A systematic overview of developments in differential evolution and particle swarm optimization with their advanced suggestion

An efficient survey of numerous traditional metaheuristic algorithms (MAs) has been investigated in this paper. Among successful MAs, differential evolution (DE) and particle swarm optimization (PSO) have been widely recognized to solve complex optimization problems and received much attention from many researchers. Therefore, DE and PSO are chosen in the present study and an extensive survey of their recent-past variants with hybrids has been inspected again. After this an advanced DE (ADE) and PSO (APSO) with their hybrid (AHDEPSO) are proposed for unconstrained optimization problems. In ADE a novel mutation strategy, crossover probability and random nature selection scheme (to avoid premature convergence) as well as in APSO novel gradually varying parameters (to avoid stagnation) are introduced. Hence, ADE and APSO affords different convergence characteristics to the solution space. Also to balance between exploration and exploitation, in AHDEPSO population is divided (multi-population approach) and merged with others in a pre-defined way. Thus, AHDEPSO achieves better solutions and it is expected to obtain productive solutions with an increasing success rate at each cycle. To verify the performance of all 3 proposed algorithms i.e. ADE, APSO, and AHDEPSO applied to solve 23 basic, 30 IEEE CEC 2017 unconstrained benchmark functions and 3 real-world problems. There are several numerical and graphical analyses have been done to verify the performances of the proposed algorithms robustly. Additionally, statistical and comparative analysis confirms the superiority of the proposed algorithms among traditional DE and PSO with their recent variants and hybrids as well as over many state-of-the-art algorithms. Finally, between 3 proposed algorithms the best one i.e. AHDEPSO is recommended to solve unconstrained optimization problems.

Automated summary

An efficient survey of numerous traditional metaheuristic algorithms has been conducted in this study. The proposed AHDEPSO algorithm achieves better solutions for unconstrained optimization problems compared to traditional DE and PSO algorithms. The performance of AHDEPSO has been demonstrated through numerical, graphical, statistical, and comparative analyses.