A study on the impact of selecting the follower’s reaction in solving semi-vectorial bilevel problems
摘要
A bilevel programming problem is a specific type of optimization problem that involves two hierarchical and interrelated decision levels, each associated with a leader and a follower. In this type of problem, the decisions of the leader restrict the solution space of the follower, who reacts rationally to optimize their own objective function. Furthermore, the follower’s reaction affects the objective function or constraints of the leader. To obtain bilevel feasible solutions, the follower must optimally solve its problem parameterized by the leader’s decision. When the follower considers two objectives simultaneously, determining their optimal reaction becomes unclear. Solving a follower’s bi-objective problem results in obtaining the non-dominated solutions that form the Pareto front. As a result, the follower must select one of these solutions as their rational reaction. However, this fundamental issue has received limited attention in the existing literature. In this study, our aim is to demonstrate the significant impact that the assumptions regarding the follower’s reaction can have on the bilevel problem. We will consider collaborative, adversarial, and various other approaches to illustrate their effectiveness in addressing these complex problems. The study is based on a novel variant of a competitive facility location problem, resulting in a binary bilevel problem with two objectives at the lower level. To solve this problem, we combine an enumerative scheme for the upper level with an