Firefly search algorithm based on leader strategy

Abstract

In the firefly search algorithm, individuals will move toward a brighter direction according to the light intensity factor in the iteration, which has a high convergence speed. It faces the problem of unbalanced exploration and exploitation. At the same time, the diversity of the algorithm is insufficient. Especially when dealing with complex benchmark functions or engineering problems, it cannot show excellent performance. This paper proposes a firefly search algorithm based on the leader and follower population model and combines the Brownian motion strategy and Levy flight strategy (FA-BMLA). Using the different performances of the Brownian motion strategy and Levy flight strategy in exploration and exploitation, adding an adaptive parameter switching that the FA-BMLA can accord to different situations change its strategy. By testing 20 benchmark functions such as single-mode, multi-mode, and CEC2014, the results are compared with advanced algorithms such as the firefly search algorithm and its variants, whale optimization algorithm, and salp swarm algorithm, and the results are evaluated by the nonparametric test method. Numerical results and statistical experiments show that the FA-BMLA has better solution quality, convergence accuracy, and stability. The FA-BMLA is applied to solve the three engineering problems of pressure vessel, welding beam, and rolling bearing. The data results and experimental comparisons show that FA-BMLA can obtain an accurate solution to engineering problems.