Research On Hybrid Particle Swarm Algorithms With Cauchy Mutation

The researches on optimization problems are to find the optimal plan in many methods, namely to meet certain constraint conditions and search a group of parameters, making system performance of maximum or minimum. It exists in a wide range of industrial, agricultural, defense, transportation, communications and other fields. Optimization technology is the way to solve optimization problems, and as an important scientific branch has attracted a wide range of people's concern, and has been applied in many fields, such as artificial intelligence, pattern recognition, control system, engineering design and so on. Applications of certain optimization techniques to solve optimization problems have a very important meaning. Domestic and international studies showed that under the same conditions, optimized processing technologies improved the efficiency of the system, reduced the energy consumption, made reasoned use of resources and enhanced economic efficiency, moreover, with the increasing size of processed objects, this effect is even more significant.As a new optimization methods of swam intelligence, PSO has some characteristics of simple principles, few parameters and fast convergence, which has been proved to be an effective global optimization methods, and showed great potential in practical applications. However, as a relatively new and rapid development of intelligent algorithms, the basis theory in its systematized and standardized is not yet complete enough. How apply PSO for more areas, while in the application of the existing problems are also worthy of concern.This article focuses the problems of PSO easily falling into local optima, and proposes PSO with Cauchy mutation. Traditional mutation methods are based on Gaussian distribution with weigh parameters of fixed steps of mutation. Through analyzing the changing patterns of average swarm velocity, this article presents an adaptive Cauchy mutation operator. On the basis of the adaptive Cauchy mutation operator, we introduce re-diversification mechanism and opposition-based learning method, and develop two new and high effective hybrid PSO algorithms. To illustrate the efficiency and superiority of the proposed methods, we conduct some comparative experiments on many carefully selected benchmark problems, and do some researches on the efficiency of the operator and learning methods. The main contributions given in this dissertation are as follows:1. Firstly, we introduce the basic PSO and the standard PSO, and analyze the convergence of the standard PSO. Furthermore, we illustrate the research status of PSO, and analyze the difficulty of PSO.2. By the inspiration of the idea of "Fast Evolutionary Programming", we introduce a Cauchy mutation operator to help the particles escape from local optima. To the problem of the hard control on the steps of mutation, we combine with the changing pattern of average swam velocity, and propose an adaptive Cauchy mutation operator. At last, experimental studies on some continuous unimodal and multimodal function optimization problems show that the adaptive Cauchy mutation operator play an important role in the performance improvement of PSO.Conducting mutations on the global best particle enhances the global search ability of PSO.The average swarm velocity could dynamically adjust the size of mutations on the global best particle.3. On the basis of the adaptive Cauchy mutation operator, we introduce a new re-diversification mechanism to maintain the swarm diversity. When the swarm diversity is poor, re-initializing some worst particles could extend the search space of swarm, and finally improve the swarm diversity and avoid premature convergence. Experimental results show that re-initializing the worst particles could improve the swarm diversity and find better solutions.4. On the basis of the adaptive Cauchy mutation operator, we introduce an opposition-based learning method to speed up the convergence of PSO. The new method does not only evaluate the fitness of current particle, and also estimate the fitness of its opposite particle. The two-way estimation could help particles move to the optima solutions more closely, and then accelerate the convergence. Conducting mutation on the global best particle could improve the search ability of PSO, and help particles jump out local optima. Experimental results show that the proposed method could help particles avoid trapping into local optima and speed up the convergence of PSO.In a word, this article does a comprehensive and in-depth research on the theory and improvement of PSO, and gives conclusions and further research directions at last.