Uniform Design Based Hybrid Genetic Algorithm for Multiobjective Bilevel Convex Programming

Multiobjective bilevel linear programming is a decentralized decision problem, it consists of many objectives at the upper level and the lower level, respectively. It has a wide field of applications and has been proven to be NP-hard. In this paper, a kind of multiobjective bilevel convex programming(MBCP) is studied, in which the lower level is first transformed into an equivalent single objective bilevel convex programming problem by weighted aggregation method. Then, for the equivalent problem, we use uniform design scheme to generate some representative weight vectors. Thereafter, a crossover operator and mutation operator are designed. Based on all these, a uniform design based hybrid genetic algorithm is proposed for MBCP. Finally, the performance of the proposed algorithm is illustrated by two numerical experiments. The results (including the compared results) show that the proposed algorithm is effective.