FUZZY BILEVEL PROGRAMMING: MULTI-OBJECTIVE AND MULTI-FOLLOWER WITH SHARED VARIABLES

Abstract

Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm.