Pessimistic Bilevel Optimization: A Survey

Bilevel optimization are often addressed in an organizational hierarchy in which the upper level decision maker is the leader and the lower level decision maker is the follower. The leader frequently cannot obtain complete information from the follower. As a result, the leader most tends to be risk-averse, and then would like to create a safety margin to bound the damage resulting from the undesirable selection of the follower. Pessimistic bilevel optimization represents an attractive tool to model risk-averse hierarchy problems, and would provide strong ability of analysis for the risk-averse leader. Since to the best of our knowledge, there is not a comprehensive review on pessimistic bilevel optimization, the goal of this paper is to provide a extensive review on pessimistic bilevel optimization from basic definitions and properties to solution approaches. Some real applications are also proposed. This survey will directly support researchers in understanding theoretical research results, designing solution algorithms and applications in relation to pessimistic bilevel optimization.