Mathematical Programming Computation, Volume 3, Issue 4, December 2011

A recipe for finding good solutions to MINLPs

Leo Liberti, Nenad Mladenovic, Giacomo Nannicini

Finding good (or even just feasible) solutions forMixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear Programming algorithm and Branch-and-Bound.We test the proposed approach on MINLPLib, comparing with several existing heuristic and exact methods. An implementation of the proposed heuristic is freely available and can employ all NLP/MINLP solvers with an AMPL interface as the main search tools.

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