A Genetic Algorithm with Dynamic Niche Clustering for Multimodal Function Optimisation

Abstract

Genetic algorithm’s (GA’s) have become a powerful search tool pertaining to the identification of global optima within multimodal domains. Many different methodologies and techniques have been developed to aid in this search, and facilitate the efficient location of these optima. What has become known as Goldberg’s standard fitness sharing methodology is inefficient and does not explicitly identify or provide any information about the peaks (niches) of a fitness function. In this paper, a mechanism is formulated that will identify the peaks of a multimodal fitness function in a one-dimensional parameter space, using a hybrid form of clustering in the framework of a genetic algorithm. It is shown that the proposed Dynamic Niche Clustering scheme not only performs as well as standard nicheing, but works in O(nq) time, rather than O(n ²) time. In addition to this, it explicitly provides statistical information about the peaks themselves. The Dynamic Niche Clustering scheme is also shown to have favourable qualities in revealing multimodal function optima when there is little or no knowledge of the fitness function itself a priori.