A new population diversity model in swarm intelligence

作者：Feng Jiqiang^*; Xie Weixin; Xu Chen; Huang Jianjun

来源：Journal of Information and Computational Science, 2009, 6(4): 1891-1898.

• Mathematical frameworks
• Numerical example
• Population densities
• Population diversity
• Probability theory
• Single peak
• Swarm Intelligence

Many researchers of swarm intelligence (SI) algorithms take their ideas from physical and biological systems. This approach, however, is mostly qualitative and many ideas remain vague and ill-defined. In this paper, a mathematical framework based on probability theory is presented that enables us to analyze one important aspect of SI algorithms: the population diversity. Firstly the population density is defined for the population in the SI algorithms. The population diversity is then discussed from the point of view of the normal distribution in statistics. We show that there is a close connection between the distribution and population diversity and that the essential structure of population diversity is quite similar to that of the distribution. A detailed construction of the population diversity model is then given that is based on probability distributions and the convergence of the model is theoretically discussed for single peak value case. The paper concludes with a generic numerical example that validates the population diversity model.

• 出版日期2009