Solving bilevel multi-criterion optimization problems with lower level decision uncertainty

Abstract

Bilevel optimization problems are characterized by a hierarchical leader-follower structure, where the leader desires to optimize her own strategy taking the response of the follower into account. These problems are referred to 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, a bilevel problem is solved by a leader who needs to take multiple objectives into account and simultaneously deal with the decision-uncertainty involved in modeling the follower’s behavior. Such problems are often encountered in strategic product design, homeland security applications, and taxation policy. However, the hierarchical nature makes the problems difficult to solve and they are commonly simplified by assuming a deterministic setup with smooth objective functions. In this paper, we focus our attention on the development of a flexible evolutionary algorithm for solving multi-criterion bilevel problems with lower level (follower) decision uncertainty. The performance of the algorithm is evaluated in a comparative study on a number of test problems. In addition to the numerical experiments, we consider two real-world examples from the field of environmental economics and management to illustrate how the framework can be used to obtain optimal strategies.