# Niching Grey Wolf Optimizer for Multimodal Optimization Problems
## 1 Introduction  
The area of nature-inspired metaheuristic algorithms is continuously evolving with newly developed algorithms. These algorithms are well known for their widespread local and global search ability, local optima avoidance, and quick convergence ability. In addition, these algorithms do not need any knowledge of a function's gradient or differentiability [1, 2]. Since the metaheuristic algorithms have these superior properties with easy applicability and fewer parameter requirements, significant variants of these algorithms are developed [3]. The most widely used algorithms are Simulated Annealing (SA) [4], Genetic Algorithm (GA) [5], Particle Swarm Optimization (PSO) [6], Differential Evolution (DE) [7], and Ant Colony Optimization (ACO) [8]. A few recent metaheuristics that seek the attention of researchers is Bee Collecting Pollen Algorithm (BCPA) [9], Black Hole (BH) [10] Algorithm, Artificial Bee Colony Algorithm (ABC) [11], Central Force Optimization (CFO) [10], Electro-search Algorithm (ESA) [12], Gravitational Search Algorithm(GSA) [13], Teaching Learning Based Algorithm (TLBO) [14], Artificial Chemical Reaction Optimization Algorithm (ACROA) [15], Firefly Algorithm (FA) [16], Big Bang-Big Crunch (BBBC) [17], Grey Wolf Optimizer (GWO) [18], Dragon Fly Algorithm [19], and Harris Hawk Optimizer (HHO) [20], Jaya Algorithm [21]. Among these recent metaheuristics, the GSA, GWO, and Jaya Algorithm is well known for simplicity, effective exploration and exploitation. Among the algorithms mentioned above, the GWO is a novel metaheuristic algorithm that falls under swarm intelligence [18]. This algorithm has been proposed mimicking the organizational order of wolves and their collective hunting nature. Due to its simplicity, fast seeking speed, good precision for search, and fewer controlling parameters, this algorithm is successfully applied to various technical fields such as feature selection [22; 23; 24], wind speed forecasting [25], optimal power flow [26; 27], pattern recognition [28], unit commitment [29; 30] parameters estimation [31; 32], wellbore trajectory optimization [31]. In addition to these applications, the GWO and variants also performed well for combinatorial optimization problems and successfully applied to different fields, such as vehicle routing problem [32], job scheduling problems [33; 34; 35], and economic dispatch [36; 37] problems. Some modifications to the GWO algorithm and its application in various optimization fields are now described. Quasi-oppositional based learning (Q-QBL) GWO called QOGWO was proposed by [PERSON] et al. [38] to control power systems load frequency. The authors designed optimal PID controller by using QOGWO for two areas and four hydrothermal power plants and showed that their proposed methods achieved promising performance like fuzzy logic, ANN, and ANFIS system. In a different research, crossover and mutation-based hybrid GWO was proposed by [PERSON] et al. [36] to optimize non-linear, non-convex, constrained, and unconstrained economic dispatch problems at different conditions. The authors claimed that their method showed promising performance. [PERSON] et al. hybridized the GWO with K-means clustering technique to solve CVRP (capacitated vehicle routing problems) and named it as K-GWO [32]. The authors further integrated a capacity constraint to their algorithm and proposed 2 clustering techniques. They follow the cluster-first route-second method to solve CVRP problems and tested their proposed technique for 20 benchmarks, and the obtained solutions are within a mean deviation of 1.76% from the known optimum solutions. [PERSON] and [PERSON] [39] proposed a hybridization of GWO with SCA in 2017. The hybrid GWOSCA shows good performance for unimodal functions but failed to perform better for multi-modal problems [39]. [PERSON] and zhang applied a hybrid Grey Wolf Optimizer algorithm for job shop scheduling and flexible job shop scheduling problems.