The supporting hyperplane optimization toolkit for convex MINLP

In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonl...

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Vydané v:	Journal of global optimization Ročník 84; číslo 1; s. 1 - 41
Hlavní autori:	Lundell, Andreas, Kronqvist, Jan, Westerlund, Tapio
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.09.2022 Springer Springer Nature B.V
Predmet:	Algorithms Approximation algorithms Benchmarking Benchmarks Computer Science Convex mixed-integer nonlinear programming Convex mixed-integer nonlinear programming (MINLP) Cutting plane algorithms Extended cutting plane (ECP) algorithm Extended cutting plane algorithm Extended supporting hyperplane (ESH) algorithm Extended supporting hyperplane algorithm Forestry Geometry Hyperplanes Integer programming Iterative methods Linear programming Linearization Mathematics Mathematics and Statistics Mixed integer Mixed-integer nonlinear programming Multi-tree and single-tree algorithm Multi-tree and single-tree algorithms Nonlinear programming Open source software Operations Research/Decision Theory Optimisations Optimization Outer approximation Polyhedral outer approximation Polyhedral outer approximation (POA) Real Functions Solvers Supporting hyperplane optimization toolkit Supporting hyperplane optimization toolkit (SHOT) Toolkits Tree algorithms Trees (mathematics) Convex mixed-integer nonlinear programming (MINLP) Multi-tree and single-tree algorithms Extended cutting plane (ECP) algorithm Polyhedral outer approximation (POA) Supporting hyperplane optimization toolkit (SHOT) Extended supporting hyperplane (ESH) algorithm
ISSN:	0925-5001, 1573-2916, 1573-2916
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Abstract	In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e. , only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set.
AbstractList	In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e. , only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set. In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e., only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set.
Audience	Academic
Author	Lundell, Andreas Westerlund, Tapio Kronqvist, Jan
Author_xml	– sequence: 1 givenname: Andreas orcidid: 0000-0002-1548-1893 surname: Lundell fullname: Lundell, Andreas email: andreas.lundell@abo.fi organization: Department of Information Technology, Faculty of Science and Engineering, Åbo Akademi University – sequence: 2 givenname: Jan orcidid: 0000-0003-0299-5745 surname: Kronqvist fullname: Kronqvist, Jan organization: Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Department of Computing, Imperial College London – sequence: 3 givenname: Tapio surname: Westerlund fullname: Westerlund, Tapio organization: Process Design and Systems Engineering, Faculty of Science and Engineering, Åbo Akademi University
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Keywords	Convex mixed-integer nonlinear programming (MINLP) Multi-tree and single-tree algorithms Extended cutting plane (ECP) algorithm Polyhedral outer approximation (POA) Supporting hyperplane optimization toolkit (SHOT) Extended supporting hyperplane (ESH) algorithm
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Snippet	In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit...
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SubjectTerms	Algorithms Approximation algorithms Benchmarking Benchmarks Computer Science Convex mixed-integer nonlinear programming Convex mixed-integer nonlinear programming (MINLP) Cutting plane algorithms Extended cutting plane (ECP) algorithm Extended cutting plane algorithm Extended supporting hyperplane (ESH) algorithm Extended supporting hyperplane algorithm Forestry Geometry Hyperplanes Integer programming Iterative methods Linear programming Linearization Mathematics Mathematics and Statistics Mixed integer Mixed-integer nonlinear programming Multi-tree and single-tree algorithm Multi-tree and single-tree algorithms Nonlinear programming Open source software Operations Research/Decision Theory Optimisations Optimization Outer approximation Polyhedral outer approximation Polyhedral outer approximation (POA) Real Functions Solvers Supporting hyperplane optimization toolkit Supporting hyperplane optimization toolkit (SHOT) Toolkits Tree algorithms Trees (mathematics)
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Title	The supporting hyperplane optimization toolkit for convex MINLP
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