Towards understanding bilevel multi-objective optimization with deterministic lower level decisions

Abstract

Bilevel decision making and optimization problems are commonly framed as leader-follower problems, where the leader desires to optimize her own decision taking the decisions of the follower into account. These problems are known as Stackelberg problems in the domain of game theory, and as bilevel problems in the domain of mathematical programming. In a number of practical scenarios, both the leaders and the followers might be faced with multiple criteria bringing bilevel multi-criteria decision making aspects into the problem. In such cases, the Paretooptimal frontier of the leader is influenced by the decision structure of the follower facing multiple objectives. In this paper, we analyze this effect by modeling the lower level decision maker using value functions. We study the problem using test cases and propose an algorithm that can be used to solve such problems.