Limiting the number of activated binary variables

回答済み

Mariano Dominguez Librandi

2023年06月28日 09:19

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Hello everyone,

I am working on the problem of topology optimisation in power grids. In this type of model there are many IF constraints which are modelled using the Big-M method. It is possible to limit the number of topology actions with an inequality constraint, e.g. sum(x_i)<= Nmax x_i \in {0,1}. As expected, the larger the Nmax, the larger the search space and the longer it takes to solve. However, this does not mean that a better solution will be found.

In a minimal example model, I have the following bestBound and Incumbent performance for an increasing number of Nmax from 1 to 5. The values are given in % of the initial incumbent, as I provide a good MIP start.

This graph shows that Nmax=2 is sufficient to find the best solution. 

My question would then be whether there is any additional insight into my model that I can derive from this (bestBound and Incumbent) performance. 

Another question would be whether it is possible to know in advance that Nmax=2 is sufficient, but I suspect that it is not the case.

Thank you very much!
Kind regards,
Mariano

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  Matthias Miltenberger

  • Gurobi Staff

  2023年06月28日 09:45

  Hi Mariano,

  One thing that comes to mind is applying a multi-objective approach: First, optimizing the main model with a large \(N_{max}\) value and in the next step trying to minimize \(\sum x_i\) so you find the smallest number leading to the same solution quality.

  You can read more about multi-objective optimization here: Multiple Objectives - Gurobi Optimization

  I hope that helps!

  Cheers,
  Matthias

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  Mariano Dominguez Librandi

  2023年07月03日 12:59

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  Dear Matthias,

  Thank you for the quick response.

  I will try that out.

  Best regards

  Mariano

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