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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Bibliographic Details
Published in:Journal of global optimization Vol. 84; no. 1; pp. 1 - 41
Main Authors: Lundell, Andreas, Kronqvist, Jan, Westerlund, Tapio
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0925-5001
1573-2916
1573-2916
DOI:10.1007/s10898-022-01128-0