Measuring Diversity in the Cooperative Particle Swarm Optimizer

Abstract

Diversity is an important aspect of population-based search algorithms such as particle swarm optimizers (PSO) since it influences their performance. Diversity is closely linked to the exploration-exploitation tradeoff. High diversity facilitates exploration, which is usually required during the initial iterations of the optimization algorithm. A low diversity is indicative of exploitation of a small area of the search space, desired during the latter part of the optimization process. The success of the Cooperative Particle Swarm Optimizer (CPSO), a variant of PSO which has outperformed the basic PSO on numerous multi-modal functions, has been ascribed to its increased diversity. Although numerous population diversity measures have been proposed for the basic PSO, not all can be readily applied to the CPSO. This paper proposes a measurement of diversity for the CPSO which is compared with three other diversity measures to establish the most appropriate diversity measure for CPSO. The proposed diversity measure is applied to the CPSO on a few well known test functions and compared with the diversity of the basic global best PSO with the objective to justify the claim that the CPSO increases diversity. The paper also investigates whether diversity increases with an increase in the number of subswarms of the CPSO.