Computing feasible points for binary MINLPs with MPECs

Lars Schewe*, Martin Schmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Nonconvex mixed-binary nonlinear optimization problems frequently appear in practice and are typically extremely hard to solve. In this paper we discuss a class of primal heuristics that are based on a reformulation of the problem as a mathematical program with equilibrium constraints. We then use different regularization schemes for this class of problems and use an iterative solution procedure for solving series of regularized problems. In the case of success, these procedures result in a feasible solution of the original mixed-binary nonlinear problem. Since we rely on local nonlinear programming solvers the resulting method is fast and we further improve its reliability by additional algorithmic techniques. We show the strength of our method by an extensive computational study on 662 MINLPLib2instances, where our methods are able to produce feasible solutions for 60 % of all instances in at most 10s.

Original languageEnglish
Pages (from-to)95-118
Number of pages24
JournalMathematical Programming Computation
Volume11
Issue number1
Early online date23 Aug 2018
DOIs
Publication statusPublished - 14 Mar 2019

Keywords

  • Complementarity constraints
  • MINLP
  • Mixed-integer nonlinear optimization
  • MPEC
  • Primal heuristic

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