A distance measure comparison to improve crowding in multi-modal optimization problems

Solving multi-modal optimization problems are of interest to researchers solving real world problems in areas such as control systems and power engineering tasks. Extensions of simple Genetic Algorithms, particularly types of crowding, have been developed to help solve these types of problems. This paper examines the performance of two distance measures, Mahalanobis and Euclidean, exercised in the processing of two different crowding type implementations against five minimization functions. Within the context of the experiments, empirical evidence shows that the statistical based Mahalanobis distance measure when used in Deterministic Crowding produces equivalent results to a Euclidean measure. In the case of Restricted Tournament selection, use of Mahalanobis found on average 40% more of the global optima, maintained a 35% higher peak count and produced an average final best fitness value that is 3 times better.