108.56706666946411\n",
            "hete us L=36 k=8 is [4, 4, 4, 4, 4, 4, 4, 8], minimum cost 170. Took time 7.009506225585938e-05\n"
          ]
        }
      ],
      "source": [
        "# hetergeneous test\n",
        "for L, k in test_list:\n",
        "    cost_e = np.random.randint(low=5,high=10,size=L)\n",
        "    cost_c = np.random.randint(low=5,high=10,size=(L-1,k-1))\n",
        "    time_s = time.time()\n",
        "    res = pipe_dp(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"hete dp L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")\n",
        "    time_s = time.time()\n",
        "    res = brute_force(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"hete bf L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")\n",
        "    time_s = time.time()\n",
        "    res = uniform_split(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"hete us L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MCxoBCT3LQRO",
        "outputId": "f6ceffda-cc37-4a1e-e300-57ae8c050d44"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "hete dp L=12 k=4 is [3, 3, 3, 3], minimum cost 68. Took time 0.04140925407409668\n",
            "hete us L=12 k=4 is [3, 3, 3, 3], minimum cost 68. Took time 2.3603439331054688e-05\n",
            "hete dp L=24 k=12 is [2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 1, 2], minimum cost 97. Took time 1.7796664237976074\n",
            "hete us L=24 k=12 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 107. Took time 4.839897155761719e-05\n",
            "hete dp L=36 k=8 is [4, 6, 4, 4, 4, 5, 5, 4], minimum cost 115. Took time 7.414276838302612\n",
            "hete us L=36 k=8 is [4, 4, 4, 4, 4, 4, 4, 8], minimum cost 161. Took time 4.6253204345703125e-05\n",
            "hete dp L=36 k=12 is [1, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3], minimum cost 121. Took time 9.608815431594849\n",
            "hete us L=36 k=12 is [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], minimum cost 126. Took time 5.3882598876953125e-05\n",
            "hete dp L=48 k=12 is [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], minimum cost 129. Took time 30.9409818649292\n",
            "hete us L=48 k=12 is [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], minimum cost 129. Took time 5.507469177246094e-05\n",
            "hete dp L=48 k=24 is [3, 3, 3, 2, 3, 4, 2, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 4, 3], minimum cost 176. Took time 55.34712266921997\n",
            "hete us L=48 k=24 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], minimum cost 197. Took time 7.867813110351562e-05\n",
            "hete dp L=64 k=12 is [5, 6, 2, 6, 6, 6, 6, 5, 4, 6, 6, 6], minimum cost 148. Took time 97.49400663375854\n",
            "hete us L=64 k=12 is [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9], minimum cost 217. Took time 7.009506225585938e-05\n",
            "hete dp L=64 k=16 is [5, 4, 2, 2, 5, 4, 5, 2, 4, 4, 4, 5, 5, 4, 5, 4], minimum cost 157. Took time 130.8333797454834\n",
            "hete us L=64 k=16 is [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], minimum cost 180. Took time 6.508827209472656e-05\n",
            "hete dp L=128 k=32 is [4, 4, 4, 4, 5, 3, 5, 2, 4, 4, 5, 4, 5, 5, 5, 4, 1, 4, 5, 6, 5, 5, 6, 4, 4, 3, 1, 5, 4, 5, 2, 1], minimum cost 242. Took time 3688.281402349472\n",
            "hete us L=128 k=32 is [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], minimum cost 264. Took time 0.00010204315185546875\n",
            "hete dp L=128 k=12 is [10, 10, 10, 12, 11, 10, 11, 9, 11, 11, 12, 11], minimum cost 227. Took time 1504.3015270233154\n",
            "hete us L=128 k=12 is [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 18], minimum cost 319. Took time 7.486343383789062e-05\n",
            "hete dp L=128 k=50 is [1, 1, 3, 5, 4, 1, 1, 4, 1, 3, 1, 4, 4, 3, 1, 1, 4, 3, 1, 3, 2, 3, 1, 4, 5, 3, 2, 3, 3, 1, 1, 1, 3, 3, 3, 2, 4, 4, 4, 1, 2, 2, 4, 1, 2, 3, 1, 4, 5, 2], minimum cost 328. Took time 5430.115435838699\n",
            "hete us L=128 k=50 is [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 30], minimum cost 782. Took time 0.00014972686767578125\n"
          ]
        }
      ],
      "source": [
        "test_list_large = [(12, 4), (24, 12), (36, 8), (36, 12), (48,12), (48, 24), (64, 12), (64, 16), (128, 32), (128, 12), (128, 50)]\n",
        "for L, k in test_list_large:\n",
        "    cost_e = np.random.randint(low=5,high=10,size=L)\n",
        "    cost_c = np.random.randint(low=5,high=10,size=(L-1,k-1))\n",
        "    time_s = time.time()\n",
        "    res = pipe_dp(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"hete dp L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")\n",
        "    time_s = time.time()\n",
        "    res = uniform_split(L, cost_e, cost_c, k, 3)\n",
        "    print(f\"hete us L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time.time() - time_s}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-E71Et0BLQRP",
        "outputId": "7ed482c1-f17d-4a1f-c97b-1e9531783201"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "homo bf_diff L=16 k=8 is (1, 3, 5, 7, 9, 11, 13), minimum cost 18.0. Took time 0.10699653625488281\n",
            "homo dp L=16 k=8 is [2, 2, 2, 2, 2, 2, 2, 2], minimum cost 18.0. Took time 0.04775094985961914\n",
            "homo bf L=16 k=8 is [2, 2, 2, 2, 2, 2, 2, 2], minimum cost 18.0. Took time 0.09821224212646484\n",
            "homo bf_diff L=17 k=8 is (0, 1, 2, 4, 7, 10, 13), minimum cost 20.0. Took time 0.1676316261291504\n",
            "homo dp L=17 k=8 is [1, 1, 1, 2, 3, 3, 3, 3], minimum cost 20.0. Took time 0.05112171173095703\n",
            "homo bf L=17 k=8 is [1, 1, 1, 2, 3, 3, 3, 3], minimum cost 20.0. Took time 0.17087149620056152\n",
            "homo bf_diff L=18 k=8 is (0, 1, 2, 5, 8, 11, 14), minimum cost 20.0. Took time 0.29040050506591797\n",
            "homo dp L=18 k=8 is [1, 1, 1, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.0729668140411377\n",
            "homo bf L=18 k=8 is [1, 1, 1, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.3119189739227295\n",
            "homo bf_diff L=19 k=8 is (0, 1, 3, 6, 9, 12, 15), minimum cost 20.0. Took time 0.49970245361328125\n",
            "homo dp L=19 k=8 is [1, 1, 2, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.07785344123840332\n",
            "homo bf L=19 k=8 is [1, 1, 2, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.4709146022796631\n",
            "homo bf_diff L=20 k=8 is (0, 1, 4, 7, 10, 13, 16), minimum cost 20.0. Took time 0.7653062343597412\n",
            "homo dp L=20 k=8 is [1, 1, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.11176872253417969\n",
            "homo bf L=20 k=8 is [1, 1, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.7484910488128662\n",
            "homo bf_diff L=21 k=8 is (0, 2, 5, 8, 11, 14, 17), minimum cost 20.0. Took time 1.186316728591919\n",
            "homo dp L=21 k=8 is [1, 2, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.11526250839233398\n",
            "homo bf L=21 k=8 is [1, 2, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 1.1125760078430176\n",
            "homo bf_diff L=22 k=8 is (0, 3, 6, 9, 12, 15, 18), minimum cost 20.0. Took time 1.734492540359497\n",
            "homo dp L=22 k=8 is [1, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.14184308052062988\n",
            "homo bf L=22 k=8 is [1, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 2.949059009552002\n",
            "homo bf_diff L=23 k=8 is (1, 4, 7, 10, 13, 16, 19), minimum cost 20.0. Took time 2.6792752742767334\n",
            "homo dp L=23 k=8 is [2, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.2986886501312256\n",
            "homo bf L=23 k=8 is [2, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 2.5854651927948\n",
            "homo bf_diff L=24 k=8 is (2, 5, 8, 11, 14, 17, 20), minimum cost 20.0. Took time 3.758545160293579\n",
            "homo dp L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 0.17891478538513184\n",
            "homo bf L=24 k=8 is [3, 3, 3, 3, 3, 3, 3, 3], minimum cost 20.0. Took time 5.2257490158081055\n"
          ]
        }
      ],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "\n",
        "test_list = [(16,8), (17, 8), (18,8), (19,8), (20, 8), (21,8), (22,8), (23, 8),(24,8)]\n",
        "dp_time = []\n",
        "bf_time = []\n",
        "bf_diff_time= []\n",
        "# homogeneous test\n",
        "for L, k in test_list:\n",
        "    cost_e = np.ones(L)\n",
        "    cost_c = np.ones((L-1, k-1)) * 2\n",
        "    time_s = time.time()\n",
        "    res = brute_force_differentiable(L, cost_e, cost_c, k, 3,epochs=int(len(test_list)/8))\n",
        "    time_elapsed = time.time() - time_s\n",
        "    bf_diff_time.append(time_elapsed)\n",
        "    print(f\"homo bf_diff L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time_elapsed}\")\n",
        "\n",
        "\n",
        "    time_s = time.time()\n",
        "    res = pipe_dp(L, cost_e, cost_c, k, 3)\n",
        "    time_elapsed = time.time() - time_s\n",
        "    dp_time.append(time_elapsed)\n",
        "    print(f\"homo dp L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time_elapsed}\")\n",
        "    time_s = time.time()\n",
        "    res = brute_force(L, cost_e, cost_c, k, 3)\n",
        "    time_elapsed = time.time() - time_s\n",
        "    bf_time.append(time_elapsed)\n",
        "    print(f\"homo bf L={L} k={k} is {res[0]}, minimum cost {res[1]}. Took time {time_elapsed}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "69nTOIEBLQRP",
        "outputId": "a9aedb4d-7a27-4bde-fa36-a64bc24dca25"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fdf3ea71fc0>"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.plot([16,17, 18, 19, 20, 21, 22, 23, 24], dp_time, label=\"ours\")\n",
        "plt.plot([16,17, 18, 19, 20, 21, 22, 23, 24], bf_time, label=\"brute force\")\n",
        "plt.plot([16,17, 18, 19, 20, 21, 22, 23, 24], bf_diff_time, label=\"brute force differentiable\")\n",
        "plt.xlabel(\"number of layers\")\n",
        "plt.ylabel(\"runtime\")\n",
        "plt.legend(loc=\"best\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b7_vTnJRLQRP"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.3"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "include_colab_link": true
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}