# Niching Grey Wolf Optimizer for Multimodal Optimization Problems
## 1 Introduction
Their hybrid algorithm is incorporated with crossover operator to handle discrete variables, whereas mutation operator helps to avoid local optima, and a neighborhood search is applied to increase exploration. Their proposed algorithm outperforms PAGA, LSGA, TLBO, EDA, BFO algorithms for both case studies [40]. [PERSON] et al. [41] recommmnded exploration-enhanced GWO (EEGWO), in which they introduced a new formula for updating the position by selecting a random wolf to guide the search and non-linearly controlling the GWO parameter \"a\". Even after making these modifications, their proposed algorithm still suffers from premature convergence and local optima. [PERSON] et al. [42] designed the selective opposition-based learning GWO (SOGWO) to improve GWO's convergence ability. To govern the omega wolves, they used Spearman's correlation coefficient and chose a few dimensions of wolves to apply opposition, which enhanced the exploration ability of the algorithm. A recent variation of the GWO is developed by [PERSON] et al. [43], where they suggested a new movement technique encouraged by the discrete hunting nature of wolves called dimension learning-based hunting (DLH) search. According to the DLH, all wolves create their neighbors, sharing information among themselves. The literature mentioned above indicates that due to easy implementation and less parameter tuning, GWO variants are already applied in every optimization field and have shown good performances empirically. However, premature convergence and the inability to balance the exploitation with exploration are still the main drawbacks of the GWO and its variants for solving complex multi-modal optimization problems [42; 43]. To overcome these limitations, we make a decent attempt to improve the GWO algorithm by adapting the niching technique. Niching techniques are well known to trace multiple optimal solutions together. These techniques increase population diversity and reduce the likelihood of being trapped in local solutions. In one iteration, they are also able to trace numerous local/global optima. A few standard niching techniques developed in recent years are clustering [44], fitness sharing [44], crowding [45], and clearing [46]. Nevertheless, niching methods need more function evaluations to reach the global optima. It has been seen from literature that various niching methods are applied to different types of metaheuristic algorithms such as GA [44; 45; 46], PSO [2; 47; 48; 49], CSA [50], and niching technique has significantly improved the performance of these optimization algorithms. Inspired by these results, we incorporate a fitness Euclidean distance ratio (FER) based niching technique with modified velocity update and local search into the GWO algorithm, which has shown to significantly improve the basic GWO algorithm's accuracy. Our proposed method also does not need any tuning parameters, which is a significant advantage. The research's key contribution is to (a) integrate FER niching technique into the GWO algorithm, (b) modify the velocity update equation, and (c) apply a local search technique at the end of the search process. To the best of our knowledge, this study first incorporates the niching technique to the GWO algorithm. Since the multi-modal function optimization also needs to allocate the desired global optima more precisely, we further incorporated the personal best feature of PSO to hold the good solutions. The remaining part of the article is organized as follows: Section 2 describes the NGWO algorithm. Section 3 illustrates the results and engineering applications of NGWO. Finally, Section 4 presents the conclusion.