Mixed Integer Bilevel Optimization through Multi-parametric Programming
نویسندگان
چکیده
Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. In this work, we present a novel algorithm 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 quadratic programming problems (B-MIQP) containing both integer and continuous variables at both optimization levels. Based on multi-parametric theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as parameters for the lower level. The resulting exact parametric solutions are then substituted into the upper level problem, which can be solved as a set of single-level deterministic mixed-integer programming problems. The algorithm will be further illustrated through two numerical examples.
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