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Does the Cutoff parameter in Gurobi do anything other than prohibit returning solutions below/above the cutoff value?

I ask in particular because I have a maximization MIP where I am trying to find a solution of at least X (don't care if it's optimal, just X or higher). Gurobi has previously found incumbent solutions of 0.8X, with an upper bound of 1.1X, before failing to improve.

So I know that 0.8X is attainable, is there any benefit to setting Cutoff to 0.8X? Would that speed up the solve time at all to get to an incumbent > 0.8X?

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  • $\begingroup$ In addition to what @fontanf recommends (hot-starting from the 0.8X solution), you might want to set the MIPFocus parameter to 1, which focuses on finding (improved) feasible solutions. $\endgroup$
    – prubin
    Jul 21 at 16:13
  • $\begingroup$ @prubin I'm using R ( ompr and ROI.plugin.gurobi ), do you know if it's possible to provide a starting solution to Gurobi using ompr? $\endgroup$ Jul 21 at 16:20
  • $\begingroup$ I'm not certain, but I don't think so. I don't see any provision in ompr for it. Dirk Schumacher, the author of ompr, is working on a newer library ("rmpk"), and there he has creation of a method for providing starting solutions as an open issue. Also, ompr relies on the ROI library, and I don't see anything about starting solutions in the ROI documentation. You might contact the author(s) of ROI and ask them. $\endgroup$
    – prubin
    Jul 21 at 16:30
  • $\begingroup$ thanks @prubin. I didn't think so either but I know you've used ompr. (Great blog post on it a while back!) I love being able to model MIPs in R with flexibility and ease using ompr, but I would definitely appreciate some more features and control in its use $\endgroup$ Jul 21 at 16:40
  • $\begingroup$ Thanks! Same here. I'm not sure, but I think Dirk's switch to the rmpk package may be motivated more by speed/model size concerns than by new features. $\endgroup$
    – prubin
    Jul 21 at 17:42

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Yes, if the solver doesn't use a pure "best bound" strategy as selection rule, then setting a cutoff might make it possible to prune some nodes which wouldn't have been pruned otherwise. So, in theory, it should slightly speed up the resolution. In practice, one can never be sure of what will happen though.

However, if you already have a solution, it's better to provide the solution directly than to give its value as cutoff.

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