A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems

Optimization in computationally expensive numerical problems with limited function evaluations provides computational advantages over constraints based on runtime requirements and hardware resources. Convergence success of a metaheuristic optimization algorithm depends on directing and balancing of its exploration and exploitation abilities. Firefly and particle swarm optimization are successful swarm intelligence algorithms inspired by nature. In this paper, a hybrid algorithm combining firefly and particle swarm optimization (HFPSO) is proposed. The proposed algorithm is able to exploit the strongpoints of both particle swarm and firefly algorithm mechanisms. HFPSO try to determine the start of the local search process properly by checking the previous global best fitness values. In experiments, several dimensional CEC 2015 and CEC 2017 computationally expensive sets of numerical and engineering, mechanical design benchmark problems are used. The proposed HFPSO is compared with standard particle swarm, firefly and other recent hybrid and successful algorithms in limited function evaluations. Runtimes and convergence accuracies are statistically measured and evaluated. The solution results quality of this study show that the proposed HFPSO algorithm provides fast and reliable optimization solutions and outperforms others in unimodal, simple multimodal, hybrid, and composition categories of computationally expensive numerical functions.