Parallel hybridization of differential evolution and particle swarm optimization for constrained optimization with its application

This paper presents a novel hybridization between differential evolution (DE) and particle swarm optimization (PSO), based on ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups—inferior group, mid group and superior group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. This proposed method is named as DPD as it uses DE–PSO–DE on the sub-populations of the same population. Two more strategies namely Elitism (to retain the best obtained values so far) and Non-Redundant Search (to improve the solution quality) have been incorporated in DPD cycle. Considering eight variants of popular mutation operators in one DE, a total of 64 variants of DPD are formed. The top four DPDs have been pointed out through 13 constrained benchmark functions and five engineering design problems. Further, based on the ‘performance’ analysis the best DPD is reported. Later to show superiority and effectiveness, the best DPD is compared with various state-of-the-art approaches. The numerical, statistical and graphical analyses reveal the robustness of the proposed DPD.