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.

翻译：本文探讨了量子行为粒子群优化（QPSO）中群体多样性的控制与分析问题，该优化方法源于量子力学概念与粒子群优化（PSO）的结合。为深入理解多样性在进化过程中的作用，我们首先利用粒子位置到平均点的距离定义了基因型多样性，并通过适应度值定义了QPSO的表型多样性。随后，在多个基准函数上测试并分析了这两种多样性与搜索性能之间的相关性，结果表明，在进化过程中，到平均点距离多样性（distance-to-average-point diversity）与搜索性能的关联更为紧密。最后，基于多样性分析结果，提出了两种用于控制到平均点距离多样性的策略，旨在提升QPSO算法的搜索能力。针对引入多样性控制方法的QPSO，我们使用CEC 2005基准测试集进行实证研究，并将所提方法的性能与原始QPSO及其他PSO变体进行了评估与对比。