The reformulation-based αGO algorithm for solving nonconvex MINLP problems - some improvements

Andreas Lundell; Tapio Westerlund

doi:10.3303/CET1332221

The reformulation-based αGO algorithm for solving nonconvex MINLP problems - some improvements

Andreas Lundell, Tapio Westerlund

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

1 Citation (Scopus)

Abstract

The alpha-reformulation (alpha R) technique can be used to transform any nonconvex twice-differentiable mixed-integer nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is implemented in the a global optimization (alpha GO) algorithm solving the specified problem type to global optimality as a sequence of reformulated subproblems where the piecewise linear functions are refined in each step. The tightness of the underestimator has a large impact on the efficiency of the solution process, and in this paper it is shown how it is possible to reduce the approximation error by utilizing a piecewise quadratic spline function defined on smaller subintervals. The improved underestimator is also applied to test problems illustrating its performance.

Original language	Undefined/Unknown
Title of host publication	11th International Conference on Chemical and Process Engineering - selected papers of ICheaP11
Editors	Sauro Pierucci, Jiří J. Klemeš
Publisher	Associazione Italiana di Ingegneria Chimica
Pages	1321–1326
Number of pages	6
ISBN (Print)	978-88-95608-23-5
DOIs	https://doi.org/10.3303/CET1332221
Publication status	Published - 2013
MoE publication type	A4 Article in a conference publication
Event	International Conference on Chemical and Process Engineering (ICheaP) - 11th International Conference on Chemical and Process Engineering (ICheaP) Duration: 2 Jun 2013 → 5 Jun 2013

Conference

Conference	International Conference on Chemical and Process Engineering (ICheaP)
Period	02/06/13 → 05/06/13

Access to Document

10.3303/CET1332221

http://www.aidic.it/cet/13/32/221.pdf

Cite this

@inproceedings{9019ce9874ec4490b8265fdb05825910,

title = "The reformulation-based αGO algorithm for solving nonconvex MINLP problems - some improvements",

abstract = "The alpha-reformulation (alpha R) technique can be used to transform any nonconvex twice-differentiable mixed-integer nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is implemented in the a global optimization (alpha GO) algorithm solving the specified problem type to global optimality as a sequence of reformulated subproblems where the piecewise linear functions are refined in each step. The tightness of the underestimator has a large impact on the efficiency of the solution process, and in this paper it is shown how it is possible to reduce the approximation error by utilizing a piecewise quadratic spline function defined on smaller subintervals. The improved underestimator is also applied to test problems illustrating its performance.",

author = "Andreas Lundell and Tapio Westerlund",

year = "2013",

doi = "10.3303/CET1332221",

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booktitle = "11th International Conference on Chemical and Process Engineering - selected papers of ICheaP11",

publisher = "Associazione Italiana di Ingegneria Chimica",

note = "International Conference on Chemical and Process Engineering (ICheaP) ; Conference date: 02-06-2013 Through 05-06-2013",

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Lundell, A & Westerlund, T 2013, The reformulation-based αGO algorithm for solving nonconvex MINLP problems - some improvements. in S Pierucci & JJ Klemeš (eds), 11th International Conference on Chemical and Process Engineering - selected papers of ICheaP11. Associazione Italiana di Ingegneria Chimica, pp. 1321–1326, International Conference on Chemical and Process Engineering (ICheaP), 02/06/13. https://doi.org/10.3303/CET1332221

The reformulation-based αGO algorithm for solving nonconvex MINLP problems - some improvements. / Lundell, Andreas ; Westerlund, Tapio.
11th International Conference on Chemical and Process Engineering - selected papers of ICheaP11. ed. / Sauro Pierucci; Jiří J. Klemeš. Associazione Italiana di Ingegneria Chimica, 2013. p. 1321–1326.

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

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