A modular hybridization of particle swarm optimization and differential evolution

In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are implemented, has been introduced to boost the empirical performance. In this paper, we first propose to combine the variants of PSO or DE by modularizing each algorithm and incorporating the variants thereof as different options of the corresponding modules. Then, considering the similarity between the inner workings of PSO and DE, we hybridize the algorithms by creating two populations with variation operators of PSO and DE respectively, and selecting individuals from those two populations. The resulting novel hybridization, called PSODE, encompasses most up-to-date variants from both sides, and more importantly gives rise to an enormous number of unseen swarm algorithms via different instantiations of the modules therein. In detail, we consider 16 different variation operators originating from existing PSO- and DE algorithms, which, combined with 4 different selection operators, allow the hybridization framework to generate 800 novel algorithms. The resulting set of hybrid algorithms, along with the combined 30 PSO- and DE algorithms that can be generated with the considered operators, is tested on the 24 problems from the well-known COCO/BBOB benchmark suite, across multiple function groups and dimensionalities.