Very slow multiplication when the output is a variable with a big set of values as domain

[AriaAhmadi]

What version of OR-Tools and what language are you using?
Version: 9.2.9972.
**Language:
Python
**Which solver are you using:
CP-SAT
**What operating system:
Linux 18.04

Hi,

I have a big problem with multiplication that I would be thankful if you could help me with.

I need to multiply a list of more than 2 variables e.g. [x1 , x2 , x3 , x4]. I understand that ortools only supports the multiplication of two varibales, thus I should calculcate the multiplication iteratively:

model.AddMultiplicationEquality(aux_var1 , [x1 , x2])
model.AddMultiplicationEquality(aux_var2 , [x3 , aux_var1])
etc.

Imagine, x1's domain is [1-1000] and x2 could only take values from the set {100 , 200}.

The most obvious way is to define aux_var1 to have a domain [100-200000]. This may not be the most efficient way as aux_var1 could only take very specific set of values in the range [100-200000]. I attempted to define aux_var1's domain as a set like {[100-100] , [200,200] , ... , [200000,200000]} but that makes the multiplication extremely slow.

Question 1: Is there any other efficient way I can calculate the multiplication of these 4 variables? (other than iterative approach)

Questin 2: In the aforementioned case, defining aux_var1's domain be [100-200000] is not efficient and my way of defining a set of numbers as domain is super slow. How else can I go about defining aux_var1's domain?

I look forward to receiving your help.
Regards,
Aria.

[lperron]

1. you should balance your expression ((x1 * x2) * (x3 * x4))
2. You should really try with 9.3
3. It now supports 1 var affine expression (a * x + b) in all terms, so {100, 200} could be 100 + 100 * bool_var
4. You can collect all scaling, and move them out of the product: {100, 200} * {50, 10, 150, 200} -> 5000 * {1, 2} * {1, 2, 3, 4}.