Study On Multi-Objective Optimization Problem Based On Particle Swarm Optimization Algorithm

It is an indispensable capability for the modern decision and assistance system to provide decision-makers with scientific, proper and timely dicision schemes. Since most of the actual decision-targets are multi-objective, the research on Multi-objective Optimization Problem (MOP ) has gained more and more attention. For the fact that the sub-objectives in MOP are contradictory to each other and they have no unified measure standards, it has become a principal concern to definite the optimal solution of MOP when soluting MOP. The definition of non-dominanced solution, based on the idea of choosing Pareto, is becoming increasingly people's general consensus. The optimal Pareto solution of MOP, however, is not an exclusive solution. Sometimes there are even numerous ones. In this case, the obtained solutions do not facilitate but trouble the dicision-makers. Furthermore, it takes a long time to obtain the optimal solutions. So it is rather important to provide proper and feasible solution schemes rapidly for the decision makers.Particle Swarm Optimization (PSO) is a kind of swarm intelligent algorithm which has been developed in recent years. It is a new intelligent search algorithm. The algorithm utilizes the effective information, which is shared by every particle in the population from its past experiences and other particles'experiences, to search the optimal solutions synergically. At present, the algorithm research based on PSO has been attached more and more importance in the field of multi-objective optimization and it is even a hot topic in the research.The relevant Pareto-εconcepts are proposed in the paper grounded on the definition of Pareto optimal solutions. By means of analysis and experiments, it can be proved that the process of optimization in solutiing MOP is improved for the usage of Pareto-εconcepts, that the searching probability is added and that the moving steps are increased. Apart from these, the comparison strategies, no matter whether they are of tolerance or of rigorousness, can evidently accelerate the speed of convergence, providing proper decision schemes rapidly for the decision-makers. Given tolerance, the bigger theεvalue is, the weaker the comparison conditions and the higher the searching probability are, and as a result, the quicker the searching speed is. Given rigorourness, although the comparison conditions are intensified, the speed of searching optimality is made quicker for the bigger moving steps.In the present paper, what is researched and what is newly found are as follows: 1. The past and present studies on MOP are discussed. The significance of the research on MOP based on PSO algorithm is analysed.This paper penetrates into the relevant theories about MOP and PSO algorithm, including the general definitions and mathematic models of MOP, the ways of obtaining solutions of MOP, the basic theories and the improved strategies of PSO algorithm as well as the key points of research on MOP grounded on PSO algorithm.2. The testing function set of MOP is researched in detail. This paper gives the definitions, binding conditions and properties of solutions of these classical functions. Also, the writer expounds the general principles on how to choose the testing function set in this paper.3. On the basis of Pareto Dominance Theory, the conception of Pareto-εdominance relation is proposed and theεvalue is modulated dynamically. The experiment proves that the conception of Pareto-εdominance relation is both valid and effective, that it accelerates the speed of searching optimality evidently and that it can provide proper and satisfying decision schemes for decision-makers rapidly. Via experiment and theoretical analysis we give the assessement of dynamic modulating strategies of Pareto-ε.4. On the basis of PSO algorithm and Pareto-εdominance relation, a new framework of PεPSO algorithm is proposed. And on the basis of Object Oriented Theory a corresponding data contruction is also proposed. This done, the generalization, reusability and compatibility, realized by the algorithm, can be advanced. In the experiment, part of ZDT series functions in classical testing function set are chosen and tested. The experiment indicates the effectiveness of PεPSO algorithm.5. After employing the strategy of dynamic modulatingε, the algolrithm approaches rapidly to the true Pareto front at the outset by means of modulating the value ofεdynamically. Theεvalue regresses to 0 gradually in the operation of algorithm. And the final solution can approach to the true Pareto front more effectively and it can not be influenced byε. In this way, not only is the search and convergence speed of algorithm accelerated, but also the influence exerted to the quality of final solution byεvalue can be eliminated.