Global Optimization Method Based on the Statistical Genetic Algorithm for Solving Nonlinear Bilevel Programming Problems

This paper presents a global optimization method based on the statistical genetic algorithm for solving nonlinear bilevel programming problems. The bilevel programming problem is firstly transformed into a single level problem by applying Karush-Kuhn-Tucker conditions, and then an efficient method based on the statistical genetic algorithm has been proposed for solving the single level problem with the complementarity constraints. By certain handling tech- nology, the simplified problem without the complementarity constraints can be gotten. If it is solvable then its optimal solution is a feasible solution of the original bilevel pro- gramming problem. At last, a global optimal solution of the original problem can be found among its feasible solutions. Numerical experiments on some benchmark problems show that the new algorithm can find global optimal solutions of the bilevel programming problems in a small number of fit- ness evaluations.