A Hybrid Approach Based on Genetic Algorithm for Mixed-Integer Bilevel Programming Problems

Bilevel programming problem is characterized as hierarchical structure, involving two optimization problems at deferent levels. When some variables are restricted into integer set, the problem is very challenging for most canonical optimization approaches. In the present paper, a class of nonlinear mixed-integer bilevel programs is taken into account in which the follower is an integer linear program, and a hybrid approach based on genetic algorithm is developed for solving the problems of this kind. Firstly, a genetic algorithm is used to explore the space of leader’s variable values. Secondly, in order to obtain the optimal solution to the follower’s problem, all potential bases of the follower's relaxed problem are determined and then the solution functions of the problem are presented by using these bases for distinct leader’s variable values. Finally, if the solution to the follower’s problem provided by the solution functions is not satisfy integer requirements, the follower is further solved by using traditional optimization 1 Department of Mathematics, Qinghai Normal University, Xining 810008, China. E-mail: [email protected] Article Info: Received : October 29, 2013. Revised : November 29, 2013. Published online : December 1, 2013. 332 A hybrid approach for mixed-integer BLPP technique. Some computational examples are solved and the results show that the proposed algorithm is efficient and robust. Mathematics Subject Classification: 90C11, 90C26, 90C30