## 1 Introduction  
Currently, fuzzy clustering is one of the important research branches in many fields, such as knowledge discovery, image processing, machine learning, and pattern recognition. With the expansion of scope of the study, more accurate clustering results are required from various aspects in scientific and practical application. Fuzzy C-Means (FCM) clustering is one of the most popular and well-recognized clustering methods. This method uses the concept of the geometric closeness of data points in Euclidean space. It allocates these data to different clustering, and the distance between these clusters is then determined. The FCM clustering algorithm is the basis of other fuzzy clustering analysis methods in theory and application respects, and it is therefore most widely-used among various clustering algorithms. However, the FCM algorithm is essentially a local search optimization algorithm. Herein, if its initial value is selected improperly, it will converge to a local minimum. Therefore, this drawback limits the FCM algorithm to be used in many applications. Aiming at the disadvantages of the FCM algorithm, researchers have proposed several methods to improve its performance. Apart from the traditional methods, recently, various metaheuristic algorithms have been proposed by the inspiration of nature and successfully addressed all kinds of application problems, such as grey wolf optimizer (GWO) [1,2], genetic algorithm (GA) [3], biogeography-based optimization (BBO) [4, 5, 6], animal migration optimization (AMO) [7], gravitational search algorithm (GSA) [8, 9, 10], cuckoo search (CS) [11, 12, 13, 14, 15], stud genetic algorithm (SGA) [16], wolf search algorithm (WSA) [17], multi-verse optimizer (MVO) [18], dragonfly algorithm (DA) [19], moth-flame optimization (MFO) [20], earthworm optimization algorithm (EWA) [21], harmony search (HS) [22, 23], firefly algorithm (FA) [24, 25, 26], particle swarm optimization (PSO) [27, 28, 29], monarch butterfly optimization (MBO) [30], ant colony optimization (ACO) [31], bat algorithm (BA) [32, 33, 34, 35, 36], differential evolution (DE) [37, 38, 39, 40], and interior search algorithm (ISA) [41]. Among them, swarm-based metaheuristic search, so called swarm intelligence methods, are one of the most well-known paradigms in nature-inspired algorithms. Due to its remarkable performance, they have dealt with a variety of applications, such as reliability [42, 43], knapsack problems [44], quantitative interpretation [45], scheduling [46], path planning [47], parameter estimation [48], global numerical optimization [49, 50, 51], neural network training [52, 53] and feature selection [54]. The KH method that is inspired by the krill herding behavior of krill in sea was first proposed by [PERSON] and [PERSON] in 2012 [55, 56]. Since it has high stability and strong robustness when solving optimization problems, many researchers have made in-depth studies about it and various improved version of KH methods have been proposed [57, 58, 59, 60]. The main differences between the KH algorithm and other swarm intelligence algorithms is that the parameters used in the KH algorithm is fully originated from the real krill herd in nature. Here, a new version of KH algorithm with elitism strategy, called KHE, is proposed. Elitism tragedy can prevent the krill population from degrading. In KHE, the well-selected parameters are used instead of originating from nature [61, 62]. Furthermore, the KHE method is applied to solve clustering problem for the purpose of escaping a local minimum. Moreover, with the aim of showing the performance of KHE method, it is compared with six other metaheuristic algorithms through seven complicated benchmark problems. The results show that the KHE method is able to find the better function values on given benchmark problems than six others; KHE is also a good choice of implementing fuzzy clustering analyses. Section 2 provides a basic knowledge of FCM clustering algorithm.