Hybrid Biogeography-based Optimization Algorithm for Solving Nonlinear Bilevel Programming

Abstract

The article deals with a class of nonlinear bilevel programming problems in which the follower’s objective is a quasi-concave function, and a new hybrid biogeography-based optimization algorithm is proposed to search for the value of the leader’s variables. First, an extreme point searching approach is constructed to obtain the optimal solution of the follower’s programming. An efficient mutation operator is then designed by using Zoutendijk feasible direction method so that it can generate high quality potential offspring. Furthermore, a new fitness function is established that can be easily used to force the individuals moving toward the feasible region and improve the feasible solutions gradually. Under some assumptions, theoretical analysis of the algorithm has been presented. Finally, to verify the effectiveness of the algorithm, numerical experiments on 8 test problems are made and performance analysis verify the proposed algorithm can converge to the global optimal solution of bilevel programming problems.