Multi population-based chaotic differential evolution for multi-modal and multi-objective optimization problems

Abstract

Differential evolution (DE) is a simple but powerful evolutionary algorithm used in multiple sciences and engineering disciplines to tackle optimization problems. DE has some disadvantages, such as premature convergence and the low convergence rate that prompts the worst DE execution structure in the constrained environment. The occurrence of these constraints split up the exploration area into viable and un-viable intervals. To overcome the abovementioned issues, we chose to take advantage of the vital characteristics of two mutation strategies: DE/rand/1 and DE/best/2. This research proposes a novel DE variant called Multi-population-based chaotic DE (MPC-DE) to solve multi-model and multi-objective optimization problems. The proposed MPC-DE is divided into two sub-populations with chaotic-based enhanced population initialization approaches, Sinusoidal and Tent map chaotic population initialization. Each sub-population follows the proposed improved mutation strategies based on two-dimensional chaotic maps, i.e., Baker’s map and Arnold’s Cat Map for DE/rand/1 in the first sub-population, and Zaslavskii Map for DE/best/2 in the second sub-population. Finally, the selection criteria are proposed to select the best offspring produced by each sub-population following the mutant vectors generated by the proposed mutation strategies. MPC-DE is evaluated on the dynamic multi-model and multi-objective optimization problems, i.e., benchmark problems for CEC 2017 and CEC 2020, respectively. To verify MPC-DE’s performance, we compare it with the latest DE variants, namely, EFADE, MPEDE, SHADE, EPSDE, L-SHADE, ESMDE, CoDE, and JADE. The proposed MPC-DE is also employed to solve the Economic Load Dispatch Problem (EDP) and reduce fuel costs. We used a 60-unit bus system and a 180-unit bus system to solve EDP and compared it to recent EDP solvers such as DPADE, JADE, EPSDE, SaDE, DE/BBO, DE, MIMO, TLBO, BPSO, CSO, ORCSA, CSA, ORCCRO, BBO, and ED-DE. The empirical results confirmed that MPC-DE outperformed other recent variants for multi-objective optimization problems and EDP.