Abstract: In terms of the Karush-Kuhn-Tucker conditions of convex programming, a special nonlinear bilevel programming problem, whose follower-level problem is a convex programming, is transformed into an equivalent single-level programming problem. To solve the transformed problem effectively by using the genetic algorithm, firstly, a new constraint-handling scheme is proposed by adding slack terms to linear inequality constraints and by solving boundary points on nonlinear constraints; secondly, a linear model is constructed to decrease the dimensions of the search space; finally, a new crossover operator is designed, based on the best individuals generated by the algorithm, and it is helpful to improve the fitness values of crossover offspring.

Key words: nonlinear bilevel programming, convex programming, constraint handling, global optimization, genetic algorithm