A Hierarchical PSO Algorithm for Solving Linear Trilevel Programming Problems

Trilevel programming deals with hierarchical optimization problems that in which the top-level, middle-level and bottom-level decision-makers attempt to optimize their individual objectives, but their decisions are affected by the optimal objective values presented at other levels. In this paper, we propose a hierarchical particle swarm optimization (PSO) method for solving linear trilevel programming problems (LTLPPs). The proposed method, solves the top-level, middle-level and bottom-level problems iteratively by three variants of PSO. Finally, we give some illustrative examples to show the efficiency of the proposed algorithm.