Affiliation:
1. Shaanxi Normal University, China
2. Southern University of Science and Technology, China
3. Shenzhen University, China
Abstract
The values and velocities of a Particle swarm optimization (PSO) algorithm can be recorded as a 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 dimensions together. In this chapter, the PSO algorithm is first represented in the matrix format. Then, based on the analysis of the relationship between pairs of vectors in the 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 10 benchmark functions (including unimodal/multimodal function, separable/non-separable function), the properties of normalized population diversities are analyzed and discussed.