Analyzing and controlling diversity in quantum-behaved particle swarm optimization

This paper addresses the issues of controlling and analyzing the population diversity in quantum-behaved particle swarm optimization (QPSO), which is an optimization approach motivated by concepts in quantum mechanics and PSO. In order to gain an in-depth understanding of the role the diversity plays in the evolving process, we first define the genotype diversity by the distance to the average point of the particles' positions and the phenotype diversity by the fitness values for the QPSO. Then, the correlations between the two types of diversities and the search performance are tested and analyzed on several benchmark functions, and the distance-to-average-point diversity is showed to have stronger association with the search performance during the evolving processes. Finally, in the light of the performed diversity analyses, two strategies for controlling the distance-to-average-point diversities are proposed for the purpose of improving the search ability of the QPSO algorithm. Empirical studies on the QPSO with the introduced diversity control methods are performed on a set of benchmark functions from the CEC 2005 benchmark suite. The performance of the proposed methods are evaluated and compared with the original QPSO and other PSO variants.