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The Supporting Hyperplane Optimization Toolkit

Andreas Lundell(andreas.lundell***at***abo.fi)
Jan Kronqvist(jan.kronqvist***at***abo.fi)
Tapio Westerlund(tapio.westerlund***at***abo.fi)

Abstract: In this paper, a recently released open-source solver for convex mixed-integer nonlinear programming (MINLP) is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) solver combines a dual strategy based on polyhedral outer approximations (POA) with several primal heuristics. The outer approximation 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 is 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, and the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This does not force the MIP solver to rebuild the branching tree in each iteration, as is the norm in most other POA-based methods. SHOT has been released as a COIN-OR open-source project, and it utilizes a flexible task-based structure which makes it easy to extend and modify. The main functionality and solution strategies available in SHOT are described, and their impact on the performance are illustrated through numerical benchmarks on all the 366 convex MINLP problems in the problem library MINLPLib. To show the effectiveness of the new solver, SHOT was also compared to other state-of-the-art solvers on the same benchmark set.

Keywords: convex mixed-integer nonlinear programming (MINLP), multi-tree vs single-tree algorithms, polyhedral outer approximation, extended supporting hyperplane (ESH) algorithm, extended cutting plane (ECP) algorithm

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Optimization Software and Modeling Systems

Category 3: Optimization Software and Modeling Systems (()

Citation:

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Entry Submitted: 06/27/2018
Entry Accepted: 06/27/2018
Entry Last Modified: 06/27/2018

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