  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.
