Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

Handle URI:
http://hdl.handle.net/10754/598906
Title:
Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems
Authors:
Domínguez, Luis F.; Pistikopoulos, Efstratios N.
Abstract:
This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.
Citation:
Domínguez LF, Pistikopoulos EN (2010) Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems. Computers & Chemical Engineering 34: 2097–2106. Available: http://dx.doi.org/10.1016/j.compchemeng.2010.07.032.
Publisher:
Elsevier BV
Journal:
Computers & Chemical Engineering
Issue Date:
Dec-2010
DOI:
10.1016/j.compchemeng.2010.07.032
Type:
Article
ISSN:
0098-1354
Sponsors:
The authors gratefully acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT), the European Research Council (MOBILE, ERC Advanced Grant, No: 226462), EPRSC (Grant EP/G059071/1), KAUST and the CPSE Industrial Consortium.
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DC FieldValue Language
dc.contributor.authorDomínguez, Luis F.en
dc.contributor.authorPistikopoulos, Efstratios N.en
dc.date.accessioned2016-02-25T13:43:28Zen
dc.date.available2016-02-25T13:43:28Zen
dc.date.issued2010-12en
dc.identifier.citationDomínguez LF, Pistikopoulos EN (2010) Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems. Computers & Chemical Engineering 34: 2097–2106. Available: http://dx.doi.org/10.1016/j.compchemeng.2010.07.032.en
dc.identifier.issn0098-1354en
dc.identifier.doi10.1016/j.compchemeng.2010.07.032en
dc.identifier.urihttp://hdl.handle.net/10754/598906en
dc.description.abstractThis work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.en
dc.description.sponsorshipThe authors gratefully acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT), the European Research Council (MOBILE, ERC Advanced Grant, No: 226462), EPRSC (Grant EP/G059071/1), KAUST and the CPSE Industrial Consortium.en
dc.publisherElsevier BVen
dc.subjectGlobal optimizationen
dc.subjectInteger and mixed-integer bilevel programmingen
dc.subjectMultiparametric programmingen
dc.subjectReformulation linearization techniqueen
dc.titleMultiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problemsen
dc.typeArticleen
dc.identifier.journalComputers & Chemical Engineeringen
dc.contributor.institutionImperial College London, London, United Kingdomen
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