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A quadratic approximation‐based algorithm for the solution of multiparametric mixed‐integer nonlinear programming problems
Author(s) -
Domínguez Luis F.,
Pistikopoulos Efstratios N.
Publication year - 2013
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.13838
Subject(s) - mathematics , iterated function , integer programming , mathematical optimization , integer (computer science) , quadratic programming , nonlinear programming , linear programming , nonlinear system , parametric statistics , quadratic equation , branch and price , linear programming relaxation , algorithm , computer science , mathematical analysis , statistics , physics , geometry , quantum mechanics , programming language
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 J, 59: 483–495, 2013