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Computing feasible points for binary MINLPs with MPECs. (English) Zbl 1411.90008
Summary: 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 MINLPLib2 instances, where our methods are able to produce feasible solutions for \(60{\%}\) of all instances in at most 10 s.

90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C11 Mixed integer programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C59 Approximation methods and heuristics in mathematical programming
90C26 Nonconvex programming, global optimization
Full Text: DOI
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