Genetic algorithm based on primal and dual theory for solving multiobjective bilevel linear programming

The multiobjective bilevel linear programming (MBLP) is a hierarchical optimization problem involving two levels, and at least one level has multiple objectives. This paper mainly studies a special kind of MBLP with one objective at the lower level. With primal and dual theory, the lower level problem is transformed into a part of constraints of the upper level problem, then by handling the feasible set of the transformed problem, several equivalent problems of MBLP are obtained. Furthermore, by designing three feasible genetic operators, a new genetic algorithm for solving MBLP is presented. The simulations on several designed multiobjective bilevel linear programming problems are made, and the performance of the proposed algorithm is verified by comparing with the existing algorithms. The results show that the proposed algorithm is effective for MBLP.