Journal of Computations & Modelling

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

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• Abstract

  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 technique. Some computational examples are solved and the results show that the proposed algorithm is efficient and robust.