Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints

Andreas Lundell; Jan Kronqvist

doi:10.1063/1.5088979

Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints

Andreas Lundell, Jan Kronqvist

Research output: Chapter in Book/Conference proceeding › Conference contribution › Scientific › peer-review

4 Citations (Scopus)

Abstract

In this paper, it is explained how algorithms for convex mixed-integer nonlinear programming (MINLP) based on polyhedral outer approximation (P0A) can be integrated with mixed-integer programming (MIP) solvers through callbacks and lazy constraints. Through this integration, a new approach utilizing a single branching tree is obtained which reduces the overhead required when rebuilding the branching tree in the MIP solver due to the continuous addition of linear constraints approximating the nonlinear feasible region of the MINLP problem. The result is an efficient strategy for implementing a POA utilized by the Supporting llyperplane Optimization Toolkit (SHOT) solver.

Original language	Undefined/Unknown
Title of host publication	Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018
Editors	Michael T. M. Emmerich, André H. Deutz, Sander C. Hille, Yaroslav D. Sergeyev
Publisher	American Institute of Physics
Pages	–
Number of pages	4
ISBN (Print)	978-0-7354-1798-4
DOIs	https://doi.org/10.1063/1.5088979
Publication status	Published - 2019
MoE publication type	A4 Article in a conference publication
Event	International Global Optimization Workshop - LeGO 14th International Global Optimization Workshop Duration: 18 Sept 2018 → 21 Sept 2018

Conference

Conference	International Global Optimization Workshop
Period	18/09/18 → 21/09/18

Access to Document

10.1063/1.5088979

Cite this

Lundell, A., & Kronqvist, J. (2019). Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. In M. T. M. Emmerich, A. H. Deutz, S. C. Hille, & Y. D. Sergeyev (Eds.), Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018 (pp. –). American Institute of Physics. https://doi.org/10.1063/1.5088979

Lundell, Andreas ; Kronqvist, Jan. / Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018. editor / Michael T. M. Emmerich ; André H. Deutz ; Sander C. Hille ; Yaroslav D. Sergeyev. American Institute of Physics, 2019. pp. –

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title = "Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints",

abstract = "In this paper, it is explained how algorithms for convex mixed-integer nonlinear programming (MINLP) based on polyhedral outer approximation (P0A) can be integrated with mixed-integer programming (MIP) solvers through callbacks and lazy constraints. Through this integration, a new approach utilizing a single branching tree is obtained which reduces the overhead required when rebuilding the branching tree in the MIP solver due to the continuous addition of linear constraints approximating the nonlinear feasible region of the MINLP problem. The result is an efficient strategy for implementing a POA utilized by the Supporting llyperplane Optimization Toolkit (SHOT) solver.",

author = "Andreas Lundell and Jan Kronqvist",

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doi = "10.1063/1.5088979",

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isbn = "978-0-7354-1798-4",

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publisher = "American Institute of Physics",

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Lundell, A & Kronqvist, J 2019, Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. in MT M. Emmerich, AH Deutz, SC Hille & YD Sergeyev (eds), Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018. American Institute of Physics, pp. –, International Global Optimization Workshop, 18/09/18. https://doi.org/10.1063/1.5088979

Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. / Lundell, Andreas; Kronqvist, Jan.
Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018. ed. / Michael T. M. Emmerich; André H. Deutz; Sander C. Hille; Yaroslav D. Sergeyev. American Institute of Physics, 2019. p. –.

Research output: Chapter in Book/Conference proceeding › Conference contribution › Scientific › peer-review

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AU - Lundell, Andreas

AU - Kronqvist, Jan

N1 - ast. De gick inte att öppna bilagan, så Linda tog bort den. Den slutliga PDF:en är öppet tillgänglig på nätet, så det räcker med den.

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N2 - In this paper, it is explained how algorithms for convex mixed-integer nonlinear programming (MINLP) based on polyhedral outer approximation (P0A) can be integrated with mixed-integer programming (MIP) solvers through callbacks and lazy constraints. Through this integration, a new approach utilizing a single branching tree is obtained which reduces the overhead required when rebuilding the branching tree in the MIP solver due to the continuous addition of linear constraints approximating the nonlinear feasible region of the MINLP problem. The result is an efficient strategy for implementing a POA utilized by the Supporting llyperplane Optimization Toolkit (SHOT) solver.

AB - In this paper, it is explained how algorithms for convex mixed-integer nonlinear programming (MINLP) based on polyhedral outer approximation (P0A) can be integrated with mixed-integer programming (MIP) solvers through callbacks and lazy constraints. Through this integration, a new approach utilizing a single branching tree is obtained which reduces the overhead required when rebuilding the branching tree in the MIP solver due to the continuous addition of linear constraints approximating the nonlinear feasible region of the MINLP problem. The result is an efficient strategy for implementing a POA utilized by the Supporting llyperplane Optimization Toolkit (SHOT) solver.

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DO - 10.1063/1.5088979

M3 - Konferensbidrag

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BT - Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018

A2 - M. Emmerich, Michael T.

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PB - American Institute of Physics

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Lundell A, Kronqvist J. Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. In M. Emmerich MT, Deutz AH, Hille SC, Sergeyev YD, editors, Proceedings LeGO : 14th International Global Optimization Workshop : Leiden, the Netherlands, 18-21 September 2018. American Institute of Physics. 2019. p. – doi: 10.1063/1.5088979