Differential Evolution Enhanced by the Closeness Centrality: Initial Study

The closeness centrality can be considered as the natural distance metric between pairs of nodes in connected graphs. This paper is the initial study of the influence of the closeness centrality of the graph built on the basis of the differential evolution dynamics to the differential evolution convergence rate. Our algorithm is based on the principle that the differential evolution creates graph for each generation, where nodes represent the individuals and edges the relationships between them. For each individual the closeness centrality is computed and on the basis of its value the individuals are selected in the mutation step of the algorithm. The higher value of the closeness centrality means the higher probability to become the parent in the mutation step. This enhancement has been incorporated in the classical differential evolution and a set of 21 well-known benchmark functions has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithm performs better or at least comparable to its original version.