How to set stopping criteria in mixed integer programming?

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Frank Dou
Frank Dou 2021-5-18
评论： Frank Dou 2021-11-25
Hi guys~
Recently, I am using mixed integer programming to solve a problem.
Actually, I want to let it stop when Relative gap is less than 2%.
So I set according to https://www.mathworks.com/help/optim/ug/intlinprog.html#btv2x05
options = optimoptions(@intlinprog,'RelativeGapTolerance',0.2,'Display','iter')
[x,fval]=intlinprog(f,iint,A,b,[],[],lb,ub,[],options);
Yet, it seems like this setting doesn't work. It have been running for 30min...
Any suggetions? Thank you very much!

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Derya
Derya 2021-5-20
Hello Frank,
The stopping tolerance is automatically modified to
tolerance = min(1/(1+|L|), RelativeGapTolerance)
As described in https://www.mathworks.com/help/optim/ug/intlinprog.html#btv2x05.
I estimate the lower bound, L, for your problem at around 96, so intlinprog tolerance for stopping on relative gap would be around 0.01, i.e. 1%. It looks like intlinprog cannot reduce the gap from 1.54% in the following 30 minutes.
You have couple of options:
  1. Increase AbsoluteGapTolerance, e.g. to 2.
  2. Divide the objective function by a factor 2 or more, perhaps 10.
  3. Set CutGeneration and/or Heuristics to 'intermediate' and see if this reduces the time to solution.
Kind Regards,
Derya
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Frank Dou
Frank Dou 2021-11-25
Btw, how could I find the running time complexity of the solver
[x,fval]=intlinprog(f,iint,A,b,[],[],lb,ub,[],options);
Thank you very much!

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