An Efficient Evolutionary Algorithm for a Kind of Nondifferentiable Nonlinear Bilevel Programming

Abstract

A special kind of nonlinear bilevel programming problems (nonlinear BLPP in short) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first design a fitness function based on entropy function. By using this fitness function, we not only can decrease the leader's objective value, but also can force the infeasible solutions moving towards the feasible region, and improve the feasible solutions gradually. Then an effective crossover operator is used to generate high quality offspring. Based on these, a new evolutionary algorithm for nonlinear BLPP is proposed. Finally, simulations on several benchmark problems are made and the results demonstrate the effectiveness of the proposed algorithm.