Research On Algorithms For Solving Bilevel Multi-Objective Programming Problem

With the development of science and technology, optimization problem is becoming more and more complex, the interaction decision-making between the superior and the subordinate is becoming more and more common. The bilevel programming problem already has a very extensive research, in recent years, the bilevel multi-objective programming problem also gradually causes the attention of people. Bilevel multi-objective programming problem is a NP-hard problem, it is difficult to use traditional methods to solve this problem. The emergence of intelligent algorithm provides a new way to solve this np-hard optimization problem, the intelligent algorithm can be used in solving bilevel multi-objective programming problem. Bacteria foraging optimization algorithm(BFO) is a new kind of intelligent algorithm, which imitations of e. coli bacteria‘s foraging. At present, it‘s still in the primary stage of research, and it is seldom used for solving bilevel programming problem.In view of the two different types of bilevel multi-objective programming problem, this paper proposes two hybrid BFO algorithm. One way is to constraint conditions of special low dimensional bilevel multi-objective programming problem is converted to a single problem solving; Another way is to use intelligent algorithm, namely improved NSGA-II algorithm, to interact through on the lower level programming problem solving high dimension bilevel multi-objective programming problem.In this paper, main work is as follows:Proposes two kinds of hybrid BFO algorithms based on BFO algorithm. In view of the shortcomings of standard BFO algorithm‘s fixed step, respectively, we combine PSO algorithm and DE algorithm with BFO algorithm, and then we improve the three main operators of BFO algorithm, finally we get two hybrid BFO algorithm which have good performance.For low dimensional bilevel multi-objective programming problem whose constraint is convex or linear, we can convert it to single layer problem, and we design a evolutionary algorithm to solve it. First of all, coefficient method is used to convert bi-level multi-objective programming problem to the bi-level single objective programming problem. Then, we use the KKT optimality conditions to convert the problem to a single level single objective programming problem, and we use the hybrid BFO which combined with PSO algorithm to solve the problem.For the more general high-dimensional bilevel multi-objective programming problem, we use evolutionary algorithm to solve it interactively. This paper improved the NSGA-II algorithm, using the proposed hybrid BFO which combined with DE algorithm to replace the original classic genetic operations, which improves the performance of NSGA-II algorithm. Coefficient method is used to convert the up level multi-objective programming problem to single objective programming problem, then we use the hybrid BFO which combined with PSO algorithm to solve the problem. We use the improved NSGA-II algorithm to solve the multi-objective problem in up and lower levels, and we use the niche technique in the lower level to increase the number of the solution of the lower problem. Solve the bi-level programming problems interactively, until we find the Pareto solutions of the problem.