A good recipe for solving MINLPs

Leo Liberti 1, Giacomo Nannicini 1 and Nenad Mladenovic 2

1 LIX, ŽEcole Polytechnique, F-91128 Palaiseau, France
{liberti,giacomon}@lix.polytechnique.fr

2 Brunel University, London, UK, and
Institute of Mathematics, Academy of Sciences, Belgrade, Serbia
nenad.mladenovic@brunel.ac.uk, nenad@turing.mi.sanu.ac.yu

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 useful task, specially
when the objective/constraints are nonconvex. We present a generalpurpose
heuristic based on Variable Neighbourhood Search, Local Branching,
Sequential Quadratic Programming and Branch-and-Bound. We
test the proposed approach on the MINLPLib, discussing optimality, reliability
and speed.