An ideal tri-population approach for unconstrained optimization and applications

The hybridization of Differential Evolution (DE) and Particle Swarm Optimization (PSO) have been well preferred over their individual effort in solving optimization problems. The way of applying DE and PSO in the hybridization process is a big deal to achieve promising solutions. Recently, they have been used simultaneously (i.e. in parallel) on different sub-populations of the same population, instead of applying them alternatively in series over the generation. An attempt is made in this paper to hybrid DE and PSO in parallel, under a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – inferior group, mid group and superior group. Based on their inherent ability, 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. The paper is designed with three major aims: (i) investigation of suitable DE-mutation strategies to support DPD, (ii) performance comparison of DPD over state-of-the-art algorithms through a set of benchmark functions and (iii) application of DPD to real life problems. Numerical, statistical and graphical analysis in this paper finally concludes the robustness of the proposed DPD.