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Top1. Introduction
Many problems in the real world can be transformed into optimization problems, but with the development of the times, these problems become more and more complex. One of the greatest challenges is high-dimensional nonlinear problems. Therefore, some new meta-heuristic swarm intelligence algorithms have been proposed, such as artificial bee colony algorithm (ABC) (Karaboga & Basturk, 2007), particle swarm optimization algorithm (PSO) (Kennedy & Eberhart, 1995) and cuckoo search (CS) (Yang & Deb, 2009). As a member of the swarm intelligence algorithm, the Firefly algorithm (FA) (Yang, 2010) has attracted many scholars' attention due to its simple structure, few parameters and easy implementation. Until now, FA has been successfully applied in various fields such as image recognition and path planning (Wang, Guo, Duan, Liu & Wang, 2012; Yang & He, 2013; Zhou, Tian, Zhao & Zhao, 2015).
However, FA also has some shortcomings. The fixed-step factor and attractiveness do not seem to match the actual situation. Too many times of mutual attraction between fireflies lead to the oscillation phenomenon (Wang, Wang, Zhou, Sun, Zhao, Yu & Cui, 2017), and is not conducive to the rapid convergence of the algorithm.
To overcome these shortcomings, some researchers first adjusted the parameters of FA. Yu et al. (Yu, Zhu, Ma & Mao, 2015) proposed a variable step size of firefly algorithm (VSSFA), which explores the space with a larger step size in the early stage, and mines the optimal solution with a smaller step size in the later stage. Gandomi et al. (Gandomi, Yang, Talatahari & Alavi, 2013) used 12 chaotic maps to adjust 
, 
and 
. Experiments have found that the best chaos algorithm is an algorithm that uses Gauss map to adjust attractiveness parameters. Yelghi (Yelghi & Köse, 2018) introduced tidal force into FA, replacing the original attractiveness parameter 
. Liu et al. (Liu, Li, Deng & Ren, 2020) proposed an attraction formula based on sigmoid, which reconstructed the definition of attraction 
and enhanced the local search ability of the algorithm. A novel courtship learning framework was proposed by Peng et al (Peng, Zhu, Deng & Wu, 2020). It uses an archive mechanism to allow a female firefly to lead a weaker male firefly. This framework uses a logistic regression function to replace 
when solving the problem that the distance between two fireflies is too large and the attraction is close to 0. This improvement well balances the exploration and exploitation of the algorithm.