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In recent years, the complex real-world problems have been solved by many swarm intelligence algorithms (Li et al., 2016; Miloud et al., 2019; Ghosh et al., 2018). Compared with traditional optimization methods, the swarm intelligence algorithm can effectively and conveniently solve optimization problems due to its advantages strong robustness, and ability of easy implementation (Liu et al., 2020; Li et al., 2017). The swarm intelligence algorithm simulates various nature behaviors to research global optimum solution, like ant colony optimization algorithm (ACO) (Dorigo et al., 1996) simulates behavior of ants; particle swarm optimization algorithm (PSO) (Kennedy et al., 1995; Eberhart et al., 2002) is based on the behavior of a particle like a bird. And, various new swarm intelligence algorithms have been appeared in the past few years. For example, bat algorithm (BA) (Yang, 2010), artificial bee colony algorithm (ABC) (Karaboga et al., 2007), cuckoo algorithm (CS) (Yang & Deb, 2009), differential evolution algorithm (DE) (Ali et al., 2015), grey wolf optimizer algorithm (GWO) (Mirjalili et al., 2014), sine cosine algorithm (SCA) (Mirjalili, 2016), polar bear optimization algorithm (PBO) (Polap & Niak, 2017), etc. One main reason that more and more swarm intelligence algorithm appears is the No Free Lunch theorem ((NFL) (Wolpert & Macready, 1997). The NFL theorem present that any swarm intelligent optimization algorithm cannot solve all the optimization problems. Therefore, it is of great significance to study new outperformance swarm intelligence algorithm in the application field of the algorithm.
Sine cosine algorithm (SCA) is recently development swarm intelligence algorithm proposed by (Mirjalili, 2016). The SCA simulates the characteristic of sine and cosine mathematical function to realize global optimization. Scholars have proposed different optimization strategies to improve the performance of SCA. Such as, (Qu et al., 2018) used the neighborhood search mechanism and the greedy Lévy mutation strategy to avoid the premature convergence of the SCA. (Nenavath et al., 2018) recently combined the PSO with the SCA to reduce the probability of jump in the local optimum. (Xu et al., 2018) proposed an improved SCA to solve optimization problems below 1000D, verified the performance of SCA was better than other comparison algorithm. (Elaziz et al., 2017) used the opposition-based learning to modify sine cosine algorithm. (Guo et al., 2019) used the elite chaos strategy and parameter adjustment strategy to increase the convergence speed of SCA, simulation results proved the superiority of the modified SCA. (Li et al., 2018) proposed a new SCA-SVR algorithm and compared with other heuristic optimization algorithm, results showing that the SCA-SVR can find the optimal value of the SVR parameters. (Tawhid & Savsani, 2019) proposed an improvement SCA to solve the Traveling salesman problem (TSP), the results shown that the SCA has outperformance other algorithms. (Gupta & Deep, 2019) proposed a hybrid self-adaptive sine cosine algorithm based on opposition learning, the range of explored is expanded to balance the global and local optimization ability.
Levy flight (LF) firstly was proposed by (Shlesinger & Klafter, 1986). In the last few years, many scholars have studied behavior of insects whose use levy flights, it has been observed that the hunting pattern of prey-predator rely on the optimal walk based on levy distribution (Humphries et al., 2010; Sims et al., 2008). The LF has been applied to optimization problems and the results show the effectiveness of the method. In addition, researchers have been added the levy flight strategy into swarm intelligence algorithm, in order to ensure the new algorithm has a better performance. (Yang & Deb, 2009) have proposed cuckoo search (CS) algorithm with levy flight. (Yang, 2010) also has used LF into firefly algorithm (FA). Other scholars also applied levy flight to improve the convergence speed of swarm intelligence algorithms. For example, researchers combine levy flight with particle swarm optimization (PSO), and then a more efficient search by the long jumps (Hakli & Uguz, 2014; Jensi & Jiji, 2016). The bat algorithm (BA) used levy flight, which makes BA had largely population diversity and better global search ability (Li, et al., 2019). In order to improve the efficacy of grey wolf optimizer (GWO), the LF is combined with the modified hunting phases (Heidari & Pahlavani, 2017).