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Background:

I am solving a non-convex MINLP with SCIP. It contains about 100 binary variables, 8000 constraints and 8000 variables. I am initializing the problem with a heuristic based on "engineering insight". The initial point is feasible and probably close to the optimal solution.

Problem:

The optimality gap starts around 75%. Unfortunately SCIP stalls out^ with a gap around 60% after 5 minutes. With display/verblevel = 5 in scip.set, I see the following message repeated many times (with different LP numbers):

(node 75) solution of LP 32563 not optimal (pfeas=1, dfeas=0) -- solving again with tighter feasibility tolerance

I recompiled SCIP with CPLEX as the linear solver. This didn't help.

Questions:

Any recommendations for improving the LP solver robustness? More specifically,

  1. There are probably parts of the model that are poorly scaled. Is there any diagnostic information I can use from SCIP (or the LP solver) to track down these scaling issues?
  2. Does anyone have recommendations for different solver tolerances to try?
  3. Is this a red herring, and is the lack of progress from SCIP likely do to something else.

Thank you, Alex.

^ By "stalls out" I mean that SCIP does not print any additional information with display/verblevel = 4.

Edit: Fix typo.

Alex D
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    May be the problem is too difficult to be able to solve to global optimality. I would try to see what other solvers say (e.g. Baron, Antigone, Couenne). If really too difficult for a global solver, you may have to settle for a local MINLP solver (e.g. Bonmin). – Erwin Kalvelagen Aug 19 '16 at 07:56
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    I suspect this problem is too difficult for global optimization solvers, although I'm surprised SCIP doesn't proceed with additional iterations. It "gets stuck" solving LPs. When I've tried with BARON with other highly nonlinear non-convex problems, I've seen the iterations continue with no progress closing the gap. I was expecting that with SCIP. I will try Bonmin and possibly Couenne. – Alex D Aug 19 '16 at 16:26

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