Improving Metaheuristic Algorithm Design Through Inequality and Diversity Analysis: A Novel Multi-Population Differential Evolution

In evolutionary algorithms and metaheuristics, defining when applying a specific operator is important. Besides, in complex optimization problems, multiple populations can be used to explore the search space simultaneously. However, one of the main problems is extracting information from the populations and using it to evolve the solutions. This article presents the inequality-based multi-population differential evo-lution (IMDE). This algorithm uses the K-means to generate subpopulations (settlements). Two variables are extracted from the settlements, the diversity and the Gini index, which measure the solutions' distribution and the solutions' inequality regarding fitness. The Gini index and the diversity are used in the IMDE to dynamically modify the scalation factor and the crossover rate. Experiments over a set of benchmark functions with different degrees of complexity validate the performance of the IMDE. Besides comparisons, statistical and ranking average validate the search capabilities of the IMDE.