A hybrid optimizer based on firefly algorithm and particle swarm optimization algorithm - Xia, Xuewen; Gui, Ling; He, Guoliang; Xie, Chengwang; Wei, Bo; Xing, Ying; Wu, Ruifeng; Tang, Yichao (Journal of computational science, 2018)
•Two sub-populations select FA and PSO as their basic algorithm, respectively.•Two sub-populations share their own optimal solutions while they have stagnated more than a threshold generations.•The population's historical knowledge is recorded to help it carry out a purposeful detecting operator.•BFGS Quasi-Newton method is introduced to improve the exploitative capability of FAPSO. As two widely used evolutionary algorithms, particle swarm optimization (PSO) and firefly algorithm (FA) have been successfully applied to diverse difficult applications. And extensive experiments verify their own merits and characteristics. To efficiently utilize different advantages of PSO and FA, three novel operators are proposed in a hybrid optimizer based on the two algorithms, named as FAPSO in this paper. Firstly, the population of FAPSO is divided into two sub-populations selecting FA and PSO as their basic algorithm to carry out the optimization process, respectively. To exchange the information of the two sub-populations and then efficiently utilize the merits of PSO and FA, the sub-populations share their own optimal solutions while they have stagnated more than a predefined threshold. Secondly, each dimension of the search space is divided into many small-sized sub-regions, based on which much historical knowledge is recorded to help the current best solution to carry out a detecting operator. The purposeful detecting operator enables the population to find a more promising sub-region, and then jumps out of a possible local optimum. Lastly, a classical local search strategy, i.e., BFGS Quasi-Newton method, is introduced to improve the exploitative capability of FAPSO. Extensive simulations upon different functions demonstrate that FAPSO is not only outperforms the two basic algorithm, i.e., FA and PSO, but also surpasses some state-of-the-art variants of FA and PSO, as well as two hybrid algorithms.