Evolutionary population management for the design of metaheuristic search algorithms: Three improved algorithms, real-time charge scheduling problems, optimal solutions and stability analysis

This paper first introduces evolutionary population management (EPM), which is based on three novel hypotheses on the design of (i) epoch, (ii) update and (iii) mating processes to improve the performance of nature-inspired search algorithms. Secondly, three different algorithms designed based on EPM are introduced. Thirdly, the benchmark suite for real-time charge scheduling problems (CSBP-2) is introduced. Fourth, optimal solutions and stability analysis results for CSBP-2 are presented. According to the results of the statistical analysis of 252 different cases on global optimisation problems and constrained engineering problems, the average Friedman scores of the three EPM-based algorithms and their base versions are (1.205/1.795), (1.276/1.724) and (1.257/1.743), respectively. According to the Wilcoxon pairwise test, the three EPM-based algorithms found better solutions than their base versions in 166 of these 252 comparisons and converged similarly to the optimum in 86 problems. In the study conducted on the CSBP-2 suite for 36 different cases, the average Friedman scores of the three EPM-based algorithms and their base versions are (1.17/1.83), (1.05/1.95) and (1.10/1.90), respectively. According to the Wilcoxon pairwise test results, in 32 of these 36 comparisons, the three EPM-based algorithms managed to find better solutions compared to their base versions, and in 4 cases they converged similarly to the optimum results.