Differential evolution based on node strength

Abstract

In this paper, three novel algorithms for optimisation based on the differential evolution algorithm are devised. The main idea behind those algorithms stems from the observation that differential evolution dynamics can be modelled via complex networks. In our approach, the individuals of the population are modelled by the nodes and the relationships between them by the directed lines of the graph. Subsequent analysis of non-trivial topological features further influence the process of parent selection in the mutation step and replace the traditional approach which is not reflecting the complex relationships between individuals in the population during evolution. This approach represents a general framework which can be applied to various kinds of differential evolution algorithms. We have incorporated this framework with the three well-performing variants of differential evolution algorithms to demonstrate the effectiveness of our contribution with respect to the convergence rate. Two well-known benchmark sets (including 49 functions) are used to evaluate the performance of the proposed algorithms. Experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions.