A Genetic Algorithm for Multiobjective Bilevel Convex Optimization Problems

Multiobjective bilevel programming problem (MBPP) has a wide field of applications and has been proven to be an NP-hard problem. In this paper, a special multiobjective bilevel convex programming problem (MBCPP) is studied, and it is first transformed into an equivalent single objective bilevel convex programming problem by weighted sum of objectives. Then, for the equivalent problem, we design a scheme for generating weight vectors. Thereafter, a crossover operator and mutation operator are designed. Based on all these, a genetic algorithm called Ga-BCPP is proposed for MBCPP. At last, the simulation is made and the performance of the proposed algorithm is compared with one peer genetic algorithm. The results show that the proposed algorithm is effective.