A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

Handle URI:
http://hdl.handle.net/10754/597383
Title:
A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems
Authors:
Domínguez, Luis F.; Pistikopoulos, Efstratios N.
Abstract:
An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).
Citation:
Domínguez LF, Pistikopoulos EN (2012) A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems. AIChE J 59: 483–495. Available: http://dx.doi.org/10.1002/aic.13838.
Publisher:
Wiley-Blackwell
Journal:
AIChE Journal
Issue Date:
25-Jun-2012
DOI:
10.1002/aic.13838
Type:
Article
ISSN:
0001-1541
Sponsors:
The authors thank 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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Full metadata record

DC FieldValue Language
dc.contributor.authorDomínguez, Luis F.en
dc.contributor.authorPistikopoulos, Efstratios N.en
dc.date.accessioned2016-02-25T12:32:05Zen
dc.date.available2016-02-25T12:32:05Zen
dc.date.issued2012-06-25en
dc.identifier.citationDomínguez LF, Pistikopoulos EN (2012) A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems. AIChE J 59: 483–495. Available: http://dx.doi.org/10.1002/aic.13838.en
dc.identifier.issn0001-1541en
dc.identifier.doi10.1002/aic.13838en
dc.identifier.urihttp://hdl.handle.net/10754/597383en
dc.description.abstractAn algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).en
dc.description.sponsorshipThe authors thank 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.publisherWiley-Blackwellen
dc.subjectMathematical modelingen
dc.subjectOptimizationen
dc.subjectProcess synthesisen
dc.titleA quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problemsen
dc.typeArticleen
dc.identifier.journalAIChE Journalen
dc.contributor.institutionDept. of Chemical Engineering; Centre for Process Systems Engineering; Imperial College; London; SW7 2AZ; U.K.en
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