Study On Adaptive Behavior Of Particle Swarm Optimization

In the real world, there are various adaptive behaviors. Both in nature and artificial systems, the adaptive behavior play a very important role. Therefore, the study of adaptive behavior is increasingly becoming a hot research topic. In terms of computer algorithm, there are many algorithms which simulate the process of biological evolution or social collaboration in recent years. So understanding the adaptive behavior mechanism helps to effectively guarantee the algorithm convergence and improve the convergence speed. In short, the existing collective behavior research mainly focuses on whether the algorithm convergence and convergence speed, but the emphasis of research on adaptive behavior should focus on the characterizing the dynamic behavior in the process of evolution.This article mainly studies the collective dynamic behavior of PSO, try to analyze and discuss the adaptive behavior in the process of evolution, measure the adaptive behavior, and discuss the way of using information in the adaptive process. Firstly, use the information entropy to describe the order degree in the process of evolution, combining with the radius to observe the change of whole order degree. Secondly, propose an adaptive behaviors analysis method which based on the information entropy and correlation. This method is mainly defines 4 indicators: relative entropy, correlation coefficient, on (70) and 2)(70). Relative entropy and correlation coefficient are used to divide collective dynamic behavior into different stages, and (70) and 2)(70) related indicators are used to judge whether the algorithm convergence.To illustrate the effectiveness of this method, we tested on 21 well-known benchmark problems in 2,5,10 and 30 dimensions separately, compared with 6 the most representative PSO. The experimental results demonstrate that through the change of information entropy can reflect the change of population orderly degree in the process of evolution, and the related indicators based on the information entropy and correlation can divide the collective dynamic behavior into three stages: Random search stage, Narrow search stage and Convergence stage. The method combining relative entropy and correlation coefficient can characterize evolutionary characteristics of evolutionary algorithm and analysis pros and cons of different types of evolutionary algorithms.Experiments verify that the proposed indices to measure adaptivity characterize effectively the population’s state transition and related behavioral characteristics in the process of evolution. By comparison of the adaptivity, we know that PSO algorithms have different convergence speed and search capabilities. This article provides a new theoretical guidance and interpreted analysis for algorithm selection and population behavior analysis.