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Vehicle routing problems with three-dimensional loading constraints

This repo is part of the manuscript A branch-and-cut algorithm for vehicle routing problems with three-dimensional loading constraints, which is currently under review.

At the moment, the repo only contains the instances, solutions, and a visualizer for the solutions and solver statistics. However, the code of the branch-and-cut algorithm will be added soon.

Abstract

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if support constraints are enabled in the loading subproblem and call this the incremental feasibility property. Consequently, different infeasible path definitions apply to different 3L-CVRP variants and we introduce several variant-depending lifting steps to strengthen infeasible path inequalities. The loading subproblem is solved exactly using a flexible constraint programming model to determine the feasibility or infeasibility of a route. An extreme point-based packing heuristic is implemented to reduce time-consuming calls to the exact loading algorithm. Furthermore, we integrate a start solution procedure and periodically combine memoized feasible routes in a set-partitioning-based heuristic to generate new upper bounds. A comprehensive computational study, employing well-known benchmark instances, showcases the significant performance improvements achieved through the algorithmic enhancements. Consequently, we not only prove the optimality of many best-known heuristic solutions for the first time but also introduce new optimal and best solutions for a large number of instances.

Instances

Instances are the classical 3L-CVRP instances introduced in Gendreau et al. (2006). We use only instances with at most 50 customer nodes.

.
└── /data/input/3l-cvrp/
    ├── E016-03m.json
    ├── E016-05m.json
    ├── ...
    └── E051-05e.json

Solutions

Gendreau et al. (2006) consider different constraints in the container loading subproblem and introduce the following five variants.

Variant Constraints
no-overlap rotation support fragility lifo
all-constraints x x x x x
no-fragility x x x x
no-lifo x x x x
no-support x x x x
loading-only x x
We provide solutions for all variants. In addition, we provide solutions for the one-dimensional approximation (CVRP) of the 3L-CVRP using weight and volume as capacities and solutions for variant all constraints applying a basic variant of the branch-and-cut algorithm (all-constraints-basic). 
.
└── /data/output/3l-cvrp/
    └── variant/
        └── name/run-0/
            ├── solution-validator/ #  files for solution validator 
            │   ├── instance-name.txt
            │   └── solution-name.txt
            ├── name.LOG #  Gurobi log-file 
            ├── solution-name.json
            ├── solution-statistics-name.json

Visualizer

This visualizer is a python app using Streamlit. We only provide a visualization of solutions and some solver statistics. The app cannot be used to check the feasibility of solutions. If you want to do this, we refer to the paper by Krebs & Ehmke (2023) and the accompanying solution validator and visualizer.

Disclaimer: It should be noted that items can hover in our solutions if support constraints are disabled as the supported area can be zero. This is prohibited in Krebs & Ehmke (2023). Thus, our solutions for variants no-support and loading-only might be infeasible using the solution validator. However, in the case of the loading-only variant, all floating items could be lowered enough to touch an underlying object, resulting in a feasible solution. This is not possible for the no-support variant due to the fragility constraint.

Requirements

Run visualizer locally

  1. Clone repository
  2. Install dependencies with
poetry install --no-root
or
pip install -r requirements.txt
  1. Run streamlit web app locally with
streamlit run python/visualization/SolutionVisualizer.py

Solutions

Select a solution file from the output directory, e.g, data/output/3l-cvrp/all-constraints/e023-03g/run-0/solution-E023-03g.json.

Solver information

Select a solution statistics file from the output directory, e.g., data/output/3l-cvrp/all-constraints/e023-03g/run-0/solution-statistics-E023-03g.json.