How to speed up a model with many binary variables and PWL constraints (including absolute values)?

Awaiting user input

Tong Zhang

• December 30, 2023 11:21
• Edited

Hiya I'm now working on an MILP model which is running super slow (tried tuning the parameters but not good enough).

In the model there is a core variable h (range:-10 to10) and also another variable abs_h representing the absolute value of h. I got two piecewise linear constraints that are built based on h or abs_h. Assumed p and q are two other continuous variables. a,b,m,n are all known parameters.
PWL constraints can be built based on abs_h

Or built using h directly, but of course more segments.

My model is a little bit big. It covers multiple time periods and nodes so there are hundreds of variables h and abs_h in the actual model. And the p and q variables are interacting with other constraints/variables---quite a complex one. 
I'm wondering which approach takes longer time? 1: only using variable h and the two PWL constraints built using h, with six segments; 2: introducing the variable abs_h, and then building PWL constraints using abs_h, fewer segments but I need extra variables.

Also would it be faster if I write PWL constraints manually (like in the older versions)? I got binary variables indicating whether abs_h>1 or not  somewhere else in this model.

I also got a bilinear term "integer var * continuous var" in my model. Would it seriously affect the convergence speed? My previous method is to introduce more binary variables and constraints to avoid it, and I think it should be another reason causing the slow speed. Any way to handle it?

Many thanks!

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  Jaromił Najman

  Gurobi Staff

  • January 02, 2024 12:57

  Hi Tong,

  I'm wondering which approach takes longer time?

  My guess would be that approach 2 would be faster. However, this is really just a gut feel so it might make sense to test both.

  Also would it be faster if I write PWL constraints manually (like in the older versions)? I got binary variables indicating whether abs_h>1 or not  somewhere else in this model.

  Theoretically, there should be no difference. I would recommend using Gurobi's built in PWL feature just to save time and avoid possible mistakes.

  I also got a bilinear term "integer var * continuous var" in my model. Would it seriously affect the convergence speed? My previous method is to introduce more binary variables and constraints to avoid it, and I think it should be another reason causing the slow speed. Any way to handle it?

  It might seriously affect performance. However, before introducing multiple binaries, I would definitely just try implementing the bilinear terms. Often Gurobi can handle them very well.
  
  Once you have a final model standing and the performance is still bad, you might want to share it so someone in the Gurobi Team would take a look. Note that uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

  Best regards, 
  Jaromił

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