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I am working with a ILP problem. In the problem I would like to minimize f(x0+..+xn) and then if multiple optimal solutions exist, minimize g(x0+..+xn) from the subset of those optimal solutions.

I am using SYMPHONY to minimize the first function. If i turn it into a bi-criteria problem, i get efficient results which i am not interested in. Is there any technique/solver out there which would allow me to do this ? Or if i can get multiple solutions i would be okay in checking each at a time to minimize g(x0+..+xn)

Abhimanyu
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1 Answers1

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May be a lexicographic approach:

  1. Solve with obj f(x0+..+xn). Let f0 be the optimal objective value.
  2. Add a constraint f(x0+..+xn)=f0 to the model. (May be add a little bit of wiggle room).
  3. Solve with obj g(x0+..+xn).
Erwin Kalvelagen
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    Yep, I do exactly this myself. But you might want to do f(x0+...+xn)<=f0 to preserve convexity. If f is linear it won't matter, but if it involves some sort of piecewise convex objective it will be best to use the inequality. – Michael Grant May 25 '16 at 15:11