A primal heuristic for nonsmooth mixed integer nonlinear optimization

Abstract

Complex real-world optimization tasks often lead to mixed-integer nonlinear problems (MINLPs). However, current MINLP algorithms are not always able to solve the resulting large-scale problems. One remedy is to develop problem specific primal heuristics that quickly deliver feasible solutions. This paper presents such a primal heuristic for a certain class of MINLP models. Our approach features a clear distinction between nonsmooth but continuous and genuinely discrete aspects of the model. The former are handled by suitable smoothing techniques; for the latter we employ reformulations using complementarity constraints. The resulting mathematical programs with equilibrium constraints (MPEC) are finally regularized to obtain MINLP-feasible solutions with general purpose NLP solvers.