A Bi-level Multiobjective PSO Algorithm

Bi-level optimization represents a class of optimization problems with two decision levels: the upper level (leader) and the lower level (follower). Bi-level problems have been extensively studied for single objective problems, but there is few research in case of multiobjective problems in both levels. This case is herein studied using a multiobjective particle swarm optimization (MOPSO) based algorithm. To solve the bi-level multiobjective problem the algorithm searches for upper level Pareto optimal solutions. In every upper level search, the algorithm solves a lower level multiobjective problem in order to find a representative set of lower level Pareto optimal solutions for a fixed upper level vector of decision variables. The search in both levels is performed using the operators of a MOPSO algorithm. The proposed algorithm is able to solve bi-level multiobjective problems achieving solutions in the true Pareto optimal front or close to it.