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

In this paper, a special nonlinear bilevel programming problem (BLPP), in which the follower's problem is a convex quadratic programming in y, is transformed into an equivalent single-level programming problem by using Karush-Kuhn-Tucker(K-K-T) condition. To solve the equivalent problem effectively, firstly, a genetic algorithm is incorporated with Lemke algorithm. For x fixed, the optimal solution y of the follower's problem can be obtained by Lemke algorithm, then (x, y) is a feasible or approximately feasible solution of the transformed problem and considered as a point in the population; secondly, based on the best individuals in the population, a special crossover operator is designed to generate high quality individuals; finally, a new hybrid genetic algorithm is proposed for solving this class of bilevel programming problems. The simulation on 20 benchmark problems demonstrates the effectiveness of the proposed algorithm.