Computing feasible points for binary MINLPs with MPECs

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 d...

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Vydáno v:Mathematical programming computation Ročník 11; číslo 1; s. 95 - 118
Hlavní autoři: Schewe, Lars, Schmidt, Martin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 14.03.2019
Springer Nature B.V
Témata:
Feasibility studies
Full Length Paper
Iterative methods
Iterative solution
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Operations Research/Decision Theory
Optimization
Production methods
Regularization
Solvers
Theory of Computation
Primal heuristic
Complementarity constraints
MPEC
90C11
90C33
90-08
MINLP
90C59
Mixed-integer nonlinear optimization
ISSN:1867-2949, 1867-2957
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Shrnutí: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 10 s .
Bibliografie:ObjectType-Article-1
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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-018-0141-x