Bilevel Multi-Objective Optimization and Decision Making

Abstract

Bilevel optimization problems are special kind of optimization problems which require every feasible upper-level solution to satisfy the optimality conditions of a lower-level optimization problem. Due to complications associated in solving such problems, they are often treated as single-level optimization problems, and approximation principles are employed to handle them. These problems are commonly found in many practical problem solving tasks which include optimal control, process optimization, game-playing strategy development, transportation problems, coordination of multi-divisional firms, and others. The chapter addresses certain intricate issues related to solving multi-objective bilevel programming problems, and describes recent methodologies to tackle such problems. The first methodology is a hybrid evolutionary-cum-local-search based algorithm to generate the entire Paretofrontier of multi-objective bilevel problems. The second methodology is a decision maker oriented approach, where preferences from the upper level decision maker are incorporated in the intermediate steps of the algorithm, leading to reduced computational expense. Both these methodologies are tested on a set of recently proposed test problems. The test problems involve various intricacies which could be encountered in multi-objective bilevel problem solving, and the algorithms have been shown to successfully handle these problems. The study opens up a variety of issues related to multi-objective bilevel programming, and shows that evolutionary methods are effective in solving such problems.