A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bilevel programming problems

In this paper, a hybrid intelligent algorithm by combining the particle swarm optimization (PSO) with chaos searching technique (CST) is presented for solving nonlinear bilevel programming problems. The bilevel programming is transformed into a single level programming problem by use of the KKT conditions of the lower level problem. Then, the hybrid intelligent algorithm is proposed to solve the transformed problem. Our approach embeds the CST into PSO. Firstly, the algorithm is initialized by a set of random particles which travel through the search space. Secondly, an optimization problem is solved by CST to judge whether the particle is feasible or not. In each iteration, all the feasible particles are ranked in ascending order. Particles in the front of list are updated by PSO, while particles in the end of list are updated by CST. The CST used here is not only to enhance the particles but also to improve the diversity of the particle swarm so as to avoid PSO trapping the local optima. Finally, the hybrid intelligent algorithm is commented by illustrating the numerical results on several benchmark problems from the references.