An analysis of the effects of clustering in graph-based evolutionary algorithms

Recently, there has been increased interest in combining work from the complex networks domain with evolutionary computation to solve challenging search and optimization problems. Typically, individuals in the evolving population occupy a node in a graph (or network) and are only allowed to mate with individuals within their local neighbourhood. The use of specific graph topologies have been shown to alter the population dynamics, which in turn impacts on the ability of the algorithm to find (near)-optimal solutions for a given problem. In this paper, we continue this line of research. Here, we have analyzed the impact of clustering on the performance of graph-based evolutionary models. We have constructed a range of alternative graphs to act as scaffolding for the evolving population by systematically rewiring some of the edges/links in a regular lattice. Significantly, we have kept the mean node degree constant in all graphs. Two different problems defined on a binary string with regulated levels of epistasis - the NK landscape problem and the hierarchical if and only if (H-IFF) problem - were used to examine the efficacy of our model. Simulation results show that the clustering coefficient of the underlying graph has a significant impact on the ability of a graph-based evolutionary algorithm to solve a given problem.