A genetic algorithm for solving a special class of nonlinear bilevel programming problems

Abstract

A special nonlinear bilevel programming problem (BLPP), whose follower-level problem is a convex programming with a linear objective function in y, is transformed into an equivalent single-level programming by using Karush-Kuhn-Tucker (K-K-T) conditions. To solve the equivalent problem effectively, a new genetic algorithm is proposed. First, a linear programming (LP) is constructed to decrease the dimensions of the transformed problem. Then based on a constraint-handling scheme, a second-phase evolving process is designed for some offspring of crossover and mutation, in which the linear property of follower's function is used to generate high quality potential offspring. © Springer-Verlag Berlin Heidelberg 2007.