Algorithms And Applications For Some Classes Of Bilevel Multiobjective Programming Problems

Bilevel programming problems are nonconvex optimization programming problems with nested structure, and proven to be NP-hard. They consist of two optimization problems, and one is existed as the constrained conditions for the other. Bilevel programming problems have been widely used in production plan,engineering design, etc. Currently, the vast majority of the existing works is concentrated on bilevel programming problems with single objective at each level, few works are undertaken for bilevel multiobjective programming problems(BMPPs). In this dissertation, several special BMPPs are studied, and the corresponding problem-dependent evolutionary algorithms are proposed, efficiency of the algorithm are demonstrated. The main contributions of this thesis are as follows:1. For BMPPs with one objective at the upper level and multiple objectives at the lower level, the lower level problem handling method is given by using induced theoretical re-sults. Based on the properties of constrained region, an extreme point based evolutionary algorithm is proposed. The efficiency of the proposed algorithm is demonstrated by nu-merical experiments.2. For BMPPs with multiple objectives at the upper level and one objective at the lower level, the lower level problem is transformed into a series of equality or inequality con-straints by primal-dual conditions. Hence the original problem is transformed into a single level problem so that the problem can be solved much easier. Then, the corresponding constraint-handling methods are proposed, and the weighted aggregation method is used to handle the upper level problem. Based on these, a primal-dual theory based evolu-tionary algorithm is proposed, and the efficiency of the proposed algorithm is proven by numerical experiments.3. For BMPPs with multiple objectives, the lower level problems is converted to a min-max problem. A multi-parent evolutionary algorithm is proposed. Benchmark problems are designed and applied to verify the efficiency of the proposed algorithm.4. For two special classes of problems with linear or convex constraints, each level is han-dled by weighted aggregation method. For the second problem, each level is also handled by weighted aggregation method, the weights are chosen by uniform design. Then, the problem-dependent evolutionary algorithm are designed for these problems, respectively. The efficiency of the proposed algorithm is proven by numerical experiments.5. A bilevel multiobjective programming model for production-transportation model is set up. By virtue of orthogonal experimental design, an orthogonal experimental design based evolutionary algorithm is proposed in order to obtain the optimal strategy for pro-ducer and transporter. The experiments on a series of benchmark problems are conducted and the results indicate the efficiency of the proposed model and algorithm.