TY - JOUR

T1 - Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

AU - Domínguez, Luis F.

AU - Pistikopoulos, Efstratios N.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/598906

UR - https://linkinghub.elsevier.com/retrieve/pii/S0098135410002802

UR - http://www.scopus.com/inward/record.url?scp=77957926100&partnerID=8YFLogxK

U2 - 10.1016/j.compchemeng.2010.07.032

DO - 10.1016/j.compchemeng.2010.07.032

M3 - Article

VL - 34

SP - 2097

EP - 2106

JO - Computers & Chemical Engineering

JF - Computers & Chemical Engineering

SN - 0098-1354

IS - 12

ER -