A Preliminary Investigation on a Graph Model of Differential Evolution Algorithm

Abstract

Graph based analysis of Evolutionary Algorithms (EAs), though having received little attention, is a propitious method of analysis for the understanding of EA behavior. However, apart from mere proposals in literature, the graph model(s) of EAs have not been aptly demonstrated of their full potential. This paper presents a critical analysis of an existing prominent graph model of EAs. The comprehensive analysis involved modelling as graphs, the interactions within Differential Evolution (DE) algorithms (DE/rand/1/bin and DE/best/1/bin by way of example), while solving CEC2005 benchmark functions. Subsequently, the graph-theoretic measures- degree centrality, clustering coefficient, betweenness centrality and closeness centrality- were deployed to investigate the potential of graph model in providing insights about EA dynamics. However, the model falls short in providing useful insights about the DE runs. The observed insights were qualitative in nature and not competitive compared to empirical analysis. This indicates the need for considerable research attention in designing robust graph models.