Non-convex QCPQ capability compared to SCIP

Answered

Tomáš Votroubek

• August 15, 2022 21:49

Dear Gurobi team,
I understand that Gurobi uses the same technique as SCIP for solving continuous non-convex QCQPs. If that is the case, I can not explain the results of QPLIB benchmarks (http://plato.asu.edu/ftp/cnconv.html), where it appears that Gurobi solves in seconds what SCIP (a highly optimized implementation of the same algorithm) fails to solve in hours.

What are the differences that make Gurobi work so much better?

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• 

  Jaromił Najman

  Gurobi Staff

  • August 16, 2022 07:56
  • Edited

  While SCIP and Gurobi use the same idea to solve (continuous) non-convex QCQPs, the algorithm aren't exactly equal. Both, SCIP and Gurobi (and many other global (MI)NLP solvers)  use the spatial B&B algorithm but they all differ in certain aspects. Different solvers use different cuts, bound tightening techniques, branching rules, and node selection rules which already account for most of the performance differences between solvers. Moreover, similar to MIPs, there are many tricks which can be applied to certain (MI)NLP problems. This means that having a bigger bag of tricks can help you solve more models (faster).

  Best regards, 
  Jaromił

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