Researches On Bilevel Multiobjective Programming Problem:the Particle Swarm Optimization Algorithm And Applications

The bilevel multiobjective programming (BLMP), where the upper level or lower level or both have multiobjectives, belongs to bilevel optimization essentially. Due to its ability of properly describing the hierarchical relationship existed in the system and fully reflecting the will of the policy makers, bilevel multiobjective programming has showed wide application prospects. On the other hand, the models of BLMP stem from practical problems in social productions. In order to solve the practical problems and to have an easy modeling condition for the scientists to narrow the gap between mathematical model and real problems, it is essential to design the effective algorithm of the general BLMP problems.However, in comparison with the application of BLMP, the research into BLMP algorithms are relatively lagged. As a matter of fact, until recently only some of the BLMP algorithms are practically realized, but the generalized and effective method of BLMP algorithms has not been achieved. In view of that, this paper takes the complicated bi-level single objective programming problem (BLP), a type of BLMP problem with two objectives at both levels and the upper decision variables being one-dimensional variables, the general BLMP and the high-dimensional BLMP problem as the research objects and applies the PSO algorithm to design the effective algorithm for them respectively. At last, it applies BLMP to the optimal allocation of water resources. The main contents of each chapter are as follows:Chapter ? is the introduction chapter on BLMP, the background of BLMP model and the significance of developing its algorithms. Also included in this chapter is a literature review of related topics as well as the main research contents of the whole article.In Chapter ?, we first introduce the definition, concepts and properties of the BLP, multiobjective programming and BLMP respectively. Secondly, we introduce the basic principle of PSO algorithm, the algorithm process and the parameter setting. Then, the convergence analysis of the PSO algorithm is presented. At last, we carry on the feasibility analysis to the PSO algorithm for the BLMP problem and set up the basic framwok to apply PSO algorithm to solve BLMP problems.In Chapter ?, we design the co-adapted co-evolutionary particle swarm optimization algorithm (CCPSO) for a type of complicated bi-level single objective programming problem. For the first step, based on the population stagnation detection technology, the CCPSO algorithm with global convergence is designed aiming to solve complicated single objective optimal problems. For the second step, the CCPSO algorithm is propsosed for the bi-level single objective programming problem based on the above algorithm and the global convergence of the algorithm is analyzed. Lastly, through simulation experiments, the new algorithm is compared with the classic ones in the previous literature review and the result turns out that the new one has better global searching ability and faster convergence speed.In Chapter ?, we design the non-dominated particle swarm optimization algorithm (NSPSO) for a type of BLMP problems with two objectives at both levels and the upper decision variables being one-dimensional variables. For the first step, based on non-domination sorting technology and grid technology, the NSPSO algorithm for the multi-objective programming problem (MOP) is designed. For the second step, the NSPSO algorithm is presented for this type of BLMP and the global convergence of the algorithm is analyzed. Lastly, through simulation experiments, the new algorithm is compared with the classic ones in the previous literature review and the result turns out that the obtained approximate Pareto solutions by the proposed method in this chapter is advantageous in spacing distribution and the degree of convergence. Additionally, the proposed algorithm also gives a result of the problem with unknown Pareto optimal front, which offering a comparison option for the follow-up researchers.In Chapter ?, we design the hybrid particle swarm optimization algorithm with crossover operator (C-PSO) for the general BLMP. For the first step, to solve the problems of local convergence and inadequacy of convergence in the final stage during computing, the C-PSO algorithm with good global convergence ability is proposed. For the second step, based on the C-PSO algorithm, crowding distance computation and non-domination sorting technology, the algorithm concerning MOP problem is designed. For the third step, an algorithm concerning general BLMP problems is designed and the global convergence of the algorithm is analyzed. Lastly, through simulation experiments, the proposed algorithm is compared with the classic ones in the previous literature review and the result turns out that the Pareto optimal front in spacing distribution from the proposed algorithm is in accordance with that from the previous literature review, but the algorithm is advantageous in the degree of convergence, proving it to be effective to solve general BLMP problems.In Chapter ?, the quantum particle swarm optimization algorithm (QPSO) concerning high-dimensional BLMP problem is introduced. For the first step, based on the rapid speed and good global convergence ability, the QPSO algorithm concerning high-dimensional multi-objective programming problems is designed. For the second step, based on the above algorithm and the self-adapting technology of the lower sub-swarm scale, the QPSO algorithm concerning high-dimensional BLMP problems is designed and the global convergence of the algorithm is analyzed. Lastly, through data simulation experiments, the result turns out that the new algorithm can have a better Pareto optimal front, proving it to be the most effective algorithm to solve high dimensional BLMP problems. Apart from that, the research provides a good example and platform of algorithm comparison for the following-up related problem researchers.In chapter VII, the BLMP is introduced into optimal allocation of water resources. In this BLMP model, the environmental predictors are added to the target function of water resources authorities, setting maximum benefit and minimum water pollution as upper objective; while the maximum benefit of different water users as the lower objective. Meanwhile, the particle swarm optimization of this model is designed, in order to provide the water authorities with an effective decisive proof.At the end of the article, a summary is given and some to-be-further-discussed issues are raised.