An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver

Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be relaxed in various ways, including via mixed-integer linear programming (MIP), nonlinea...

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Bibliographic Details
Published in:Journal of global optimization 2018-03, Vol.70 (3), p.497-516
Main Authors: Zhou, Kai, Kılınç, Mustafa R., Chen, Xi, Sahinidis, Nikolaos V.
Format: Article
Language:English
Subjects:
Activation
Algorithms
Branch & bound algorithms
Computer Science
Deactivation
Integer programming
Investment analysis
Linear programming
Mathematical optimization
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Real Functions
Solvers
Strategy
Tradeoffs
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Summary:Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be relaxed in various ways, including via mixed-integer linear programming (MIP), nonlinear programming, and linear programming. There is a tradeoff between the quality of the bounds and CPU time requirements of these relaxations. Unfortunately, these tradeoffs are problem-dependent and cannot be predicted beforehand. This paper proposes a new dynamic strategy for activating and deactivating MIP relaxations in various stages of a branch-and-bound algorithm. The primary contribution of the proposed strategy is that it does not use meta-parameters, thus avoiding parameter tuning. Additionally, this paper proposes a strategy that capitalizes on the availability of parallel MIP solver technology to exploit multicore computing hardware while solving MINLPs. Computational tests for various benchmark libraries reveal that our MIP activation strategy works efficiently in single-core and multicore environments.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0559-0