## 1 Introduction  
Data clustering is an aspect of data mining that aims at classifying or grouping data objects within a dataset based on their similarities and dissimilarities. A dataset is segmented into clusters so that the data objects within the same cluster are more similar than those in other clusters. In other words, data grouping is performed to reduce the intra-cluster distance among data objects while increasing the inter-cluster distance. Data clustering has been very useful for classifying data in many applications such as biological data analysis, social network analysis, mathematical programming, customer segmentation, image segmentation, data summarization, and market research [1]. There are several methods used for clustering datasets. These methods are majorly classified into two categories: the hierarchical clustering methods and the partitional clustering methods. In the hierarchical clustering technique, data objects are iteratively grouped in a hierarchical format to generate a dendrogram that depicts the clustering sequence of the dataset. The partitional clustering technique generates a single dataset partition to recover the natural groupings within the dataset without any hierarchical structure using a specific objective function. Among the many partitional clustering methods is the well-known K-means clustering algorithm. The K-means clustering algorithm is a partitional non-deterministic method that [PERSON] proposed in 1967 [2]. For the K-means algorithm, objects are grouped into a user-specified '\(k\)' number of clusters based on the minimum distance between the data objects and cluster centers [3]. According to [PERSON] et al. [4], the K-means clustering algorithm is straightforward to implement, flexible, and efficient. It has been rated among the top ten algorithms most used in data mining, and it has enjoyed wide acceptability in many domains due to its low computation complexity and implementation simplicity. The dependability of the algorithm on the user's specification of the number of clusters and the random initialization of the initial cluster center limits the performance and the accuracy of the cluster results. Different initial values of \(k\) produce different clustering results, and the random selection of the initial clusters makes the algorithm tends toward converging into local minimal. Choosing appropriate cluster numbers for datasets containing high dimensional data objects with varying densities and sizes is difficult without prior domain knowledge [5]. The requirement for pre-defining the number of clusters makes the K-means algorithm inefficient for automatic clustering. Because, for the automatic clustering methods, the adequate number of clusters in a dataset are determined automatically without any background information of the data objects in the dataset. In view of this, nature-inspired metaheuristics have been adopted in finding solutions to automatic clustering problems [6; 7]. A few nature-inspired metaheuristics algorithms have been combined with the traditional k-means algorithm to optimize its performance and increase its ability to handle automatic clustering problems. In this study, we review and analyze the different nature-inspired metaheuristic algorithms that have been integrated with K-means or any of its variants in recent times to solve the automatic data clustering problems. There are many published articles on reviews regarding the use of nature-inspired clustering algorithms focusing on automatic clustering alone. An up-to-date study of all major nature-inspired metaheuristic algorithms for solving automatic clustering problems was presented by [PERSON] and [PERSON] [6]. [PERSON] et al. [8] presented a systematic taxonomical overview and bibliometric analysis of the trends and progress in nature-inspired metaheuristic clustering approaches, with emphasis on automatic clustering algorithms. There are domain-specific review works where different metaheuristics techniques were utilized [9; 10; 11].