# Enhancing Backtracking Search Algorithm using Reflection Mutation Strategy Based on Sine Cosine
## 1 Introduction
The third category is improved parameter-based variants. BSA has a crossover probability parameter \(mixrate\) and an adaptive mutation control parameter \(F\). In [PERSON] et al. [26], [PERSON] et al. proposed an adaptive parameter \(F\) strategy which obeys Maxwell Boltzmann distribution since parameter \(F\) value influences the convergence speed of the algorithm. [PERSON] et al. [27] introduced a fitness distance-based adaptive parameter \(F\) and \(mixrate\) with experience parameters to accelerate convergence speed. [PERSON] et al. [28] used a fitness information-based feedback mechanism to design a more available adaptive parameter F which can vary in [0.45, 1.99] with the change of fitness. Meanwhile, \(mixrate\) randomly varied in [0,1] is designed to improve search efficiency of the algorithm. [PERSON] et al. [29] proposed a new adaptive parameter \(F\) with experience parameter, which can adaptively reduce with iteration increase of the algorithm, to effectively balance exploration and exploitation of the BSA. [PERSON] et al. [30] employed burger chaotic mapping to adjust parameter \(F\), but two experience parameters are introduced into the strategy. [PERSON] et al. [31] analyzed five different distributions \(F\) to impact algorithm performance and select the best available design of \(F\). The fourth category is with the local search mechanisms embedded. To improve local exploitation of BSA and convergence speed, some search mechanisms are embedded into the framework of BSA. A chaotic mapping-based local search is embedded into BSA and combines with another algorithm to solve the hydrothermal generator set problem. [PERSON] et al. [32] added a random walk guided local exploration strategy into BSA after selection-II of BSA, enhancing exploration performance of the algorithm. To solve the displacement flow shop scheduling problem, [PERSON] et al. [33] proposed three different strategies to improve BSA. A new initial generator is constructed to improve the quality of the initial solution. In addition, the selection mechanism accepting a worse solution in the Simulated Annealing (SA) is employed to avoid trapping in local optimum. A local search mechanism randomly inserted is introduced to enhance exploitation ability of BSA. Moreover, due to its flexibility and efficiency, BSA and its variants have been widely applied to a wide range of real-world optimization problems, such as economic dispatch problems [34], optimal power flow [35], parameter identification [36; 37],feature selection [38], artificial neural network [25], flow shop scheduling [39], and nonlinear optimal control problem [40]. However, BSA still has some drawbacks and its performance needs to be further improved. The first is that only the historical population information is adopted to guide the search and the information in current population is not used sufficiently, which cannot maintain the population diversity efficiently and thus the exploration ability of BSA is weak. The second is that there is no guidance regarding the approach to the current best individual during the evolution process, which leads to slow convergence speed and poor exploitation ability of BSA. Based on the above discussion, in this paper, an enhancing backtracking search optimization algorithm with reflection mutation strategy based on sine cosine, named RSCBSA, is proposed. In RSCBSA, inspired by reflection operation in Nelder-Mead method [41] and Sine Cosine Algorithm (SCA) [42], a new reflection mutation strategy based on sine cosine is developed to address the above-mentioned drawbacks, in which the best solution and sine and cosine math models are introduced to balance exploration and exploitation ability of BSA. The contributions of the paper are listed as follows:  
1. A new reflection mutation strategy based on sine cosine is proposed to balance exploration and exploitation ability of BSA.