On solving nonconvex MINLP problems with SHOT

Andreas Lundell, Jan Kronqvist

Research output: Chapter in Book/Conference proceedingConference contributionScientificpeer-review

2 Citations (Scopus)
26 Downloads (Pure)


The Supporting Hyperplane Optimization Toolkit (SHOT) solver was originally developed for solving convex MINLP problems, for which it has proven to be very efficient. In this paper, we describe some techniques and strategies implemented in SHOT for improving its performance on nonconvex problems. These include utilizing an objective cut to force an update of the best known solution and strategies for handling infeasibilities resulting from supporting hyperplanes and cutting planes generated from nonconvex constraint functions. For convex problems, SHOT gives a guarantee to find the global optimality, but for general nonconvex problems it will only be a heuristic. However, utilizing some automated transformations it is actually possible in some cases to reformulate all nonconvexities into linear form, ensuring that the obtained solution is globally optimal. Finally, SHOT is compared to other MINLP solvers on a few nontrivial test problems to illustrate its performance.

Original languageEnglish
Title of host publicationOptimization of complex systems: Theory, models, algorithms and applications
EditorsHoai An Le Thi, Hoai Minh Le, Tao Pham Dinh
ISBN (Electronic)978-3-030-21803-4
ISBN (Print)978-3-030-21802-7
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventWorld Congress on Global Optimization (WCGO) - 6th World Congress on Global Optimization, WCGO 2019
Duration: 8 Jul 201910 Jul 2019

Publication series

Name Advances in Intelligent Systems and Computing
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365


ConferenceWorld Congress on Global Optimization (WCGO)


  • Feasibility relaxation
  • Nonconvex MINLP
  • Reformulation techniques
  • Supporting Hyperplane Optimization Toolkit (SHOT)


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