## 1 Introduction
A review of nature-inspired algorithms that have been employed to solve partitional clustering problems, including the major areas of application, was presented by [PERSON] and [PERSON] [10]. [PERSON] and [PERSON] [12] presented an overview of the nature-inspired techniques used for data clustering. Their study covers the hybridization of several nature-inspired techniques with some traditional clustering techniques to improve the performance of the existing clustering approaches. This study presents a systematic review on the different nature-inspired metaheuristic algorithms integrated with K-means or any of its variants for cluster analysis in the last two decades, emphasizing automatic clustering. A total of 147 articles were considered in the review. Despite the various review papers published on the nature-inspired algorithm and clustering algorithms, including the traditional clustering and automatic clustering methods, to the best of our knowledge, at the point of writing this paper, no extensive review study on the hybridization of nature-inspired algorithms with the K-means clustering algorithm exist with a primary focus on automatic clustering. Because of this limitation and identified gap, an up-to-date and in-depth review of hybridization of nature-inspired metaheuristic algorithm with K-means clustering algorithm and its variants over the last two decades is presented in this paper. This study is significant in many ways, and more specifically due to its advantages of (i) identifying, categorizing, and analyzing the various improvement methods and hybridization techniques for the classical K-means algorithms in solving various automatic data clustering problems, (ii) identifying the variants of the K-means based nature-inspired metaheuristic algorithms, (iii) presentation of further comparative analysis of data in the form of charts and tables across a wide variety of hybridization techniques attributes, (iv) identifying the strengths and weaknesses of the existing implementation of hybrid K-means based nature-inspired metaheuristic algorithms, (v) identifying recent trends of hybridizing nature-inspired metaheuristic algorithms with the classical K-means algorithm for solving automatic data clustering problems and open challenges, and (vi) suggesting new possible future research directions for the domain enthusiasts. It is also noteworthy that researchers and practitioners interested in exploiting and harnessing the advantages of K-means clustering with those of nature-inspired algorithms for implementing a better-performed automatic clustering technique will find this work useful. It will also be helpful for researchers in the domain of constrained and unconstrained optimization techniques. The remaining sections of the paper are structured as follows: Section 2 gives a brief description of the scientific background of K-means clustering algorithm, nature-inspired metaheuristic algorithms, and automatic clustering problems. The section similarly reiterates the research methodology approach to the systematic literature review and analysis of the study. The existing integration of the K-means clustering algorithm with nature-inspired metaheuristic algorithms in literature is presented in Section 3. Section 4 discusses the critical issues of integrating the K-means clustering algorithm with nature-inspired metaheuristic algorithms for automatic clustering. Subsequently, open challenges and future research directions are also covered in this section. Finally, Section 5 gives the study concluding remarks.