A Genetic Algorithm for Solving a Class of Multi-objective Bilevel Programming Problems

At present, most of the researches on bilevel programming problems are focused on single objective cases. This paper discusses a bilevel programming problem with upper level multi-objective optimization. In order to solve the problem efficiently, we present a genetic algorithm using interpolation. This method does not require solving lower optimization problem frequently. In the proposed algorithm, firstly, the interpolation functions are adopted to approximate lower level solution functions. As a result, the original problem can be approximated by a single-level multi-objective programming. In addition, the corresponding interpolation functions are updated such that these functions can approximate the lower level solution function very well. Finally, the multi-objective programming is solved for obtaining an optimal solution set of the original problem. The simulation on two examples indicates the proposed algorithm is effective and feasible.