A hybrid intelligent algorithm by combining particle swarm optimization with variable neighborhood search for solving nonlinear bilevel programming problems

In this paper, a hybrid intelligent algorithm by combining the particle swarm optimization (PSO) with variable neighborhood search (VNS) is presented on the basis of analyzing the problem of nonlinear bilevel programming. This method integrates the fast search capability of PSO with the global search ability of VNS. Firstly, the bilevel programming is transformed into a single level programming problem by use of the Kuhn-Tucker conditions. Then, the preferable swarm is obtained by PSO algorithm. Furthermore, the swarm get into local optima, which is estimated by convergence criterions, is optimized by VNS algorithm. Finally, the result of benchmark problems demonstrates the proposed algorithm is effective than the compared algorithms. ©, 2015, Systems Engineering Society of China. All right reserved.