Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. In this work, we present novel algorithms for the exact and global solution of two...
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Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. In this work, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametricprogramming theory, the main idea is to recast the lower level problem as a multiparametricprogramming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems. (C) 2019 Elsevier Ltd. All rights reserved.
作者：
Dua, VivekUCL
Ctr Proc Syst Engn Dept Chem Engn London WC1E 7JE England
The mixed integer polynomial programming problem is reformulated as a multi-parametricprogramming problem by relaxing integer variables as continuous variables and then treating them as parameters. The optimality con...
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The mixed integer polynomial programming problem is reformulated as a multi-parametricprogramming problem by relaxing integer variables as continuous variables and then treating them as parameters. The optimality conditions for the resulting parametricprogramming problem are given by a set of simultaneous parametric polynomial equations which are solved analytically to give the parametric optimal solution as a function of the relaxed integer variables. Evaluation of the parametric optimal solution for integer variables fixed at their integer values followed by screening of the evaluated solutions gives the optimal solutions. (C) 2014 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
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