DMDE: Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition large-scale global optimization

Abstract

DE algorithms have outstanding performance in solving complex problems. However, they also have highlighted the need for an effective approach to alleviating the risk of premature convergence and loss of population diversity, particularly for non-decomposition large-scale global optimization (N-LSGO) problems. In this study, first, the multi-trial vector (MTV) approach is improved by adding a population diversity component, then, a diversity-maintained multi-trial differential evolution (DMDE) algorithm is proposed using the improved approach for N-LSGO problems. The DMDE algorithm produces solutions during six phases: initializing, subpopulation constructing, movement, evaluating and updating, archiving, and diversity maintaining. In initializing, the population is located in the search space and partitioned into three subpopulations using a success-rate based policy. Then, the subpopulations are independently evolved using the proposed meaningful search strategies to decrease the risk of stagnation. The DMDE algorithm introduces an archiving mechanism to maintain population diversity, which prevents premature convergence. Finally, the individuals' behavior is analyzed using the diversity maintaining phase, and those dimensions that have lost their diversity will be enriched. The effectiveness and scalability of the DMDE algorithm are evaluated using benchmark functions CEC 2018 with dimensions 30, 50, and 100 and CEC 2013 with dimension 1000 as LSGO problems. Moreover, the performance of the proposed algorithm was statistically analyzed using Wilcoxon signed-rank sum, ANOVA, and the Friedman tests. In addition, the applicability of the DMDE was assessed by solving seven well-known real-world problems including large-scale problems selected mostly from test-suite CEC 2020. In all experiments and tests, several well-known and N-LSGO algorithms have competed with DMDE through which the comparison results prove that the proposed DMDE algorithm is superior to competitor algorithms.