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A recipe for finding good solutions to MINLPs

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Abstract

Finding good (or even just feasible) solutions for Mixed-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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Correspondence to Giacomo Nannicini.

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This paper extends [41].

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Liberti, L., Mladenović, N. & Nannicini, G. A recipe for finding good solutions to MINLPs. Math. Prog. Comp. 3, 349–390 (2011). https://doi.org/10.1007/s12532-011-0031-y

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