A Study of Normalized Population Diversity in Particle Swarm Optimization

Shi Cheng, Yuhui Shi and Quande Qin
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Shi Cheng: Department of Electrical Engineering and Electronic, University of Liverpool, Liverpool, UK
Yuhui Shi: Department of Electrical and Electronic Engineering, Xi’an Jiaotong-Liverpool University, Suzhou, China
Quande Qin: College of Management, Shenzhen University, Shenzhen, China

International Journal of Swarm Intelligence Research (IJSIR), 2013, vol. 4, issue 1, 1-34

Abstract: The values and velocities of a Particle swarm optimization (PSO) algorithm can be recorded as series of matrix and its population diversity can be considered as an observation of the distribution of matrix elements. Each dimension is measured separately in the dimension-wise diversity, on the contrary, the element-wise diversity measures all dimension together. In this paper, PSO algorithm is first represented in the matrix format, then based on the analysis of the relationship between pairs of vectors in PSO solution matrix, different normalization strategies are utilized for dimension-wise and element-wise population diversity, respectively. Experiments on benchmark functions are conducted. Based on the simulation results of ten benchmark functions (include unimodal/multimodal function, separable/non-separable function), the properties of normalized population diversities are analyzed and discussed.

Date: 2013
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