Computational methods through particle swarm optimization for obtaining Stackelberg solutions to two-level nonlinear programming problems

Abstract

In this paper, we focus on two-level nonlinear programming problems, in which there is not coordination between the decision maker at the upper level (the leader) and the decision maker at the lower level (the follower), and propose a computational method using Particle Swarm Optimization (PSO) for obtaining Stackelberg solutions to two-level nonlinear programming problems. In our computational method, as we consider the above mentioned property of two-level programming problems, we introduce PSO to a PSO operating on each level by distinguishing a PSO operating on decisions of the leader (the upper level PSO) from a PSO operating on decisions of the follower (the lower level PSO). We carry out numerical experiments in order to demonstrate feasibility and effectiveness of the proposed method.