Journal of Global Optimization

, Volume 70, Issue 3, pp 497–516 | Cite as

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

  • Kai Zhou
  • Mustafa R. Kılınç
  • Xi ChenEmail author
  • Nikolaos V. SahinidisEmail author


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.


Global optimization Mixed-integer nonlinear programming Mixed-integer linear programming Parallel computing Multicore architectures Portfolios of relaxations 



We gratefully acknowledge the financial support of National Natural Science Foundation of China–Zhejiang Joint Fund for the Integration of Industrialization and Informatization (No. U1509209) and China Scholarship Council for the joint Ph.D. program.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Industrial Control Technology, College of Control Science and EngineeringZhejiang UniversityHangzhouChina
  2. 2.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA

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