Solving bi-level programming with multiple linear objectives at lower level using particle swarm optimization

Bi-level programming is a tool for modeling decentralized decisions that consists of the objective of the leader at its first level and that of the follower at the second level. This paper deals with general bi-level optimization problems with multiple objectives at the lower level of decision making. We present Particle swarm optimization (PSO) algorithm for solving this problem. Also, two numerical examples are given to illustrate efficiency of the proposed algorithm.