K-Means-Based Nature-Inspired Metaheuristic Algorithms for Automatic Data Clustering Problems: Recent Advances and Future Directions

Abstract

K-means clustering algorithm is a partitional clustering algorithm that has been used widely in many applications for traditional clustering due to its simplicity and low computational complexity. This clustering technique depends on the user specification of the number of clusters generated from the dataset, which affects the clustering results. Moreover, random initialization of cluster centers results in its local minimal convergence. Automatic clustering is a recent approach to clustering where the specification of cluster number is not required. In automatic clustering, natural clusters existing in datasets are identified without any background information of the data objects. Nature-inspired metaheuristic optimization algorithms have been deployed in recent times to overcome the challenges of the traditional clustering algorithm in handling automatic data clustering. Some nature-inspired metaheuristics algorithms have been hybridized with the traditional K-means algorithm to boost its performance and capability to handle automatic data clustering problems. This study aims to identify, retrieve, summarize, and analyze recently proposed studies related to the improvements of the K-means clustering algorithm with nature-inspired optimization techniques. A quest approach for article selection was adopted, which led to the identification and selection of 147 related studies from different reputable academic avenues and databases. More so, the analysis revealed that although the K-means algorithm has been well researched in the literature, its superiority over several well-established state-of-the-art clustering algorithms in terms of speed, accessibility, simplicity of use, and applicability to solve clustering problems with unlabeled and nonlinearly separable datasets has been clearly observed in the study. The current study also evaluated and discussed some of the well-known weaknesses of the K-means clustering algorithm, for which the existing improvement methods were conceptualized. It is noteworthy to mention that the current systematic review and analysis of existing literature on K-means enhancement approaches presents possible perspectives in the clustering analysis research domain and serves as a comprehensive source of information regarding the K-means algorithm and its variants for the research community.

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 MacQueen 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 Ezugwu 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 Jose-Garcia and Gomez-Flores [6]. Ezugwu 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]. A review of nature-inspired algorithms that have been employed to solve partitional clustering problems, including the major areas of application, was presented by Nanda and Panda [10]. Mane and Gaikwad [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 re-iterates 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.

2. Scientific Background

The K-means clustering algorithm is a partitional clustering technique that splits a dataset into $k$ number of clusters using a specific fitness measure. That is, given a dataset $X, X$ is divided into $K$ non-overlapping groups $C=\left\{c_1, c_2,\dots ,c_k\right\}$, $c_i \ne \varnothing , i=1,\dots$, and such that ${\cup }_1^k{c}_i=X$; $c_i{\displaystyle \cap }{c}_j=\varnothing , i,j=1\dots k$ and $i\ne j$. The partitioning process is handled as an optimization problem with the fitness measure taking as the objective function such as minimizing the distances between data objects or maximizing the correlation between data objects [10]. Mathematically, the optimization problem for cluster analysis is defined as follows:

Given a dataset $X=\left\{x_i\right\}$, where $i=1,2,\dots n$ of d-dimension data points of size $n$, $X$ is partitioned into ‘$k$’ clusters such that

$$J\left(c_k\right)={\displaystyle \sum }_{x_iϵc_k}{\left|\left|x_i-{\mu }_k\right|\right|}^2$$

(1)

with the objective function: minimize the sum of the square error over all the $k$ clusters. That is, minimize

$$J\left(C\right)={\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{x_iϵc_k}{\left|\left|x_i-{\mu }_k\right|\right|}^2$$

(2)

In automatic clustering, the main concerns are determining the best estimate for cluster number $k$ and correct identification of all the partitions [6]. In other words, an automatic clustering algorithm seeks to optimize the number of combinations in the assignments of $N$ objects into $k$ clusters. This is mathematically represented as:

$$S\left(N,K\right)=\frac{1}{K!}{\displaystyle \sum }_{i=0}^K{\left(-1\right)}^{K-i}\left(\begin{array}{c}K\\ t\end{array}\right)t^N$$

(3)

In finding the optimal cluster number, the search space is mathematically represented as:

$$B\left(N\right)={\displaystyle \sum }_{K=1}^{N}S\left(N,K\right)$$

(4)

The task of finding an optimal solution for this problem when $k>3$ is NP-hard [6,13] and this makes the search computationally expensive for moderately sized problems [6,14]. In recent times, there has been an immeasurable increase in the magnitude of data being generated. The current real-world datasets are characterized as being high dimensional and massive in size. Automatic clustering of such datasets with no background knowledge of the features of the data objects can be termed a difficult task. Without prior domain knowledge, it is difficult to determine the appropriate number of clusters for a massive, high-dimensional dataset. Moreover, due to the enormous size of data objects in real-world datasets, the distribution of data objects into appropriate clusters to produce an optimal cluster result is computationally intensive and time-consuming.

2.1. Nature-Inspired Metaheuristics for Automatic Clustering Problems

Metaheuristics are global optimization techniques used to solve complex real-life problems [8,15]. A higher-level procedure applies simpler procedures in solving optimization problems [16]. In optimization, inputs to an objective function are adjusted to find the optimum solution. According to Engelbrecht [17], it is possible to formulate clustering problems as an optimization problem that can be comfortably solved using single objective and multi-objective metaheuristics. Metaheuristics can find the optimum solution to global optimization problems with less computational effort. They find an approximate solution and are non-deterministic as well as non-problem dependent. Agbaje et al. [18] stated that most metaheuristic algorithms can partition datasets automatically into an optimal number of clusters when a good validity measure is applied.

The nature-inspired metaheuristic algorithms are modeled after the behavioral pattern of natural phenomena exhibiting the learning ability and adaption to emerging situations in finding appropriate solutions to problems in changing and complex environments [17]. According to Ezugwu et al. [8], nature-inspired algorithms are designed practically to find a solution to high-dimensional and complex real-world problems. They have satisfactorily proffer suboptimal solutions to automatic clustering problems within an acceptable time limit [7]. As a result of their capability for higher heuristic search, they seek the most appropriate solution in the search space and at the same time try to maintain the balance between intensification (local optimal search) and diversification (global optimal search) [19]. The nature-inspired metaheuristic uses the population to explore the search space, ensuring a greater probability of achieving optimal cluster partitions [10].

Alongside the successes recorded with solving automatic clustering problems using nature-inspired metaheuristic algorithms, it has been observed that hybridizing two or more metaheuristics for the same purpose produces better clustering performance. According to Nanda and Panda [10], the performance of the hybrid algorithms is superior to that of the individual algorithms in terms of robustness, efficiency, and accuracy. Nature-inspired metaheuristics have also been hybridized with some of the traditional clustering algorithms to improve their performance [5]. K-means clustering algorithm is one of the most fundamental and popular traditional partitional clustering algorithms that has been used in many applications. In order to improve its performance for the general clustering problem, several variants of K-means have been proposed in the literature. The traditional K-means algorithm, with its numerous variants though credited with computational simplicity, are however limited in their performance due to the possibility of getting trapped in the local optimum because of its hill-climbing approach. As a result, some of the metaheuristic algorithms have been hybridized with it to improve its performance.

2.2. Review Methodology

A comprehensive literature review includes the basic introduction to a specific problem and the critical assessment, evaluation, and interpretation of existing related literature and materials. When considering the authors, countries, publishers, studies, journals, and universities, there should be no bias. In this comprehensive review, three major phases are considered: the review planning, the conducting of the review, and the review reporting. This methodology process is illustrated in Figure 1. The primary aim of the planning phase is the identification of the need and worth of this review. It includes designing the research questions that guide selecting relevant related manuscripts for the review and analysis processes. It also addressed the strategy adopted for literature search from the relevant academic databases to ensure unbiased and extensive primary studies.

Figure 1. Adopted review of research methodology.

2.2.1. Research Questions

In this study, answers are provided to the following research questions:

• RQ1: What are the various nature-inspired meta-heuristics techniques that have been hybridized with the K-means clustering algorithm?
• RQ2: Which of the reported hybridization of nature-inspired meta-heuristics techniques with K-means clustering algorithm handled automatic clustering problems?
• RQ3: What various automatic clustering approaches were adopted in the reported hybridization?
• RQ4: What contributions were made to improve the performance of the K-means clustering algorithm in handling automatic clustering problems?
• RQ5: What is the rate of publication of hybridization of K-means with nature-inspired meta-heuristic algorithms for automatic clustering?

It is equally important to note that providing answers to these research questions establishes this study’s primary goal and specific objectives. In other words, the responses help define the study’s motivation and focus relative to the reader’s interest.

2.3. Adopted Strategy for Article Selection

In determining and shortlisting relevant articles that cover and answer all the designed research questions stated in Section 2.2.1 successfully, the quest approach was adopted. To extract relevant articles from the database with better coverage for the study, different keywords that basically relate to the study along with their synonyms were used in the search. Relevant articles on “nature-inspired metaheuristic”, “K-means clustering algorithm”, and “automatic clustering” published in the last two decades were obtained. The search for articles was performed on seven different academic databases: ACM Digital Library, Elsevier Journal, Wiley Online Library, IEEE Explore, Springer Link, DLBP, and CiteSeer. The search for relevant articles was streamlined to the last two decades to reduce the number of articles. A total number of 3423 articles were extracted, and 1826 duplicate copies were removed from the lot. The selected articles were restricted to those published only in the English language. On careful investigation of the articles’ title, abstract, and contents, the remaining 1597 articles were further reduced to 147, which made up the final most relevant articles selected for the study.

3. Data Synthesis and Analysis

This section covers the answers to the designed research questions stated in Section 3.1, with each subsection distinctly handling answers to each research question.

3.1. RQ1. What Are the Various Nature-Inspired Meta-Heuristics Techniques That Have Been Hybridized with the K-Means Clustering Algorithm?

Meta-heuristics techniques are developed for providing optimal solutions to optimization problems through iterative exploration and exploitation of the entire search space [20]. A number of these algorithms have been integrated with the traditional K-means algorithm to improve the process of data clustering. The following section presents the various nature-inspired meta-heuristics techniques that have been hybridized with the K-means clustering algorithm.

3.1.1. Genetic Algorithm

The genetic algorithm (GA) was introduced by Holland in 1975 [21] based on the evolutionary principle of Charles Darwin [22]. The evolutionary principle states that “only the species that are fit to survive can reproduce their kind”. The computer simulation of this evolutionary process produced the Genetic Algorithm [21]. The earliest work on hybridizing the K-means clustering algorithm with GA for data clustering was reported by Krishna and Murty [23] in their paper titled ‘Genetic K-Means Algorithm’. The main purpose of the hybridization was to find a global optimal partition of a given dataset based on a given number of clusters. It also addressed the problem of expensive crossover operators and costly fitness functions common with the traditional GA. Even though GKA was able to converge to the best-known optimum, the number of clusters needs to be specified. Bandyopadhyay and Maulik [24] introduced KGA-clustering, which exploits the searching capability of K-means while avoiding the problem of local optimal convergence. Cheng et al. [25] presented prototypes-embedded genetic K-means (PGKA) where prototypes of clusters were encoded as chromosomes. Laszlo and Mukherjee [26] evolve centers for K-means clustering algorithm using GA by constructing hyper-quad tree on the datasets to represent cluster centers set. In their paper, Laszlo and Mukherjee [27] also proposed a novel crossover operator for neighboring centers exchange for superior partitions of large simulated datasets. Dai, Jiao, and He [28] proposed parallel genetic algorithm-based K-means clustering adopting the variable-length chromosome encoding strategy. Chang, Zhang, and Zheng [29] integrated the K-means algorithm with GA with gene rearrangement (GAGR) to improve clustering performance. Sheng, Tucker, and Liu [30] proposed niching genetic K-means algorithm (NGKA) for the partitional clustering algorithm. KMQGA was proposed by Xiao et al. [31] as a quantum-inspired genetic algorithm for K-means clustering with the Q-bit-based representation for exploration and exploitation purposes. It was able to obtain the optimal number of clusters and also provide the optimal cluster centroid. Rahman and Islam [32] proposed a novel GA-based clustering technique that automatically finds the correct numbers of clusters and produces high-quality cluster centers that serve the initial seeds for the K-Means algorithm to produce a high-quality clustering solution. Kapil, Chawla, and Ansari [3] optimized the K-means algorithm using GA.

In more recent works, Sinha and Jana [33] combined GA with Mahalanobis distance and K-means for clustering distributed datasets using the MapReduce framework. Islam et al. [34] extended GENCLUST by combining genetic operators’ capacity to combine the different search space solutions with the K-means’ hill climber exploitation. Zhang and Zhou [35] proposed NClust, which combined novel niching GA (NNGA) with K-means to determine clusters number automatically. Mustafi and Sahoo [36] explored the GA framework and differential evolution (DE) heuristic to improve the cluster center selection and obtain the required number of clusters respectively for the traditional K-means algorithm. El-Shorbagy et al. [37] proposed an enhanced GA with a new mutation where the K-means algorithm initializes the GA population for finding the best cluster centers. Genetic K-Means clustering (GKMC) was proposed by Ghezelbash, Maghsoudi, and Carranza [38] for optimally delineating multi-elemental patterns in stream sediment geochemical data.

Kuo et al. [39] integrated self-organizing feature maps neural network with genetic k-means for Market segmentation. Sheng, Tucker, and Liu [30] employed NGKA in clustering gene expression data. Li et al. [40] combined GA with an improved K-means clustering algorithm for video image indexing. Karegowda et al. [41] used GA and entropy-based fuzzy clustering (EFC) to assign initial cluster centers for the K-means algorithm for PIMA Indian diabetic dataset clustering. Eshlaghy and Razi [42] used an integrated framework that combines a grey-based K-means algorithm with GA for project selection and project management. Lu et al. [43] combined GA and K-means to solve the multiple traveling salesman problem (MTSP). K-means was combined with improved GA by Barekatain, Dehghani, and Pourzaferani [44] for energy consumption reduction and network lifetime extension in wireless sensor networks. Zhou et al. [45] proposed NoiseClust, which combines GA and K-means++ with an improved noise method for mining better origins and destinations in global position system (GPS) data. Mohammadrezapour, Kisi, and Pourahmad [46] used K-means clustering with GA to identify homogeneous regions of groundwater quality.

3.1.2. Particle Swarm Optimization

The particle swarm optimization (PSO) is a population-based metaheuristic search algorithm that is based on the principle of social behavior of swarms [47]. It is a powerful optimization tool credited with implementation simplicity, fewer parameter configuration, and global exploration ability [48]. According to Niu et al. [48], diverse versions of PSO have been reported in the literature with a number implemented for clustering purposes [49,50,51,52,53,54,55,56,57]. Several pieces of literature report the hybridization of PSO with the K-means clustering algorithm. Van der Merwe and Engelbrecht [49] proposed two different approaches of integrating PSO with K-means clustering algorithm for data clustering. In one of the approaches, PSO was used to find centroid for a specified number of clusters, while in the other approach, K-means was used to find the initial swarm for PSO. Omran, Salman, and Engelbrecht [58] presented a dynamic clustering approach (DCPSO) based on the integration of PSO with the K-means clustering algorithm. The PSO is used to select the best number of clusters with the K-means clustering algorithm used to refine the chosen clusters’ centers.

Chen and Zhang [59] combined K-means and PSO to propose RVPSO-K for clustering Web Usage patterns achieving better stability. Kao, Zahara, and Kao [60] proposed K-NM-PSO, which hybridized PSO and Nelder–Mead simplex search with K-means clustering algorithm. Kao and Lee [61] presented KCPSO—K-means and combinatorial particle swarm optimization, which do not require the specification of cluster number a priori. K-harmonic means (KHM) was hybridized with PSO by Yang, Sun, and Zhang [62] to fully use the advantages of the two algorithms for better cluster analysis. Niknam and Amiri [53] introduced FAPSO-AC-K, which combines fuzzy adaptive particle swarm optimization with ant colony optimization and K-means clustering algorithm for better cluster partition. Tsai and Kao [63] presented a selective regeneration PSO (SRPSO), which was hybridized with a K-means clustering algorithm to develop an efficient, accurate and robust K-means selective regeneration PSO (KSRPSO) for data clustering. Prabha and Visalakshi [64] proposed an improved PSO-based K-means clustering algorithm that integrates PSO and the traditional K-means clustering algorithm with normalization as a preprocessing step for transforming the dataset attributes values.

Emami and Derakhshan [65] proposed PSOFKM, which combined PSO with fuzzy K-means to explore the merits of the two algorithms solving the problem of initial states sensitivity of the traditional K-means clustering algorithm. Hybridization of K-means with improved PSO and GA for improved convergence speed and global convergence was proposed by Nayak et al. [66]. The IPSO handled the global search for optimal cluster center while GA was used to improve the particles quality and diversification of solution space. Niu et al. [48] proposed a population-based clustering technique that integrates PSO with the traditional K-means algorithm. Six different variants of PSO were integrated with the Lloyd’s K-means [67] separately, varying the PSO’s neighbor social communications. Ratanavilisagul [68] proposed an improvement on the regular hybridization of PSO and K-means clustering algorithm by applying mutation operation with PSO particles. Paul, De, and Dey [69] presented a modified PSO (MfPSO) based K-means algorithm where the MfPSO is employed to generate initial cluster centers for the K-means clustering algorithm. Jie and Yibo [70] proposed a technique for outlier detection by combining PSO with K-means for fault data sorting of feeder in distribution network information system. The PSO was used to optimize the cluster centroid while the K-means algorithm determined the optimal number of clusters. Chen, Miao, and Bu [71] presented an aggregation hybrid of K-means clustering algorithm with PSO for image segmentation.

3.1.3. Firefly Algorithm

The firefly algorithm (FA) is a swarm intelligence metaheuristic optimization technique that was first introduced by Yang in 2009 [72]. According to Xie et al. [73], FA has a unique capability of automatic subdivision compared with other metaheuristic search algorithms. Hassanzadeh and Meybodi [74] presented a hybrid algorithm K-FA that combined the K-means algorithm and firefly algorithm. The firefly algorithm was used to find centroid for specified k number of clusters with K-means algorithm used for refining the centroid. Mathew and Vijayakumar [75] proposed using a firefly-based clustering method to parallel K-means for handling a large number of clusters. Similar to Hassanzadeh and Meybodi [74], the FA finds the initial optimal centroid, which is then refined using K-means for improved clustering accuracy. Nayak et al. [76] presented an integrated clustering framework combining optimized K-means with firefly algorithm and Canopies for better clustering accuracy.

To address K-means’ initialization sensitivity and local optimal convergence, Behera et al. [77] proposed FCM-FA, hybridizing fuzzy C-means with a firefly algorithm for faster convergence. Nayak, Naik, and Behera [78] proposed a novel firefly-based K-means algorithm—FA-K-means, in which the global search capacity of the FA was used to resolve the problem of local convergence of the K-means for efficient cluster analysis. Xie et al. [73] proposed two variants of the FA (IIEFA—inward intensified exploration FA and CIEFA—compound intensified exploration FA) which are incorporated into the K-means clustering algorithm for improved clustering performance. Jitpakdee, Aimmanee, and Uyyanonvara [79] proposed a hybrid firefly algorithm and K-means algorithm for color image quantization. Kuo and Li [80] integrate a firefly-algorithm-based K-means algorithm with a firefly-algorithm-based support vector regression with wavelet transform in developing an export trade value prediction system. Kaur, Pal, and Singh [81] introduced a K-means and firefly algorithm hybridization for the intrusion detection system.

Langari et al. [82] proposed KFCFA—K-member fuzzy clustering and firefly algorithm, which is a combined anonymizing algorithm for protecting anonymized databases against identity disclosure in social networks. HimaBindu et al. [83] proposed a firefly-based K-means algorithm with global search capability for clustering big data. Wu et al. [84] proposed a novel kernel extreme learning machine model coupled with K-means clustering and firefly algorithm (Kmeans-FFA-KELM) for the monthly reference evapotranspiration estimation in parallel computation.

3.1.4. Bat Algorithm

The bat algorithm (BA), introduced by Xin-She Yang in 2010 [85], is one of the nature-inspired optimization algorithms based on the echolocation behavioral pattern of bats. K-Medoids was combined with the bat algorithm by Sood and Bansal [86] for partitioning clustering using the echolocation behavior of bats to determine the initial cluster number. Tripathi, Sharma, and Bala [87] hybridized the K-means algorithm with a novel dynamic frequency-based bat algorithm variant (DFBPKBA) as a new approach for clustering in a distributed environment with a better exploration and exploitation capability. The MapReduce model in the Hadoop framework was used to parallelize the hybrid algorithm to ensure satisfactory results within a reasonable time limit. Pavez, Altimiras, and Villavicencio [88] introduced the K-means binary bat algorithm (BKBA) using a generalized K-means-based binarization mechanism applied to the bat algorithm to solve multidimensional backpack problems. Gan and Lai [89] introduce a bat algorithm clustering based on K-means (KMBA) for automated grading of edible birds nest, which produce nearly 86% dataset clustering accuracy compared with the standard bat algorithm. Chaudhary and Banati [90] hybridized K-means and K-medoids with an enhanced shuffled bat algorithm (EShBAT). K-means and K-medoids were used in generating a rich starting population for EShBAT to produce an efficient clustering algorithm.

3.1.5. Flower Pollination Algorithm

The flower pollination algorithm (FPA) is a metaheuristic optimization algorithm motivated by the process of pollinating flowering plants. Xin-She Yang developed the first FPA in 2012 [91] as a global optimization technique. Jensi and Jiji [92] proposed a novel hybrid FPAKM clustering method that combines the flower pollination algorithm with the K-means clustering algorithm. Kumari, Rao, and Rao [93] introduce a flower pollination-based K-means clustering algorithm using vector quantization for better medical image compression.

3.1.6. Artificial Bee Colony

The artificial bee colony (ABC) is a swarm intelligence algorithm inspired by bees’ search mode and division of labor in fining the maximum amount of nectar [94]. Armano and Farmani [95] proposed kABC, which combined K-means and ABC to improve K-means capability in finding global optimum clusters. Tran et al. [96] presented EABCK, an enhanced artificial bee colony algorithm, and K-means to improve the performance of the K-means clustering algorithm. The ABC was guided by the global best solution with mutation operation to produce an enhanced version of EABC. Bonab et al. [97] combined an artificial bee colony algorithm and differential evolution with a modified K-means clustering algorithm to address the problem of local optimum convergence of K-means in color image segmentation.

The CAABC-K, which is a hybrid of chaotic adaptive artificial bee colony algorithm (CAABC) with K-means algorithm, was proposed by Jin, Lin, and Zhang [98]. The CAABC-K had better convergence speed and accuracy compared with some conventional clustering algorithms. Dasu, Reddy, and Reddy [99] integrate the K-means clustering algorithm and ABC optimization algorithm for remote sensing images classification. K-means algorithm was used for image segmentation, while ABC was used for classification. Huang [100] combined ABC with an accelerated k-means algorithm for color image quantization. Wang et al. [101] proposed the ABC-KM algorithm for the improvement of wind farm clustering. Modified artificial bee colony combined with K-means clustering algorithm—MABC-K, was proposed by Cao and Xue [102] to establish a hybrid algorithm framework for clustering problems.

3.1.7. Grey Wolf Optimizer

Mirjalili, Mirjalil, and Lewis [103] proposed the grey wolf optimizer (GWO) as a metaheuristic optimization algorithm mimicking grey wolves’ hunting mechanism and leadership hierarchy. Katarya and Verma [104] combined fuzzy c-mean (FCM) with grey wolf optimizer as a collaborative recommender system proposed to enhance system accuracy and precision. Korayem, Khorsid, and Kassem [105] proposed ‘K-GWO’—a combination of GWO and traditional K-means clustering algorithm into which a capacity constraint was incorporated for solving capacitated vehicle routing problems. Pambudi, Badharudin, and Wicaksono [106] enhanced the K-means clustering algorithm using GWO. The GWO rule was used in minimizing the SSE of the population and searching for a new cluster center. Mohammed et al. [107] introduced KMGWO, in which the K-means clustering algorithm was used to enhance GWO’s performance.

3.1.8. Sine–Cosine Algorithm

The sine–cosine algorithm (SCA) is a population-based optimization algorithm that uses a mathematical model based on sine and cosine function in finding the optimal solution to optimization problems [108]. The SCAK-means is a hybridization of the sine-cosine algorithm and K-means clustering algorithm proposed by Moorthy and Pabitha [109]. They integrated with a resource discovery system adopted in cloud computing resource sharing management.

3.1.9. Cuckoo Search Algorithm

The cuckoo search (CS) algorithm is a nature-inspired metaheuristic algorithm developed by Xin-She Yang in 2009 [110]. It imitates the obligate parasitism of special female cuckoo species, which mimic the color and pattern of their chosen host birds. Step size affects the precision of the cuckoo search metaheuristic algorithm [111]. Saida, Kamel, and Omar [112] combined the K-means algorithm with CS for document clustering to avoid the problem of a drastic increase in iterations in the standard CS. Girsang, Yunanto, and Aslamiah [113] proposed a combination of cuckoo search algorithm and K-means called FCSA to accelerate the computational time of the clustering algorithm. The FCSA uses CS in building robust initialization while K-means was used to accelerate the building of the solutions. Ye et al. [111] presented an improved cuckoo search K-means algorithm (ICS-Kmeans) to address the step size problem common with the cuckoo search algorithm. Lanying and Xiaolan [114] used the CS algorithm in optimizing the K-means algorithm for collaborative filtering recommendations. Tarkhaneh, Isazadeh, and Khamnei [115] introduced a hybrid algorithm combining the K-means algorithm with CS and PSO that yields more optimized results than each of the individual standard algorithms.

Singh and Solanki [116] integrate K-means with a modified cuckoo search algorithm (K-means modified cuckoo search) to achieve a global optimum solution in a recommender system. Arjmand et al. [117] proposed a hybrid clustering algorithm that combined the K-means clustering algorithm used for segmentation with cuckoo search optimization for generating the initial centroids for the K-means algorithm in breast tumor segmentation. García, Yepes, and Martí [118] proposed a K-means cuckoo search hybrid algorithm with the cuckoo search metaheuristics serving as the continuous space optimization mechanism and using the learning technique of the unsupervised K-means algorithm in the discretization of the obtained solution. Multiple kernel-based fuzzy c-means algorithm was hybridized with cuckoo search to produce MKF-cuckoo by Binu, Selvi, and George [119] with more effective objective functions designed by the researchers instead of using the K-means objective function. Manju and Fred [120] solved the problem of segmentation and compression of compound images using a hybrid of K-means clustering algorithm and multi-balanced cuckoo search algorithm. Deepa and Sumitra [121] combined cuckoo search optimization with a K-means clustering algorithm to achieve an optimal global solution in an intrusion detection system.

3.1.10. Differential Evolution

The differential evolutionary (DE) algorithm is a powerful and efficient population-based optimization algorithm based on evolutionary theory. It is presented as a floating-point encoding evolutionary algorithm for minimizing possibly nonlinear and non-differentiable continuous space functions [122,123]. Kwedlo [124] introduced DE-KM, a combination of differential evolution algorithm and K-means clustering algorithm. The mutation and crossover operation of DE generates each candidate solution, which is then fine-tuned using the K-means algorithm. Cai et al. [125] proposed a hybrid of DE and one-step K-means algorithm termed CDE (clustering-based DE) for solving unconstrained global optimization problems. The one-step K-means was introduced to enhance DE performance by acting as several multi-parent crossover operators to utilize the population information efficiently. Kuo, Suryani, and Yasid [126] proposed ACDE-K-means integrating automatic clustering based differential evolution algorithm with K-means algorithm seeking to improve ACDE algorithm’s performance by the use of the K-means algorithm for tuning the cluster centroids.

Sierra, Cobos, and Corrales [127] hybridized the K-means clustering algorithm and DE for continuous optimization using the DE operators to work on the groups generated by the K-means algorithm for better diversification and escaping from local convergence. Hu et al. [128] proposed an improved K-means clustering algorithm using a hybrid of DE and FOA (fruit fly optimization algorithm) embedded into K-means. Wang [129] proposed a weighted K-means algorithm based on DE with an initial clustering center and strong global search capability. Silva et al. [130] used a u-control chart (UCC) to automatically determine the k activation threshold for ACDE with the cluster number generated serving as the specified k value for the K-means algorithm, thus improving the performance of the clustering algorithm. Sheng et al. [131] presented a combination of differential evolution algorithms with adaptive niching and K-means termed DE-NS-AKO for partitional clustering. The K-means-based adaptive niching adjusts each niche size to avoid premature convergence. As reported earlier, Bonab et al. [97] presented a combination of DE with a modified K-means algorithm with ABC for color image segmentation. Mustafi and Sahoo [132] explored the combination of GA and DE to find the original seed point and determine the required cluster numbers for the traditional K-means algorithm to reduce the possibility of its convergence into local optimal.

3.1.11. Invasive Weed Optimization

The invasive weed optimization (IWO) proposed by Mehrabian and Lucas in 2006 [133] is a stochastic optimization algorithm that was inspired by a common agricultural phenomenon of invasive weeds colonization. IWO has a powerful exploitative and explorative capability [134]. Fan et al. [134] proposed a clustering algorithm framework for hybridizing IWO with a K-means algorithm to improve the performance of the traditional K-means algorithm. Pan et al. [135] presented a clustering algorithm combining IWO and K-means based on the cloud model—CMIWOKM. The cloud model-based IWO directs the K-means algorithm iterative search operation to ensure a definite evolution direction to improve the proposed algorithm’s performance. Boobord, Othman, and Abubakar [136] proposed a WK-means hybrid clustering algorithm combining IWO and K-means clustering. In WK-means, the initial solutions for the K-means algorithm are generated by the IWO algorithm. They further proposed hybridized clustering algorithm PCAWK adopting principal component analysis method to reduce redundant dimensionality of a real-world dataset and employed their WK-means algorithm to generate optimal clusters from the dataset [136]. Razi [137] presented a hybridization of IWO and DEA-based K-means algorithm for facility location problems where K-means was used for maintenance stations clustering while a zero-one programming model based on IWO was used to conduct the Pareto analysis of rank and distance.

3.1.12. Imperialist Competitive Algorithm

The imperialist competitive algorithm (ICA) is an evolutionary optimization algorithm inspired by imperialistic competition [138]. Niknam et al. [139] proposed a robust and efficient hybrid evolutionary clustering algorithm called hybrid K-MICA. K-MICA is a combination of K-means clustering algorithm and modified imperialist competitive algorithm where MICA is used to generate the population and form the initial empires; the K-means algorithm is then used to improve the empire’s colonies and imperialists’ positions, which are then fed back into MICA. Abdeyazdan [140] presented ICAKHM, a hybridization of modifier imperialist competitive algorithm and K-harmonic means to solve the problem of local optimum convergence of the K-harmonic means. Emami and Derakhshan [65] proposed ICAFKM combining imperialist competitive algorithm with fuzzy K-means to assist the regular FKM escape from converging into local optimum and increase convergence speed.

3.1.13. Harmony Search

The harmony search (HS) is a metaheuristic optimization algorithm that imitates musicians’ music improvisation process of searching for a perfect state of harmony [141]. Forsati et al. [141] presented a pure HS clustering algorithm for a globalized search in the solution space. The proposed HSCLUST was then hybridized with a K-means clustering algorithm in three different modes to avoid the problem of initial parameter dependence of the K-means algorithm. Each proposed hybridization depended on the stage at which the K-means algorithm is performed in the clustering process. Mahdavi and Abolhassani [142] proposed harmony K-means (HKA) based on an HS optimization algorithm for document clustering for faster global optimum convergence. Cobos et al. [143] hybridized the K-means algorithm with global best HS, frequent term sets, and Bayesian information criterion termed IGBHSK for automatic Web document clustering. The Global-Best HS performs the global search in the solution space while the K-means algorithm seeks the optimum value in the local search space. Chandran and Nazeer [144] proposed an enhanced K-means clustering algorithm based on hybridization of the K-means with improved HS optimization technique for finding global optimum solutions. Nazeer, Sebastian, and Kumar [145] presented HSKH—harmony search K-means hybrid for gene expression clustering, which produced a more accurate gene clustering solution. Raval, Raval, and Valiveti [146] proposed a combination of HS and K-means for optimizing wireless sensor network clustering. The HS was used to generate the initial solution, which is then fed into the K-means algorithm for a more precise solution. Kim et al. [147] proposed a scheme for load balancing with switch migration for the distributed software-defined network (SDN) employing a combination of HS and K-means for clustering the switches.

3.1.14. Blackhole Algorithm

The phenomenon of the black hole in astrophysics inspired the design of the blackhole (BH) algorithm. During optimization, the best candidate acts as the black hole in each iteration and pulls other candidates to itself [148]. It does not require manual parameter setting [149], and it lacks the capability for exploring the search space [150]. Eskandarzadehalamdary et al. [151] proposed BH-BK comprising blackhole and bisecting K-means algorithms for precise clustering and global optimal convergence with local refinement. Pal and Pal [152] hybridized the K-means clustering algorithm with the BH optimization approach for data clustering. Some better results from the K-means algorithm are used in initializing a portion of the population while the rest are randomly initialized. The BH algorithm was used by Feng, Wang, and Chen [153] in determining the K-means algorithm’s initial centroids for their proposed new clustering method for Image classification based on the improved spatial pyramid matching model.

3.1.15. Membrane Computing

Membrane computing (MC) is a P system classified under a distributed parallel computing model [154]. A K-means clustering method based on the P system and DNA genetic was proposed by Jiang, Zang, and Liu [155]. The initial cluster center was analyzed using DNA encoding, and the clustering was realized using the P system. Zhao and Liu [156] proposed a GKM-genetic K-means membrane-clustering algorithm combining genetic K-means algorithm and membrane computing for clustering multi-relational dataset harnessing the benefit of the P system parallelism with the K-means algorithm local search capability and the good convergence of the GA. Weisun and Liu [157] proposed a new P system hybridized with a modified differential evolution K-means algorithm to improve the K-means algorithm’s initial centroids.

Zhao, Liu, and Zhang [158] constructed a P system for solving the K-medoids algorithm providing a new idea for great parallelism and lower computational time complexity for cluster analysis. Wang, Xiang, and Liu [159] designed a tissue-like P system for their proposed hybrid algorithm of K-medoids and K-means algorithms. The K-means algorithm is used to obtain the elementary clustering result, and the K-medoids is then used to optimize the results. The tissue-like P system creates a parallel platform for the execution, thus efficiently improving the computational time. Wang, Liu, and Xiang [160] proposed an effective method for initial centroid selection for the K-means algorithm, which incorporates a tissue-like P system to avoid the boundedness of the K-means initialization method.

3.1.16. Dragonfly Algorithm

The dragonfly algorithm (DA) is inspired by the natural static and dynamic swarming behaviors of dragonflies. In DA, the exploration and the exploitation phases are modeled using the dragon flies social interaction in their navigation, food searching, and enemy avoidance while swarming statically or dynamically [161]. Angelin [162] proposed a dragonfly-based K-means clustering combined with a multi-layer feed-forward neural network for outlier detection using an optimization-based approach. Kumar, Reddy, and Rao [163] combined the fuzzy c-means algorithm with the wolf hunting-based dragonfly to detect change in synthetic aperture radar (SAR) images.

3.1.17. Ant Lion Optimizer

The ant lion optimizer (ALO) is inspired by the hunting mechanisms of antlions in nature. It involves five main steps: ants’ random walks, traps building, entrapments in traps, prey catching, and traps rebuilding. Majhi and Biswal [164] proposed a K-means clustering algorithm with ALO for optimal cluster analysis, which performed better in terms of F-measure and sum of intra-cluster distances. Chen et al. [165] combined quantum-inspired ant lion optimizer with K-means algorithm to propose QALO-K, an efficient hybrid clustering algorithm. Murugan and Baburaj [166] integrated improved K-medoids with ant lion optimizer and PSO to proposed ALPSOC, which can obtain optimized cluster centroid with improved clustering performance while preserving the computational complexity. Naem and Ghali [167] proposed a hybridized clustering algorithm termed K-median modularity ALO that combined K-median with ant lion optimizer to handle the problem of community detection in the social network. Dhand and Sheoran [168] proposed a secure multi-tier energy-efficient routing protocol (SMEER) that combined an ant lion optimizer (as cluster head selector) with a K-means algorithm (for clustering).

3.1.18. Social Spider Algorithm

The social spider optimization (SSO) algorithm was proposed by Cuevas in 2013, simulating the cooperative behavior of social spiders based on the biological laws of a cooperative colony [169]. Chandran, Reddy, and Janet [170] proposed a hybrid of social spider optimization and K-means termed SSOKC to speed up the clustering process of SSO. Thiruvenkatasuresh and Venkatachalam [171] employed the fuzzy c-means clustering process, which adopted the social spider optimization technique with GA for finding optimized cluster centroid in their proposed brain tumor images segmentation process.

3.1.19. Fruit Fly Optimization

The fruit fly (FFO) is inspired by the fruit fly’s foraging behavior in nature [172]. A hybrid of K-means and fruit fly optimization termed Kmeans-FFO was proposed by Sharma and Patel [173] for optimal clustering quality. Jiang et al. [174] used a fruit fly algorithm and K-means clustering algorithm to optimize earthquake rescue center site selection and layout. Gowdham, Thangavel, and Kumar [175] proposed using the fruit fly algorithm to select the initial cluster centroid for the k-means clustering algorithm in finding the optimal number of clusters in a dataset. Hu et al. [128] proposed DEFOA-K-means, an improved K-means clustering algorithm that uses a hybrid of fruit fly optimization algorithm and differential evolution (DEFOA) for optimal cluster solutions that are not zero. Wang et al. [176] proposed FOAKFCM, a kernel-based fuzzy c-means clustering based on fruit fly algorithm where the initial cluster center is determined using the fruit fly algorithm first, and then the kernel-based fuzzy c-means is applied in classifying the data.

3.1.20. Bees Swarm Optimization

The bees swarm optimization (BSO) is a swarm-intelligence-based optimization algorithm inspired by the foraging behavior of bees such that a swarm of bees cooperates together in finding a solution to a problem [177]. Djenouri, Belhadi, and Belkebir [178] used the combination of the K-mean algorithm and bee swarm optimization in document information retrieval. The K-means algorithm generates similar clusters from the collection document, while the BSO was used to deep explore the document clusters. Aboubi, Drias, and Kamel [179] proposed BSO-CLARA for clustering large datasets combining K-medoids clustering and bees swarm optimization behavior. Djenouri, Habbas, and Aggoune-Mtalaa [180] used the K-means clustering algorithm as a decomposition tool in their proposed improved version of the BSO metaheuristic, termed BSOGD1, which incorporates the decomposition method for solving the MAX-SAT problem.

3.1.21. Bacterial Colony Optimization

The bacterial colony optimization (BCO) algorithm is inspired by the basic growth law of bacterial colonies [181]. It requires a high computational cost for completing a given solution. Revathi, Eswaramurthy, and Padmavathi [182] hybridized the K-means clustering algorithm with BCO to produce a BCOKM clustering algorithm for better cluster partition with reduced computational cost compared with BCO clustering. The BCO searches for the global optimum solution in the search space and then hands the clustering process to the K-means algorithm. Vijayakumari and Deepa [183] combined the fuzzy c-means algorithm with the fuzzy BCO (FBCO) to propose a hybrid fuzzy clustering algorithm (HFCA) for higher cluster analysis performance.

3.1.22. Stochastic Diffusion Search

The stochastic diffusion search (SDS) is a multi-agent global search and swarm intelligence optimization algorithm based on simple iterated agents’ interactions [184]. The strong mathematical framework of the SDS algorithm describes its behavior in relation to resource allocation, global optimum convergence, and linear time complexity with robustness and criteria for minimal convergence. Karthik, Tamizhazhagan, and Narayana [185] proposed a stochastic diffusion search K-means clustering technique named ‘scattering search K-means’ (SS-K means) for locating optimal clustering points for the identification of points of data leakage in social networks.

3.1.23. Honey Bee Mating Optimization

The honey bee mating optimization (HBMO) is a swarm-based optimization algorithm inspired by the natural process of real honey bees mating [186]. Teimoury et al. [187] hybridized K-means with the honey bee mating algorithm to resolve the problems associated with the K-means clustering algorithm to improve the performance of the clustering algorithm. Aghaebrahimi, Golkhandan, and Ahmadnia [188] combined the K-means algorithm with HBMO to solve the problem of localization and sizing of flexible AC transmission systems (FACTS) in a power system to reduce the generation, transmission, and power costs.

3.1.24. Cockroach Swarm Optimization

The cockroach swarm optimization (CSO) is a swarm intelligence algorithm inspired by the social behavior of cockroaches mimicking their ruthless social behavior, chase swarming, and dispersion [189]. Senthilkumar and Chitra [190] combined the K-means algorithm and cockroach swarm optimization (MCSO) in their proposed novel hybrid heuristic–metaheuristic load balancing algorithm for IaaS-cloud computing resource allocation. K-means clustering was used to cluster the files into small chunks to reduce the time required for file download, while the MCSO was employed in measuring the load ratio.

3.1.25. Glowworm Swarm Optimization

The glowworm swarm optimization (GSO) is a nature-inspired optimization algorithm based on lighting worms’ natural behavior, which controls their light emission using it for different purposes [191]. K-means algorithm was combined with basic glowworm swarm optimization by Zhou et al. [192] for their proposed novel K-means image clustering algorithm based on GSO termed ICGSO to effectively override the problems inherent in the K-means algorithm and produce better clustering qualities. Onan and Korukoglu [193] presented a cluster analysis approach based on GSO and K-means clustering algorithms. Tang et al. [194] hybridized the k-means algorithm with an improved GSO self-organizing clustering algorithm for automatic cluster analysis with better cluster quality.

3.1.26. Bee Colony Optimization

The bee colony optimization (BCO) is a swarm-intelligence-based algorithm that simulates the bee swarm’s autonomy and self-organizing with distributed functioning behavior [195]. The intelligence of collective bees’ is explored in BCO for possible applications in finding the solution to combinatorial problems which are characterized by uncertainty. Das, Das, and Dey [196] integrate the K-means algorithm and modified bee colony optimization algorithms producing MKCLUST and KMCLUST to improve the performance of MBCO in terms of global optimum convergence and diverse clustering solutions. In MKCLUST, the K-means algorithm was used to fine-tune MBCO explorative power further, while in the KMCLUST, the local optimal problem of K-means was dealt with improving the exploration capability and solution’s diversity. Four different K-means algorithms with BCO algorithm hybrids were proposed by Forsati, Keikha, and Shamsfard [197] which solved the problem of local optimum convergence for large and high dimensional datasets.

3.1.27. Symbiotic Organism Search

The symbiotic organism search (SOS) is a nature-inspired metaheuristic algorithm based on the three symbiosis relationships mechanism often employed by the individual prescribed for survival in the ecosystem. These relationship behaviors include mutualism, commensalism, and parasitism, denoting the biological interactions between organisms. SOS has only one control parameter, which makes its implementation easier compared with other metaheuristic optimization approaches. In Yang and Sutrisno [198], automatic K-means was applied to symbiotic organisms search algorithm initial solution for the creation of subpopulation which enhances the quality and efficiency of searching. The sub-ecosystem created through the automatic K-means enables the CSOS algorithm to combine the local and global searches on the dataset.

3.2. RQ2. Which of the Reported Hybridization of Nature-Inspired Meta-Heuristics Techniques with K-Means Clustering Algorithm Handled Automatic Clustering Problems?

Table 1 presents the summary of the reviewed literature on hybridized algorithms. It includes a hundred and forty-seven (147) hybridized K-means with 28 different MOA clustering algorithms. The fifth column indicates the characteristic of each hybridized clustering algorithm as either automatic or non-automatic. The role of the corresponding MOA and K-means algorithms in the hybridized algorithms was stated in columns eight and nine, respectively. In contrast, columns ten and eleven, respectively, report the dataset used for the algorithm testing and the criteria for their performance measure. From the 147 reviewed articles, only 23 K-means/MOA hybrid algorithms addressed the issue of automatic data clustering.

Table 1. List of hybridized algorithms combining K-means algorithm with various MOA.

	Metaheuristic Algorithm		Objective		Application	Method for Automatic Clustering	MOA Role	K-Means Role	Dataset Used for Testing	Compared with	Performance Measure
Genetic Algorithm (GA)
1	Zhou et al., [45]-NoiseClust	Niche Genetic Algorithm (NGA) and K-means++		Automatic	Global Positioning System	Density-Based Method				Adaptive probabilities of crossover and mutation
2	Dai, Jiao & He, [28]-PGAClust	Parallel Genetic Algorithm (PGA) and K-means		Automatic		Dynamic mining of cluster number
3	Li et al. [40]	GA and K-means		Automatic		Adopting a k-value learning algorithm using GA
4	Kuo et al. [39]-SOM+GKA	SOM and Modified GKA		Automatic	Market Segmentation in Electronic Commerce	Self-Organizing Feature Maps (SOM) neural networks				SOM+K, K-means	Within Cluster Variations (SSW) and number of misclassifications
5	Eshlaghy & Razi [42]	Grey-based K-means and GA		Non-Automatic	Research and Project selection and management		Project allocation selection	clustering of different projects			SSE
6	Sheng, Tucker & Liu [30]-NGKA	Niche Genetic Algorithm (NGA) + one step of K-means	Improving GA optimization procedure for general clustering	Non-Automatic	Gene Expression				Gene Expression Data (Subcellcycle_384 subcellcycle_2945 data, Serum data Subcancer data	GGA and GKA	Sum of Square Error (SSE)
7	Karegowda et al. [41]	K-means + GA	Avoidance of random selection of cluster centers	Non-Automatic	Medical Data Mining		initial cluster center assignment	Clustering of dataset	PIMA Indian diabetic dataset		Classification error and execution time
8	Bandyopadhyay & Maulik [24]-KGA	GA + K-means	Escape from local optimum convergence	Non-Automatic	Satellite image classification		GA perturb the system to avoid local convergence	determining new cluster center for each generation	Artificial Data Real-life data sets (Vowel data, iris data, Crude oil data)	K-means and GA-Clustering
9	Cheng et al. [25]-PGKA	Prototype Embedded GA + K-Means	Encoding Cluster prototypes for general GA clustering	Non-Automatic					SKY testing data	K-Means, GKA and FGKA	Ga based criteria
10	Zhang & Zhou [35]-Nclust	novel niching genetic algorithm (NNGA) + K-means	Finding better cluster number automatically	Automatic	General Cluster Analysis	Improved canopy and K-means ++			UCI dataset	GAK and GenClust	SSE, DBIPBM, COSEC, ARI and SC
11	Ghezelbash, Maghsoudi & Carranza [38] -Hybrid GKMC	Genetic K-means clustering + Traditional K-means algorithm	General Improvement of K-Means	Non-Automatic	Geochemical Anomaly Detection from stream sediments		Determining cluster center locations	General Clustering	GSI Analytical Data	Traditional K-Means Clustering (TKMC)	Prediction rate curve based on a defined fitness function
12	Mohammadrezapou, Kisi & Pourahmadm [46]	K-means + Genetic Algorithm and Fuzzy C-Means + Genetic Algorithm	Avoidance of random selection of cluster centers	Automatic	Homogeneous regions of groundwater quality identification	GA method	Determining the optimum number of clusters	General Clustering			Av. Silhouette width Index; Levene’s homogeneity test; Schuler & Wilcox classification; Piper’s diagram
13	El-Shorbagy et al. [37]	K-means + GA	Combining the advantages of K-means and GA in general clustering	Non-Automatic	Electrical Distribution system		GA Clustering with a new mutation	GA population Initialization for best cluster centers	UCI dataset	K-means Clustering and GA-Clustering
14	Barekatain, Dehghani & Pourzaferani [44]	K-means + Improved GA	New cluster-based routing protocols	Automatic	Energy Reduction and Extension of network Lifetime		Determine the optimum number of clusters	Dynamic clustering of the network	Ns2Network (Fedora10)	Other network routing protocols, i.e., LEACH, GABEEC and GAEEP.
15	Lu et al. [43]	K-means + GA	Combining the advantages of the two algorithms	Non-Automatic	Multiple Travelling Salesman Problem
16	Sinha & Jana [33]	GA with Mahalanobis distance + K-Means with K-means++ Initialization	clustering algorithm for distributed dataset	Automatic		GA method	Initial clustering using GA method	Fine-tuning the result obtained from GA clustering	Breast Cancer Iris Glass Yeast)	Map Reduced-based Algorithms, MRk-means, parallel K-means and scaling GA	Davies-Bouldin index, Fisher’s discriminant ratio, Sum of the squared differences
17	Laszlo & Mukherjee [26]	GA + K-means	improving GA-based clustering method	Non-Automatic			Evolving initial cluster centers using hyper-quad tree	To return the fitness value of a chromosome	GTD, BTD, BPZ, TSP-LIB-1060 TSP-LIB-3038; Simulated dataset	GA-based clustering, J-Means
18	Zhang, Leung & Ye [199]	GA + K-means	Improving accuracy	Non-Automatic	Credit Scoring		Reduce data attribute’s redundancy	Removal of noise data	German credit dataset Australian credit dataset	C4.5, BPN, GP, SVM+GA and RSC
19	Kapil, Chawla & Ansari [3]	K-means + GA	Optimizing the K-means	Automatic	General Cluster Analysis	GA method	Generating initial cluster centers	Basic K-means clustering	Online User dataset	K-means	SSE
20	Rahman & Islam [32]-GENCLUST	GA + K-means	Finds cluster number with high-quality centers	Automatic	General Cluster Analysis	Deterministic selection of Initial Genes	Generating initial cluster centers	Basic K-means clustering	UCI dataset	RUDAW, AGCUK, GAGR, GFCM and SABC	Xie-Beni Index, SSE, COSEC, F-Measure, Entropy, and Purity
21	Islam et al. [34] GENCLUST++	GA + K-means	Computational complexity reduction	Automatic	General Cluster Analysis	GA method	Generating initial cluster centers	Basic K-means clustering	UCI dataset	GENCLUST-H, GENCLUST-F, AGCUK, GAGR, K-Means	GA Performance Measure
22	Mustafi & Sahoo [36]	GA + DE + K-means	Choice of initial centroid	Automatic	Clustering Text Document	Using DE	Generating initial cluster centers	Basic K-means clustering	Corpus	K-Means	Standard clustering validity parameters
23	Laszlo & Mukherjee [27]	GA + K-means	Superior Partitioning	Non-Automatic					German credit dataset Australian credit dataset
24	Patel, Raghuwanshi & Jaiswal [200]-GAS3KM	GAS3 + K-means	Improving the performance of GAS3	Automatic		GA method	Generating initial cluster centers	Basic K-means clustering	Unconstrained unimodal and multi-modal functions with or without epistasis among n-variables.	GAS3	GA Performance Measure
25	Xiao, Yan, Zhang, & Tang [31]-KMQGA	K-means + QGA	Quantum inspired GA for K-means	Automatic		GA method	Generating initial cluster centers	Basic K-means clustering	Simulated datasets Glass, Wine, SPECTF-Heart, Iris	KMVGA (Variable String Length Genetic Algorithm)	Davies–Bouldin rule index
Particle Swarm Optimisation (PSO)
26	Jie and Yibo [70]	PSO + K-means	Outlier detection	Non-Automatic	Distribution Network Sorting		Optimizing the clustering center	Determining the optimal number of Clusters	Simulated datasets	K-Means	SSE
27	Tsai & Kao [63]-KSRPSO	Selective Regeneration PSO + K-means	SRPSO Performance improvement	Non-Automatic			Global optimal convergence	Basic K-means clustering	Artificial datasets, Iris, Crude oil, Cancer, Vowel, CMC, Wine, and Glass	SRPSO, PSO and K-Means	Sum of intra-cluster distances and Error Rate (ER)
28	Paul, De & Dey, [69]-MfPSO based K-Means	MfPSO + K-Means	Improved multidimensional data clustering	Non-Automatic			Cluster center generation	Basic K-Means clustering	Iris, Wine, Seeds, and Abalone	K-Means and Chaotic Inertia weight PSO	DBI, SI, Means, SD and computational time, ANOVA test and a two-tailed t-test conducted at 5% significance
29	Prabha & Visalakshi [64]-PSO-K-Means	PSO + Normalisation + K-Means	Improving performance using normalization	Non-Automatic			Global optimal convergence	Basic K-means clustering	Australian, Wine, Bupa, Mammography, Sattelite Image, and Pima Indian Diabetes	PSO-KM, K-Means	Rand Index, FMeasure, Entropy, and Jacquard Index
30	Ratanavilisagul [69]-PSOM	PSO + K-Means + mutation operations applied with particles	Avoidance of getting entrapped in local optima	Non-Automatic			Global optimal convergence	Basic K-means clustering	(Iris, Wine, Glass, Heart, Cancer, E.coli, Credit, Yeast	Standard PSO, PSOFKM, PSOLF-KHM	F-Measure (FM), Average correct Number (ACN), and Standard Deviation (SD)of FM.
31	Nayak et al. [66]	Improved PSO + K-Means	optimal cluster centers for non-globular clusters	Non-Automatic			Global optimal convergence	Basic K-means clustering		K-Means, GA-K-Means, and PSO-K-Means
32	Emami, & Derakhshan [65]-SOFKM	PSO + FKM	Escape from local optimum with increased convergence speed	Non-Automatic			Global optimal convergence	Fuzzy K-means clustering	FKM, ICA, PSO, PSOKHM, and HABC algorithms	Sample, Iris, Glass, Wine, and Contraceptive Method Choice (indicated as CMC)	F-Measure (FM) and Runtime Metrics
33	Chen, Miao & Bu [71]	PSO + K-Means	Solving initial center selection problem and escape from local optimal	Non-Automatic	Image Segmentation		Global optimal convergence	Dynamic clustering using k-means algorithm	Lena, Tree and Flower images from the Matlab Environment	K-Means PSOK	Sphere function and Griewank function
34	Niu et al. [48]	Six different PSOs with different social communications + K-means	Escape from local optimum convergence with accelerated convergence speed	Non-Automatic			Global optimal convergence	Refining partitioning results for accelerating convergence	Iris, Wine, Coil2, Breast Cancer, German Credit, Optdigits, Musk, Magic 04, and Road Network with synthetic datasets	PSC-RCE, MacQueens K-Means, ACA-SL, ACA-CL, ACA-AL and Lloyd’s K-means	Mean squared error (MSE—sum of intra-cluster distances)
35	Yang, Sun & Zhang [62]-PSOKHM	PSO + KHM	Combining the merits of PSO and KHM	Non-Automatic			Global optimal convergence	Refining cluster center and KHM clustering	Artificial datasets, Wine, Glass, Iris, breast-cancer-Wisconsin, and Contraceptive Method Choice.	KHM, PSO	Objective function of KHM and F-Measure
36	Chen & Zhang [59]-RVPSO-K	PSO + K-means	Improved stability, precision, and convergence speed.	Non-Automatic	Web Usage Pattern Clustering		A parallel search for optimal clustering	Refining cluster center and K-means clustering	Two-day Web log of a university website	PSO-K	Fitness Measure and Run-time
37	Niknam, & Amiri, [53]-APSO-ACO-K	Fuzzy Adaptive PSO + ACO + K-means	Solving non-linear partitioning clustering problem	Non-Automatic			Provide Initial state for K-means algorithm	Basic K-means clustering	Artificial datasets, Iris, Wine, Vowel, Contraceptive Method Choice (CMC), Wisconsin breast cancer, and Ripley’s glass	PSO, ACO, SA, PSO–SA, ACO–SA, PSO–ACO, GA, TS, HBMO, and K-means	Total mean-square quantization error and F-Measure
38	Kao, Zahara & Kao [60]-K-NM-PSO	K-means + + PSO	Effective global convergence	Non-Automatic			Providing more accurate clustering	Provide initial seedling	Artificial datasets, Vowel, Iris, Crude-oil, CMC, Cancer, Glass, and Wine	PSO, NM–PSO, K–PSO, and K-means	Sum of the intra-cluster distances and the Error Rate
39	Omran, Salman & Engelbrecht [58]-DCPSO	Dynamic Clustering PSO + K-means	An automatic clustering with reduced effect of initial conditions	Automatic	Image Segmentation	Binary PSO optimization	Basic PSO clustering	Refine cluster center	Lenna, mandrill, jet, peppers, one MRI, and one satellite image of Lake Tahoe	GA and Random Search dynamic Clustering	Dunn’s index, Validity index proposed by Turi, S_Dbw validity index
40	Van der Merwe & Engelbrecht [49]	PSO + K-means	Improving the performance of PSO	Non-Automatic			PSO clustering	Initial Seedling for PSO	Artificial datasets Iris, Wine, Breast cancer, and Automotives	K-Means and PSO	The Quantization error, the intra-cluster distances and the inter-cluster distances
41	Kao & Lee [61]-KCPSO	Combinatorial PSO + K-means		Automatic		Discrete PSO to optimize cluster numbers	Optimizing the number of clusters	Basic K-means clustering	Artificial datasets, Iris, and Breast Cancer	DCPSO and GCUK	DB index
Firefly Algorithm (FA)
42	Mathew & Vijayakumar [75]-MPKM	K-means + Firefly	Parallelization of K-Means	Non-Automatic			Initial optimal cluster centroid	Refine optimized centroid	Wisconsin diagnostic breast cancer, Wine, Glass, and Credit data	Parallel K-means	Accuracy, SSW, SSB, DBI, DDI and SC.
43	Jitpakdee, Aimmanee & Uyyanonvara [79]- FA-K	K-means + Firefly	Hybrid-clustering-based color quantization	Non-Automatic	Colour Image Quantization		Initial cluster centroids and Global optimal convergence	Refine initial centroids	Three images from USC-SIPI Image Database (Lena, Peppers, and Mandrill)	FA and K-Means	Mean Square Error (MSE) and Peak Signal-to-Noise Ratio (PSNR)
44	Kuo & Li [80]	Wavelet Transform + FA based K-Means + F A based SVR	Forecasting model with wavelet transform	Non-Automatic	Export Trade Forecasting		Noise detection and Normalisation	Basic clustering		GA-SVR, PSO-SVR, FA-SVR and DE-SVR	Mean Square Error (MSE)
45	HimaBindu et al. [83]	Firefly + K-Means	Improved Big Data Clustering	Non-Automatic			Generate initial cluster centroids	Basic K-means clustering	Iris Plants database, Glass, Wine, two microarray information indexes and Artificial datasets.	K-Means, K-Means++	Total computation time, centroid selection time and accuracy
46	Langari et al. [82]-KFCFA	K-member Fuzzy clustering + FA	A combined anonymizing algorithm	Non-Automatic	Social Network Privacy Preservation		Optimizing the primary clusters	The use of the K-member version of fuzzy c-means	Social network databases from Facebook, Twitter, Google + and YouTube
47	Kaur, Pal & Singh [81]	K-means + Firefly	IDS training model for data classification	Non-Automatic	Intrusion Detection		Initialize method for the K-Means	Clustering for Classification	NSL-KDD dataset	K-Means + Bat K-Means + Cuckoo, K-Means++, K-Means, Farthest First and Canopy	CCI, TP, FP Precision, Recall, F-Measure, ROC and Time to build training model.
48	Nayak et al. [77]	Optimized K-means with firefly and Canopies	A hybrid algorithm for classification	Non-Automatic			Pre-clustering	Basic Clustering	Haberman’s survival dataset	K-means algorithm	Classification accuracy
49	Xie et al. [74]-IIEFA and CIEFA	K-means + Improved Firefly	resolve initialization sensitivity and local optimal traps	Non-Automatic			FA Clustering	Generate Initial Cluster Models as seed solution	ALL-IDB2 database Sonar, Ozone, Wbc1, Wbc2 Wine, Iris, Balance, Thyroid, and E. coli	GA, ACO, K-means, FA, DA, SCA, CFA, CFA2, NaFA, VSSFA, and MFA	Sum of intra-cluster distances Av.accuracy Av.sensitivity, Av.specificity & macro-average F-score
50	Wu et al. [84]-Kmeans-FFA-KELM	K-means + FFA + Kernel Extreme Learning Machine Model		Non-Automatic	Evapotranspiration Estimation		Building various sub-models	Decomposition of training dataset into multiple subsets	meteorological data (Tave, Tmax, and Tmin), wind speed, relative humidity and sunshine	FFA-KELM	Coefficient of determination, RMSE, MAE, SI and NSE
51	Behera et al. [77] -FCM-FA	Fuzzy C-Means + FireFly Algorithm	tackles Fuzzy C-Means problems	Non-Automatic
52	Nayak, Naik & Behera [79]-FA-K-means	Firefly + K-means	global search capacity for K-means	Non-Automatic
53	Hassanzadeh & Meybodi [74]-K-FA	K-means + Firefly	Finding initial centroids	Non-Automatic			Finding initial centroids	Refining the centroids	Standard data set from UCI (Iris, WDBC, Sonar, Glass, and Wine)	K-means, PSO, KPSO	Intra-cluster distance and clustering error
Bat Algorithm (BAT)
54	Tripathi, Sharma & Bala [87]-DBPKBA	Bat algorithm + K-means	the parallelized approach in a distributed environment	Non-Automatic			Obtaining global optimum convergence	better population initialization	Wine, Magic, Poker hand and Replicated wine	K-means, PSO, and Bat Algorithm	Best and Average intra-cluster distance
55	Chaudhary & Banati [90]-HESB	EShBAT + K-medoids + K-means	Leveraging optimisation capabilities	Non-Automatic			Dividing populations into groups	starting population and refining solutions		BA, EShBAT, K-means, K-Medoids
56	Gan, & Lai [89]-KMBA	K-means + Bat Algorithm	Classification of EBN	Non-Automatic	EBN Classification		Basic Bat Algorithm Clustering	Initiating Initial points for BA	Three classes of data (Grades AA, A, and B)		Classification Accuracy
57	Pavez, Altimiras, & Villavicencio [88]	K-means + Binary Bat Algorithm	demonstrate K-means technique utility in binarization	Non-Automatic	Multidimensional Backpack Problem
58	Sood & Bansal [86]	K-Medoids + Bat Algorithm		Automatic			Generating initial cluster center for K-Medoids	K-Medoids clustering		K-Medoids
Flower Pollination Algorithm (FPA)
59	Jensi & Jiji [92]-FPAKM	K-means + FPA	Combining the advantages of the two algorithms	Non-Automatic			Provide Initial seedlings for K-means	K-means Clustering	Artificial dataset iris, thyroid, wine, CMC, crude oil, and glass	FPA, K-means	Mean-square quantization error (MSE)
60	Kumari, Rao & Rao [93]	K-means + FPA	optimum solutions in Image compression		Image Compression						Peak signal to noise ratio (PSNR), mean square error (MSE) and fitness function.
Artificial Bee Colony (ABC)
61	Armano & Farmani [95]-kABC	K-means + ABC	finding a global optimum solution	Non-Automatic			ABC Clustering	Use K-means for initial seedlings	Iris, Wine, and Contraceptive Method Choice (CMC)	K-means	Distortion Criterion, Computational Cost, SD and F-Measure
62	Cao & Xue [102]-MABC-K-means	Modified ABC + K-means	hybridized framework for cluster analysis.	Non-Automatic	Customer Relationship Management		Provide initial cluster center	Basic K-means Clustering	Simple dataset of customers and their orders of an e-commerce platform in the first quarter.	Differential Evolution algorithm (DEA), standard Genetic algorithm (GA) and standard Artificial Bee Colony algorithm (ABC)	The mean and variance of Griewank, Rastrigin, Rosenbrock, Ackley and Schwefel functions.
63	Wang et al. [101]-ABC-KM	ABC + K-means	Improving the effectiveness of Wind farm clustering	Non-Automatic	Modeling of Farms with DFIGs		Provide initial cluster center	Basic K-means Clustering	MW DFIG	K-means	Wind speed disturbances and short-circuit faults
64	Huang [100]	ABC + Accelerated K-means		Non-Automatic	Colour Image Quantization		Provide initial cluster center	Basic K-means Clustering	Lena, Baboon, Lake, Peppers, and Airplane with a size of 512 × 512	SFLA-CQ	Average mean square, error, the standard deviation, and average computation time.
65	Tran et al. [96] -EABCK	Enhanced ABC + K-means	improvement for K-means algorithm	Non-Automatic			Generate initial cluster center	Basic K-means Clustering	Artificial datasets (Iris, Wine, Glass, E.coli, Liver disorder, Vowel, Pima, WDBC, and CMC	ABC, CABC, K-means, HABC, K-means++ and FAPSO-ACO-K	Mean square error (MSE) and Euclidean distance.
66	Bonab et al. [97]	Modified K-means + ABC + DE	escape from local optimum	Non-Automatic
67	Jin, Lin & Zhang [98]-CAABC-K-means.	CAABC + K-means	for optimal clustering	Non-Automatic			Generate initial points for K-means	clustering	Iris, Balance-Scale, Wine, E.coli, Glass, Abalone, Musk, Pendigits, Skin Seg, CMC, and Cancer	ABC, IABC, HABC, CAABC, DFSABCelite and PSO+K-means	Sphere, Rosenbrock, Rastrigin, Alpine and Ackley
68	Dasu, Reddy & Reddy [99]	K-means + ABC	Satellite Image Classification	Non-Automatic	Image Classification		Classification	Segmentation	Remote sensing Images	PSO	Sensitivity, Specificity, Overall accuracy and Kappa Coefficient.
Grey Wolf Optimization (GWO)
69	Pambudi, Badharudin & Wicaksono [106]-GWO-K-means	GWO + K-means	Optimizing the weakness of K-means through GWO	Non-Automatic	Image Segmentation		Generate initial points for K-means	initial centroid refinements, final optimal solution	Brain MRI	K-means	Sum of Square Error (SSE)
70	Korayem, Khorsid & Kassem [105]-K-GWO	K-means + GWO	cluster analysis performance improvement	Non-Automatic	Capacitated vehicle routing Problem		Generate initial points for K-means	K-means clustering	Benchmark problems downloaded from the web http://www.branchandcut.org/ accessed on 17 October 2021.	Compared three different versions of the proposed algorithm	Total distance travelled
71	Katarya & Verma [104]	Fuzzy-C-Means + GWO		Non-Automatic	Recommender System		Generating Initial Clusters and initial clusters centroids	Classification by similarity of user ratings	Movie lens dataset	PCA, PCA-SOM, K-means, PCA-K-means, K-means improved, SOM-Cluster, FCM, KM-PSO-FCM, PCA-GAKM and GAKM-Cluster	Mean absolute error, standard deviation, precision and recall
72	Mohammed et al. [107]-KMGWO	K-means + GWO	Performance Enhancement of GWO using K-means		Classical Engineering problem				CEC2019 benchmark test functions	GWO, CSO, WOA-BAT, WOA
Sine-Cosine Algorithm (SCA)
73	Moorthy & Pabitha [109]-SCAK-means	SCA + K-means	resource discovering for cloud resources	Non-Automatic	Cloud computing		Updating initial centroid position	Generate initial clusters	Cloud resources	K-means	Intra Cluster similarity, Inter-Cluster similarity, the similarity of cloud resources, and convergence rate
Cuckoo Search Algorithm (CSA)/Cuckoo Search Optimizatin (CSO)
74	García, Yepes & Martí [118]	CSO + K-means	solving combinatorial optimization problems	Non-Automatic	Design of counterfort retaining walls		Production of new solution in continuous space	Generate initial solution (Discretization)	The emission and cost values obtained from [34,66]	K-means, HS	Wilcoxon signed-rank; the Shapiro–Wilk or Kolmogorov—Smirnov-Lilliefors normality test
75	Manju & Fred [120]	CSO + K-means	Optimization-based segmentation and compression		Compound images segmentation &compression
76	Deepa, & Sumitra [121]-CSOAKM	CSO + K-means	optimal global solution	Non-Automatic	Intrusion Detection System			Generate initial cluster centroid	NSL-KDD dataset	IGNB chi square selection, and COFS	Image quality index, PSNR, RMSE, SSIM and SDME
77	Arjmand et al. [117]		an automatic tumor segmentation algorithm	Non-Automatic	Breast tumor segmentation		Generate initial Centroids for K-means algorithm	Clustering for segmentation	RIDER breast dataset	K-means and Fuzzy C-Means
78	Binu, Selvi & George [119]-MKF-Cuckoo	Cuckoo Search Algorithm + Multiple Kernel-based Fuzzy C-Means	Searching for the best cluster centroids	Non-Automatic					Iris and wine datasets		Cluster accuracy, rand coefficient, jacquard coefficient and computational time.
79	Girsang, Yunanto & Aslamiah [113]-FCSA	Cuckoo search algorithm + K-means	faster cluster analysis	Non-Automatic			Exploration	Convergence	Iris, Wine, Yeast, Abalone, Breast cancer, Glass, E.coli, Haberman, Sonar, and Parkinson	K-means	Mean and Standard Deviation
80	Tarkhaneh, Isazadeh & Khamenei [115]-HCSPSO	CS + PSO + K-means	More optimized cluster result	Non-Automatic			Clustering	PSO and K-means produces new nest for CS	Standard benchmark datasets	CS, k-means, PSO, Improved Cuckoo Search ICS, ESA), BFGSAand EBA
81	Ye et al. [111]-ICS-Kmeans	Improved Cuckoo search + K-means	Better clustering, accuracy, and faster convergence rate	Non-Automatic			initial centroids for K-means algorithm	Basic K-means Clustering	UCI standard dataset (Iris, Wine, Seeds, and Haberman)	CS-Kmeans, K-Means, PSO-Kmeans	Sum of Square Error (SSE)
82	Lanying & Xiaolan [114]	Cuckoo Search + K-means	Optimization of cluster center in K-Means	Non-Automatic	Recommender System		Optimizing the clustering center	Basic K-Means Clustering	Movie Lens dataset	K-Means, PSO-Kmeans and GA-Kmeans	Clustering accuracy and convergence speed
83	Saida, Kamel & Omar [112]	Cuckoo Search + K-Means	Reduction of the number of CS iteration	Non-Automatic	Document clustering		Clustering	Generate Initial Cluster Centroids	Reuters 21578 Text Categorization Dataset and the UCI Dataset		F-Measure
84	Singh & Solanki [116]	K-means + Modified Cuckoo Search	Global optimum convergence	Non-Automatic			Initial centroids for K-means algorithm	K-means clustering			Sum of Square Error (SSE)
Differential Evolution (DE)
85	Kwedlo [124]-DE-KM	DE + K-means	High-quality clustering solutions.	Non-Automatic			Production of candidate solutions	initial centroids fine-tuning solution	UCI dataset, TSPLIB library, USC-SIPI repository	Global K-means, DE, two K-means variants algorithm Genetic K-means algorithm	Sum of Square Errors (SSE)
86	Wang [129]	DE + K-means		Non-Automatic			Determine the initial cluster centers	Clustering using weighted K-means algorithm	Iris, Wine, Seed, and Page Blocks
87	Silva et al. [130]	ACDE + K-means	Automatically determine k activation threshold	Automatic		DE approach	Automatic determination of cluster number	Basic K-means clustering	UCI standard dataset		Davies Bouldin Index (DBI) and Cosine Similarity (CS) measure
88	Cai et al. [125]-CDE	DE + one-step K-means	Improvement of DE	Automatic		DE approach	Clustering	multi-parent crossover operator	unconstrained single-objective benchmark functions with different characteristic	DE	Number of fitness function evaluations (NFFEs) and quality of the final solutions.
89	Mustafi & Sahoo [36]	GA + DE + K-means	To improve the initial cluster centroids	Automatic	Text Document Clustering	DE approach	Generating improving cluster centers	Basic K-means clustering		Basic implementations of K-Means
90	Bonab et al. [97]	ABC + DE + Modified K-means	To solve initialization problems				initial cluster centers, find global solution	Clustering	Standard UCI dataset
91	Sierra, Cobos, & Corrales [127]	DE + K-Means	A hybrid for continuous optimization	Non-Automatic			DE clustering	Generation of initial groups for DE	A large set of test functions	DE and PSO	Fitness function value reached, av. number of fitness function evaluation to obtain optimal value. Friedman and Wilcoxon signed test, with a 95% significance.
92	Sheng et al. [131]-DE-ANS-AKO	DE + Adaptive niching + K-means	Dynamic adjustment of niche size to prevent premature convergence	Non-Automatic			DE clustering	Use of one iteration of k-means for fine-tuning the initial solution	Synthetic datasets, Letter, Connectionist, Shuttle, MFCCs, Isolet1, Isolet2, HARs Flowers17, Mnist, Cancer728, Yeast2945	DE-AKO, DE-ANS-KO, GKA, MEQPSO, EPSONS, PSOKM, CGABC, SHADE, TSMPSO, ICMPKHM, FPAGA	Mean ICV Mean ARI Mean AC, Mean runtimes and Wilcoxon’s rank-sum tests.
93	Kuo, Suryani & Yasid [126]-CDE-K-Means	ACDE + K-means	An Automatic clustering algorithm	Automatic			Clustering	Tuning cluster centroids to improve performance	Iris and Wine	DE
94	Hu et al. [128]	DEFOA + K-means	Improving K-means	Non-Automatic					Sales database	K-Means	the error sum of squares criterion function as fitness function
Invasive Weed Optimisation (IWO)
95	Fan et al. [134]-IWO-KMEANS	IWO + K-means	Improve global optimization while utilizing local optimization power	Non-Automatic	Text Clustering		Selection of initial cluster center	Basic K-means clustering	Chinese documents (history, transportation, medical, and sports) from the corpus of Fudan University	K-Means, DE-K-Means	F-Measure
96	Pan et al. [135]-CMIWO K-Means	IWO + K-means	Overcome the drawbacks of K-Means	Non-Automatic			Direct K-means search for definite evolution direction	Clustering
97	Razi [137]	DEA based K-means + IWO	Clustering algorithm for better facility location	Non-Automatic	Facility Location problem		Determining the Pareto solution for the bi-objective model	Clustering
98	Boobord, Othman, & Abubakar [136]-PCAWK	PCA + IWO + K-means		Non-Automatic			PCA for dimensionality reduction	WK-means for clustering	Wine, Cancer, USCensus90, SPECTF Heart and Musk2000	PCAK	Sum of Square Error (Best, Average, Worst and Standard deviation)
Imperialist Competition Algorithm (ICA)
99	Emami & Derakhshan [65]-ICAFKM	ICA + Fuzzy K-means	Escape from local optimal and increased convergence speed	Non-Automatic			Clustering in an alternate manner with the FKM	Clustering in an alternate manner with the ICA	Iris, Glass, Sample, Contraceptive Method Choice (CMC), and Wine	ICA, PSOKHM, PSO, FKM and HABC	F-measure and runtime metrics
100	Abdeyazdan [140]-ICAKHM	Modifier ICA + K-Harmonic means	Compensate existing problems in cluster analysis	Non-Automatic	Milling Machines classification		generates the initial population and empires	Generates initial empires for the modified ICA	Iris, Glass, Contraceptive Method Choice, and Wine	ICAKM, KHM, GSOKHM and PSOKHM methods.	F-measure, KHM (X, C), Runtime (s)
101	Niknam et al. [139]-K-MICA	K-means + Modified Imperial Competitive Algorithm	Optimum clustering	Non-Automatic			Generates population and forms the initial empire	Improve empires’ colonies & imperialists position	Iris, Vowels, Wine and Contraceptive method choice	ACO, MICA, SA, PSO, GA, HBMO, TS and K-Means	The best, average, worst of the fitness function and Standard deviation of the fitness function.
Harmony Search (HS)
102	Nazeer, Sebastian & Kumar [145]-HSKH	Harmony Search + K-Means	Better cluster accuracy	Non-Automatic	Clustering Gene expression Data		Determining the initial cluster centroids	Clustering	Human Fibroblast Serum data and the Rat CNS data	K-Means, SOM, IFCM, VGA, CRC	Silhouette Index
103	Forsati et al. [141]-HSCLUST	Harmony Search + K-Means	Less dependent on initial parameters	Non-Automatic	Document Clustering		Initial centroids	Obtain the best vector from the HS		K-Means, HSCLUST	F measure
104	Chandran & Nazeer [144]	Enhanced K-Means + Harmony Search	Better cluster solution	Non-Automatic			Determining the initial cluster centroids	Clustering	UCI Machine Learning Repository dataset (Iris, New-Thyroid and Breast Cancer)	K-Means, HS-K-means	Cluster Purity metric.
105	Raval, Raval & Valiveti [146]	Harmony Search + K-Means	Cluster Analysis Optimization	Non-Automatic	Sensor Network Energy Utilization		Finding initial cluster centers called Clustering Hierarchy (CH)	Fine-tuning the initial CH obtained from HS	Dataset simulation using NS2 simulator	K-Means, HSA	Energy dissipation, Total data transfer in number of packets
106	Cobos et al. [143]-IGBHSK	Global best Harmony Search + K-Means	Hybridizing Global best Harmony Search with K-Means	Automatic	Web document clustering	Using BIC or Davies-Bouldin index	Providing global search strategy in the solution space	Finds the optimum value in a local search space	Datasets based on Reuters-21578 and DMOZ	Carrot2	BIC, Precision, Recall, F-measure, NRL, OTC
107	Mahdavi & Abolhassani [142]-HKA	K-means + Harmony Search	An algorithm based on HS optimization	Non-Automatic	Web document clustering		Global search for optimum solutions	Localize search in the proximity of the obtained global solution	TREC-5, TREC-6, TREC-7, DMOZ, and 20 Newsgroup	K-Means, GA, PSO AND GM	Quality and speed of convergence, F-Measure
108	Kim et al. [147]	Harmony Search + K-means	Clustering-based SDN load balancing scheme	Non-Automatic	SDN load balancing		Fine-tuning the solution from K-means clustering	Basic clustering	100 to 1000 switches and 10 to 100 controllers are randomly placed in an area of 100 × 100	HS, P-HS, and P-HS-K.	Measure of accuracy
Black Hole (BH) Algorithm
109	Eskandarzadehalamdary, Masoumi, & Sojodishijani [151]-BH-BK	Black Hole + Bisecting K-means	Improve performance of bisecting K-means	Non-Automatic			Generates initial cluster centroids for BK-means	Basic clustering and refinement	Iris, Glass, Vowel, and Contraceptive Method Choice (CMC)	Bisecting K-Means, BH, PSO	Sum of intra-cluster distances and Error Rate (ER)
110	Feng, Wang & Chen [153]	Black Hole + K-means	Initial cluster centers for K-means	Non-Automatic	Image Classification		Determining the initial cluster center for K-means	Basic clustering and refinement
111	Pal & Pal [152]	Black Hole + K-means	Improved cluster analysis	Non-Automatic			Clustering	Partly generates initial cluster center		K-Means
Membrane Computing (P System)
112	Jiang, Zang & Liu [155]	K-means + DNA genetic Algorithm + P system	K-means based on DNA genetic algorithm and P system	Non-Automatic			Analyze the initial cluster center with P system		Randomly generated dataset		Convergence rate, Measure of accuracy and intra cluster distance
113	Wang, Xiang & Liu [159]	K-means + K-medoids + Tissue-like P system	Handling noises and outliers	Non-Automatic			Tissue-like P system to present parallel operation	optimizing the result with K-medoids	UCI dataset	K-means and K-medoids
114	Zhao, Liu & Zhang [158]	P system + K-medoids	Using P system to realize K-medoids algorithm	Non-Automatic			Provide parallel operation for lower time complexity	Clustering
115	Weisun & Liu [157]	MDE K-means + P system	Improved initial cluster center for K-means	Non-Automatic			Evolve the objects with MDE	Clustering	Artificial data sets, the iris, wine	K-means algorithm and DE -K-means algorithm	Cluster validity index, Xie-Beni index, the PBMF index
116	Zhao & Liu [156]-GKM	K-Means + GA + Tissue-like P system	Improved initial cluster center for K-means	Non-Automatic			P system for parallelism and GA for good convergence	Clustering
117	Wang, Liu & Xiang [160]	K-means + Tissue-like P system	Improved initial cluster center for K-means	Non-Automatic			Selection of initial cluster centers	Clustering	UCI datasets -Wine, Glass, Haberman, Soybean-small, and Zoo	K-means, CCIA, kd-tree, K-means++, FSDP, Bai’s, Khan’s	No of initialisation cells
Dragonfly Algorithm (DA)
118	Angelin [162]	K-means + Dragonfly	Outlier detection	Non-Automatic			Optimizing the generated clusters	Initial cluster generation	Arrhythmia, Diabetics and Epileptic seizure	K-means and K-median	Detection rate, ROC as objective function
119	Kumar, Reddy,& Rao [164]-WHDA-FCM	Wolf hunting-based dragonfly + Fuzzy C-means	SAR Images change detection	Non-Automatic	SAR Image Change detection		Selection of optimal coefficients (cluster center)	Clustering	SAR Images	DWT-FCM, NR-ELM, GADWT-FCM, ABDWT-FCM, PSDWT-FCM, FFDWT-FCM, GWDWT-FCM, AGWDWT-FCM and DADWT-FCM	accuracy, specificity, sensitivity, precision, negative predictive value, F1 score and Matthew’s correlation coefficient. False positive rate, false negative rate and false discovery rate
Ant Lion Optimizer (ALO)
120	Chen et al. [165]-QALO-K	Quantum-inspired ant lion optimizer + K-Means	An efficient algorithm for intrusion detection	Non-Automatic	Intrusion detection		Generate initial cluster center for K-means	Clustering	KDD Cup datasets and Iris, Glass, Wine, Cancer, Vowel, CMC and Vehicle	GA, ACO, MBCO, MKCLUST and ALO-K	Accuracy rate (AR), Detection Rate (DR), False positive rate (FPR) and F-measure (F1)
121	Murugan & Baburaj [166]-ALPSOC	Improved K-medoids + Ant lion + PSO	Computational efficiency and better performance	Non-Automatic			Optimized the generated initial clusters	Generate initial clusters	UCI datasets—Glass, Leaf, Seeds, Soybean and Ionosphere	K-Means, K-Means -FA, KMeans—PSO	Intra-cluster distance, F-measure, Rand Index, Adjusted Rand Index, Entropy and Normalized Mutual Information
122	Dhand & Sheoran [168]	Ant Lion Optimizer + K-Means algorithm	Energy-efficient routing protocol	Non-Automatic	Energy-efficient routing protocol			Clustering
123	Majhi & Biswal [164]	K-Means + Ant Lion Optimizer	Optimal cluster analysis	Non-Automatic			Optimized the generated clusters	Generate initial clusters	Glass, vowel, ionosphere, leaf, gene expression cancer RNA-seq, waveform database generator (version 2), immunotherapy, and soybean	K-Means, KMeans-PSO, KMeans-FA, DBSCAN and Revised DBSCAN	Sum of intra-cluster distances and F-measure.
124	Naem & Ghali [167]-K-median Modularity ALO	K-Median + Ant Lion Optimizer	Social network community detection	Non-Automatic	Social Networks community detection		Optimized the generated clusters	Generate initial clusters	Zachary karate Club, Bottlenose Dolphins network, American College football network, Polbooks network	K-means Modularity PSO, K-means Modularity Bat optimization, K-means Modularity CSO, K-median Modularity PSO, K-median Modularity Bat optimization, K-median Modularity CSO, GN, FN, BGLL, HSCDA.	Normalized Mutual Information (NMI), Measure of Modularity for community quality
Social Spider Algorithm (SSO)
125	Thiruvenkatasuresh & Venkatachalam [171]	Social Spider Algorithm + Fuzzy C-means	classify and segment Brain tumor images	Non-Automatic	Tumor detection in Brain images		Optimizing Centroid	Clustering		ANFIS and FCMGWO
126	Chandran, Reddy, & Janet [170]-SSOKC		Balance local and global searches with improved convergence speed.	Non-Automatic			To find the vicinity of optimal solution	initial centroid refinements and final optimal solution	UCI datasets (Iris, Glass, Vowel, Wine, Ruspini, and Cancer)	Kbat, KFA, KPA,	CPU Elapse Time
Fruit Fly Optimization (FFO)
127	Sharma & Patel [173]-K-Means-FFO	K-means + FFO	Optimal clustering quality	Non-Automatic			Optimize initial Clusters	Generate initial clusters	20NewsGroup, Reuters-21578, and Classic4 dataset	K-means, K-means-PSO and K-means-ALO	Intra-cluster distance, Purity Index, F-Measure and Standard Deviation
128	Jiang et al. [174]	K-means + FOA	Optimal clustering quality	Non-Automatic	Earthquake Rescue center Site Selection and Layout		Optimize initial Clusters	Generate initial clusters	Integrated data of affected areas	RWFOA and MFOA	Weighted sum of construction costs, transportation costs and penalty costs of emergency rescue centers
129	Wang et al. [176]-FOAKFCM	Kernel-based Fuzzy C-means + FOA	Integrating kernel-based fuzzy c-means and FOA	Non-Automatic			Initialize initial cluster centroids	Classifying/Clustering the data	Iris, Glass, and Seeds	FCM, KFCM	Classification evaluation index (XB index
130	Hu et al. [128]	DEFOA + K-means	Improving K-means for universal continuous optimization	Non-Automatic			Generate initial cluster centroids	Optimize the initial clustering	Sales database	K-means	Convergence performance
Bees Swarm Optimization (BSO)
131	Aboubi, Drias & Kamel [179]-BSO-CLARA	BSO + K-medoids	Effective and efficient algorithm	Non-Automatic						PAM, CLARA and CLARANS
132	Djenouri, Habbas & Aggoune-Mtalaa [180]		Using K-means as decomposition	Non-Automatic				Clustering	DIMACS
133	Djenouri, Belhadi & Belkebir [178]	BSO + K-means	Document Information Retrieval Problem		Document Information Retrieval		Exploration of already created clusters	Clustering	CACM collection, TREC, Webdocs and Wikilinks	PTM, SVMIR, KNNIR and ARMIR	F-measure, Runtime
Bacterial Colony Optimization (BCO)
134	Revathi, Eswaramurthy, & Padmavathi [182]-BCO + KM	BCO + K-means	Reduced computational cost	Non-Automatic			Selection of initial cluster centroids	Optimizing the initial clusters for optimal solution	2 Artificial datasets; UCI datasets (CMC, Glass WBC, Heart, Iris, Wine, Vowel, Balance)	K-means, PSO, BFO and BCO	Sum of Square Errors (SSE)
135	Vijayakumari & Deepa [183]-HFCA	FCM + Fuzzy BCO	High efficiency	Non-Automatic			Selection of initial cluster centroids	Optimizing the initial clusters for optimal solution	Iris, WBC, Glass, Wine, Vowel, and CMC	FBFO, FBCO, FCM AND FPSO	IntraCluster distance
Stochastic Diffusion Search (SDS)
136	Karthik, Tamizhazhagan, & Narayana [185]-SS-KMeans	SDS + K-means	Finding optimal clustering points	Non-Automatic	Data Leak Prevention in Social Medial		Select initial centroid for clustering	Clustering	S		True Positive Rate (TPR)
Modified Honey Bees Mating Optimization (HBMO)
137	Teimoury et al. [187]-HMBK	HBMO + KMeans	An optimized hybrid clustering algorithm	Non-Automatic			Selection of Initial Cluster centroids	Clustering	Wine, Iris and B.C	SA, PSO, TS, ACO, GA, K-means	Sum of Square Error (SSE)
138	Aghaebrahimi, Golkhandan & Ahmadnia [188]	HBMO + KMeans	Localization and sizing of flexible AC transmission system	Non-Automatic	Localization and sizing of Flexible AC Transmission System		Determining the best fitness function	Data Classification—Clustering	TCSC, UPFC AND SVC		Average Installation Cost, total generation cost and cost of power transmission losses
Cockroach Swarm Optimization (CSO)
139	Senthilkumar & Chitra [190]-HHMA	MCSO + K-means	Load balance in cloud networks	Non-Automatic			Measuring the load ratio	Clustering			Overall Response time and Processing time
Glowworm Swarm Optimization (GSO)
140	Onan & Korukoglu [193]	K-means + GSO	An efficient and effective hybrid algorithm	Non-Automatic			Find initial Cluster Centroids	Clustering	Iris, Breast Cancer, E.coli, Diabetes, Haberman’s survival data	K-means, Fuzzy C-Means, GSO	F-measure and Rand Index
141	Tang et al. [194]-VSGSO-D KMeans	Improved GSO + K-means	Multi-modal optimization for optimal cluster analysis	Non-Automatic			Generates the initial cluster center	Clustering	Iris dataset	K-means, K-means++, K-means||, GSO + K-means,	Run time, minimum number of iterations, SSE, NMI, Purity and Rand Index
142	Zhou et al. [192]	GSO + K-means	Avoid the effect of the initial condition	Non-Automatic	Image Classification		Generates the initial cluster center	Clustering	Pepper, Lena, and Mandrill	K-means, Fuzzy C-Means	Quantization error, the maximum intra-distance, the minimum inter-distance
Bee Colony Optimization (Bee)
143	Das, Das & Dey [196]-MKCLUST & KMCLUST	MBCO + K-means	Faster convergence	Non-Automatic			Either generate initial centroids or does the clustering	Either generate initial centroids or does the clustering	Glass, Wine, Vowel, CMC, Cancer, HV, Iris	MBCO, K-NM-PSO, K-PSO, K-HS, KIBCLUST, IBCOCLUST, PSO	Percentage Error (PE)
144	Forsati, Keikha & Shamsfard [197]	Improved BCO + K-means	An efficient algorithm for large and high dimensional dataset	Non-Automatic	Document Clustering		Generates initial cluster centroids	Clustering	Wine, Iris, Glass, Vowel, Cancer Document dataset (Politics, TREC, DMOZ, 20 Newsgroup and Web Ace)	GA, ACO, K-means, PSO, CABC, IBCOCLUST, HSCLUST, K-NM-PSO, K-PSO, K-GA, K-HS, K-ABC	Cluster Quality and Rate of Convergence
Bacteria Foraging Optimization (BFO)
145	Niu, Duan & Liang [201]-BFCA	BFO + K-means	Efficient algorithm with global and parallel search capacities	Non-Automatic			Generates initial cluster centroids	Clustering
Cuckoo Optimization Algorithm (COA)
146	Lashkari & Moattar [202]-ECOA-K	ECOA + K-means	Fast convergence algorithm with intelligent operators	Non-Automatic			Generate initial cluster centroids	Clustering	UCI dataset (CMC, Iris, and Wine)	BH, Big Bang Big Crunch (BBBC), CSA, COA, K-means	Purity Index, Convergence rate, Coefficient of Variance, time complexity
Symbiotic Optimization Search (SOS)
147	Yang, & Sutrisno [198]-CSOS	SOS + K-means	An automatic hybrid clustering algorithm	Automatic		Assigning half the population size as the number of clusters	Clustering	Generate initial cluster centroids automatically	28 benchmark functions,	CRPS, SaNSDE, rCMA-ES, GA, SOS and GWO	Number of successful runs, Average computational time, and Average number of evaluations

3.3. RQ3. What Were the Various Automatic Clustering Approaches Adopted in the Reported Hybridization?

Different authors have varied approaches in achieving automatic clustering in integrating K-means with the corresponding MOA in the reviewed literature. Zhou et al. [45] adopted the Noise Method [203] and the K-means++ method [204]. Dai, Jiao, and He [28] achieved automatic clustering through dynamic optimization of cluster number k through heredity, mutation with parallel evolution, and community intermarriage of the parallel genetic algorithm coupled with variable-length chromosome encoding. From the work of Li et al. [40], an optimal K-value was generated from the initial seed of chromosomes ranging between 1 and MaxClassVal, expressing the K-value by a byte classified into 255 kinds. Kuo et al. [39] employed the self-organizing feature map (SOM) neural network method [205,206] which involves the projection of high dimensional input space into a low-dimensional topology for the visual determination of the cluster number. An improved canopy [207] with K-means++ [204] techniques were used by Zhang and Zhou [35], where the canopy technique leverages domain-specific attributes to design a cheap distance metric for creating canopies using Euclidean distance. Mohammadrezapour, Kisi, and Pourahmad [46] generated the initial number of clusters from a uniform distribution over a specified range of 2 to M, where M is the number of objectives in a multi-objective optimization algorithm [208]. Patel, Raghuwanshi, and Jaiswal [200] used the approach of determining the female chromosomes using the sex determination method (SDM) in the genetic algorithm and assigning the number of females as $k$.

In Barekatain, Dehghani & Pourzaferani [44], the dataset was segmented into nonequivalent cells, and the nodes whose residual energy is more than the average of its cell were selected as cluster heads. The number of cluster heads is then taken as $k$. The use of Mahalanobis distance to consider the covariance between data points for better representation of initial data and the number of generated groups using the MapReduce framework forms the number of clusters was adopted by Sinha & Jana [33]. In Kapil, Chawla & Ansari [3], data objects act as candidates for cluster centroids. The GA operators are executed to find the fittest instance that serves as the initial cluster centroids. The number of fittest instances obtained automatically determines the number of clusters. Rahman and Islam [32] used a fixed number of chromosomes (half selected deterministically and the other half randomly) for the initial population for the GA process from which the fittest instance is obtained as cluster centroids. The method of allocating a range of values for k (between 2 and 10) and selecting the best value that produced the optimal solution was used by Islam et al. [34]. Mustafi and Sahoo [36] combined the GA framework with differential evolution for obtaining the number of clusters, while Xiao et al. [31] employed a GA-based method that adopts a Q-bit representation for the dataset pattern with a single run of the conventional K-means on each chromosome. Omran, Salman, and Engelbrecht [58] used PSO to find the best set of cluster centroids among the existing data object to produce the optimum number of clusters, and Kao and Lee [61] used discrete PSO in optimizing the number of clusters. In the case of Sood and Bansal [86], the Bat algorithm was employed in optimizing the initial representative objects for each cluster.

The idea of using a manual strategy to find $k$ activation threshold by DE to automatically determine the number of clusters was adopted by Silva et al. [130]. At the same time, Cai et al. [125] used the idea of random generation of $k$ values, where $k$ is an arbitrarily generated integer number [36,97]. Kuo, Suryani, and Yasid [126] also used the DE approach in obtaining the number of clusters. The use of Bayesian information criterion (BIC) [209] or the Davies–Bouldin Index (BDI) [210] in automatically finding the number of clusters was employed by Cobos et al. [143]. Yang and Sutrisno [198] used the idea of specifying the initial number of clusters as half of ecosize generated as sub-ecosystems, in which CSOS then optimizes to generate the correct cluster number in a dataset. Table 2 present the list of adopted automatic clustering approaches, which have been reported in the literature.

Table 2. List of adopted automatic clustering approaches.

S/N	Authors	Adopted Automatic Clustering Approach
1	Zhou et al. [45]	Noise method combined with K-means++
2	Dai, Jiao and He [28]	Dynamic optimization through heredity, mutation with parallel evolution, and community intermarriage
3	Li et al. [40]	Determined optimal number of k from the initial seed of chromosomes ranging between 1 and MaxClassVal,
4	Kuo et al. [39]	Self-organizing feature map (SOM) neural network method
5	Zhang & Zhou [35]	An improved canopy with K-means++
6	Mohammadrezapour, Kisi and Pourahmad [46]	Optimizing a uniform distribution over a specified range of values
7	Patel, Raghuwanshi and Jaiswal [200]	Sex determination method
8	Barekatain, Dehghani & Pourzaferani [44]	Segmented into nonequivalent cells and selection of nodes whose residual energy is more than the cell’s average
9	Sinha & Jana [33]	The use of Mahalanobis distance and MapReduce framework
10	Kapil, Chawla & Ansari [3]	Executing GA operators on data objects as candidates for cluster centroids to find the fittest instance
11	Rahman and Islam [32]	Selecting a fixed number of chromosomes (half selected deterministically and the other half randomly) as the initial population for the GA process to obtain the fittest instances
12	Islam et al. [34]	Allocating a range of values for k (between 2 and 10) and selecting the best value that produced the optimal solution
13	Mustafi and Sahoo [36]	Combining GA framework with differential evolution
14	Xiao et al. [31]	Employing GA-based method that adopts Q-bit representation for dataset pattern with a single run of the conventional K-means on each chromosome
15	Omran, Salman and Engelbrecht [58]	Using PSO to find the best set of cluster centroids among the existing data objects
16	Kao and Lee [61]	Using discrete PSO in optimizing the number of clusters
17	Sood and Bansal [86]	Using Bat algorithm to optimize the initial representative objects for each cluster
18	Silva et al. [130]	Using a manual strategy to find $k$ activation threshold by DE
19	Cai et al. [125]	Random generation of $k$ value as $k$ = rndint [2] where NP is the population size and rndint is a random integer number
20	Kuo, Suryani and Yasid [126]	DE approach in obtaining the number of clusters
21	Cobos et al. [143]	Optimizing Bayesian information criterion (BIC) or the Davies–Bouldin index (BDI)
22	Yang and Sutrisno [198]	Specifying the initial number of clusters as half of ecosize generated as sub-ecosystems which CSOS then optimizes

3.4. RQ4. What Were the Contributions Made to Improve the Performance of the K-Means Clustering Algorithm in Handling Automatic Clustering Problems?

Zhou et al. [45], in their hybridization of K-means with the corresponding MOA, were able to achieve an automatic selection of high-quality initial seeds without specifying the number of clusters to be generated as well as avoidance of premature convergence. From the work of Dai, Jiao, and He [28], the blind estimate of the cluster number by the K-means algorithm was avoided ensuring precision and reducing the influence of the cluster number; the algorithm search time was also reduced. The use of SOM in determining the number of clusters and starting points made the resulting integrated clustering algorithm more robust [39]. Rahman and Islam [32] and Zhang and Zhou [35] reported high-quality cluster results in their proposed clustering algorithm but with higher time complexity. Further work by Islam et al. [34] reportedly yielded higher-quality clusters with equivalent computational resources.

Patel, Raghuwanshi, and Jaiswal [200] reportedly achieved well distributed and well-separated clusters, which evolved faster with fewer functions evaluation for obtaining the optimal. Kapil, Chawla, and Ansari [3] obtained correct clusters from their k-means/GA integrated clustering algorithm. Mustafi and Sahoo [36] observed a significant reduction in the possibility of convergence of the K-means algorithm to local optimal. Xiao et al. [31] in their Q-bit-based GA/K-means integrated clustering algorithm, was able to achieve effective clustering without knowing cluster numbers beforehand. Omran, Salman, and Engelbrecht [58] obtained the correct number of clusters with the corresponding clusters with minimum interference from a user using their proposed integrated K-means/PSO clustering algorithm. According to Kao and Lee [61], combining K-means with discrete PSO enhanced the performance of K-means in finding an optimal solution to dynamic clustering problems.

Sood and Bansal [86] achieved better and efficient cluster analysis while integrating K-medoids with the bat algorithm. According to Silva et al. [130] and Kuo, Suryani, and Yasid [126], the integration of K-means with DE yielded an excellent cluster result. Cai et al. [125] reported a balance between exploration and exploitation in the search algorithm and improving the quality of the final cluster result. A superior and higher performance of K-means clustering integrated with ABC and DE was reported by Bonab et al. [97]. Cobos et al. [143] reported promising experimental results in their automatic hybridized clustering algorithm that combined global best harmony search with K-means. In the same vein, Yang and Sutrisno [198] reported promising performance of their automatic K-means algorithm hybridized with SOS, which was found faster in high dimensional problems alleviating the dimensionality effect.

In summary, the performance of the K-means clustering algorithm in handling automatic clustering problems was substantially improved in terms of determination of the correct number of clusters, high-quality cluster results, performance enhancements and computational efficiency, and avoidance of convergence into local optimal.

3.5. RQ5. What Is the Rate of Publication of Hybridization of K-Means with Nature-Inspired Meta-Heuristic Algorithms for Automatic Clustering?

This section examines the rate of publications of articles on hybridization of K-means with nature-inspired meta-heuristic based on the selected article.

Publications Trend of K-Means Hybridization with MOA

Figure 2 presents the publication trend of K-means hybridization with MOA in the last 20 years. There is significant growth in research involving hybridization of K-means with MOA, with 2020 having the highest number of articles. The bifurcated distribution of this publication is presented in Table 3, showing at least each MOA having a publication on its hybridization with K-means with reference to its proposed year. K-means hybridization with CS having the highest number of publications (4) in the year 2019. The total of each publication per MOA as well as per year is shown on the last but one column and last row of Table 3, respectively, with GA having the highest number of articles (25) followed by PSO (16), FA (12), CS (11), DE (10), ABC (8), HS (7), and MC (6). ALO and BAT have the same number of articles (four each) followed by GWO, IWO, and FFO, each having four articles; ICA, BH, and GSO came next with three articles each; FPA, DA, Bacterial CO, HBMO, and BCO has two articles each while the rest has one article each. Due to the fact that each algorithm has a different year of proposal, the normalized rate of publication of each MOA is presented in Figure 3. The normalized rate of publication was calculated using the equation below, where N_i is the number of publications in a year, with $j$ and $i$ representing the current year and MOA proposal year, respectively

$$\mathrm{Normalize} \mathrm{rate} \mathrm{of} \mathrm{publication}=\left({\displaystyle \sum }_i^j{N}_i\right)/\left(j-i\right)$$

(5)

Figure 2. Rate of Publications on K-means hybridization with MOA.

Table 3. The year-wise bifurcated K-means hybridization with MOA Publication Report.

MOA	2002	2003	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	Total	Norm. Ra
ALO (2015)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	1	2	1	5	0.83
ABC (2005)	-	-	-	-	-	-	-	-	-	-	1	3	-	-	-	-	3	1	8	0.50
BAT (2010)	-	-	-	-	-	-	-	-	-	1	-	-	-	-	1	1	2	-	5	0.45
Bacterial CO (2012)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	-	1	2	0.22
BFO (2000)	-	-	-	-	-	-	-	-	-	1	-	-	-	-	-	-	-	-	1	0.05
BCO (2012)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	-	1	2	0.22
BSO (2012)	-	-	-	-	-	-	-		-	-	-	1	1	-	1	-	-	-	3	0.33
BH (2013)	-	-	-	-	-	-	-	-	-	-	1		-	-	1	-	1	-	3	0.38
CS (2009)	-	-	-	-	-	-	-	-	-	1	1		-	-	3	4	2	-	11	0.92
Cockroach SO (2010)	-	-	-	-	-	-	-	-					-	-	-	-	1	-	1	0.09
DE (2013)	-	-	-	-	-	-	-	2	-	1	1	1	-	1	1	2	1	-	10	1.25
DA (2015)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	1	2	0.33
COA (2011)	-	-	-	-	-	-	-	-	-	-	-	-		1		-	-	-	1	0.10
FFA (2008)	-	-	-	-	-	-	-	-	1	-	1	2	2	1	1	1	2	1	12	0.92
FFO ((2000)	-	-	-	-	-	-	-	-	-	-	-	-		2	-	-	2	-	4	0.19
FPA (2012)	-	-	-	-	-	-	-	-	-	-	-	1	-	-	-	-	-	1	2	0.22
GA (1988)	1		3	2	1	1	3	-	-	1	1	2	2	1	3	2	2	-	25	0.76
GSO (2009)	-	-	-	-	-	-	-	-	1	1	-	-	-	-	-	1	-	-	3	0.25
GWO (2014)	-	-	-	-	-	-	-	-	-	-	-	1	-	-	1	-	-	2	4	0.57
HS (2001)					1	1	1	1	-	1	-	-	1	-	-	1	-	-	7	0.35
ICA 92007)	-	-	-	-	-	-	-	1	-	-	1	1	-	-	-		-	-	3	0.21
IWO (2010)	-	-	-	-	-	-	-	-	-	-	1	2	-	-	-	1	-	-	4	0.36
MC (1998)	-	-	-	-	-	-	-	-	-	1	3	-	-	-	1		-	1	4	0.20
HBMO (2011)	-	-	-	-	-	-	-	-	-	-	-	-	2	-	-	-	-	-	2	0.20
PSO (1995)		1	1	1	1	2	1	-	-	-	1	1	2	1	-	2	2	-	16	0.62
SCA (2016)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	-	1	0.20
SDS (2011)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	1	0.10
SOS (2014)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	-	1	0.14
Social Spider O (2015)	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1	1	-	-	2	0.33
Total/Year	1	1	4	3	3	4	5	4	2	8	12	15	10	7	15	19	22	11	147

Figure 3. Publication rate of K-means hybridization with MOA for automatic clustering.

The normalized rate of publication of K-means hybridization with MOA is displayed in the last column of Table 3. The rate of publication of hybridization of K-means with MOA for automatic clustering is shown in Figure 3.

The highest number of articles published with respect to this was recorded in the year 2010, 2018, and 2019 with three articles each; 2006, 2009, 2013, and 2015 had two articles each while the remaining years had only one article each. The automatic/non-automatic K-means hybridization per MOA is illustrated in Figure 4. Moreover, Figure 4 reveals that most of the publications on K-means hybridization with MOA addressed general clustering with less attention paid to automatic clustering. Only 23 articles out of 147 selected articles reported on automatic clustering. This shows that only 16% of the total articles published in the last two decades on K-means hybridization with MOA addressed the problem of automatic clustering. Among the MOA hybridized with K-means, only 7 MOAs (GA, PSO, BA, ABC, DE, HS, and SOS) out of the 28 reviewed MOA, which amounts to 20.6% that directed their hybridization towards solving automatic clustering problems. In general, it can be observed that the rate of publication on K-means hybridization with particular MOA is relatively low. There is a need for more research in this aspect to explore more possibilities of improving the performance of the existing hybridized algorithm. This implies that hybridizing the K-means with these other MOAs for solving automatic clustering problems needs to be explored. Table 3 shows the year-wise bifurcated K-means hybridization with MOA publication report. Similarly, the details of the articles selected and used in the analysis of the study are presented in Table 4.

Figure 4. MOA-based automatic vs. non-automatic K-means hybridization (Total number of articles considered = 147).

Table 4. The selected study articles publication details.

Authors	Publishers	Journal/Conference	Indexing					Citation	Impact Factor
			SCI	WOS	Scopus	Google Scholar	DBLP
Abdeyazdan [140]	Springer	Journal of Supercomputing	√		√	√	√	15	2.474
Aboubi, Drias & Kamel [179]	Springer	Conf						2
Aghaebrahimi, Golkh&an & Ahmadnia [188]	IEEE	Conf						8
Angelin, B. [162]		Turkish Journal of Computer & Mathematics Education			√	√		0	0.33
Arjmand et al. [117]	IEEE	Conf				√		5
Armano & Farmani [95]	IRIS	Int’l Journal of Computer Theory & Engineering				√		36
Bandyopadhyay & Maulik [24]	Elsevier	Information Sciences	√	√	√	√		465	6.795
Barekatain, Dehghani & Pourzaferani [44]	Elsevier	Procedia Computer Science			√			38	2.09
Behera et al. [77]	Inderscience	Int’l Journal of Fuzzy Computation & Modelling					√	2
Binu, Selvi & George [119]	Elsevier	AASRI Procedia	√			√		17
Bonab et al. [97]	Springer	Computational Intelligence in Information Systems						12
Boobord, Othman, & Abubakar [136]	i-csrs.org	Intl. Journal of Advance Soft Computer Appl			√			1	0.79
Cai et al. [125]	Elsevier	Applied Soft Computing			√	√		120	6.725
Cao & Xue [102]	IEEE	Int’l Conf on Network & Information Systems for Computers						4
Chandran & Nazeer [144]	IEEE	Recent Adv. in Intelligent Computational Systems			√	√		13
Chandran, Reddy, & Janet [170]	IEEE	Second Int’l Conf on Intelligent Computing & Control Systems						1
Chaudhary & Banati [90]	Inderscience	Int’l Journal of Advanced Intelligence Paradigms			√	√	√	0	0.63
Chen & Zhang [59]	IEEE	Int’l Conf on Wireless Comms, Networking & Mobile Computing						31
Chen et al. [166]	Elsevier	Knowledge-Based Systems	√	√	√	√		13
Chen, Miao & Bu [72]	IEEE	Int’l Conf on Power, Intelligent Computing & Systems						2
Cheng et al. [25]	IEEE	Int’l Conf on Pattern Recognition (ICPR’06)						23
Cobos et al. [143]	IEEE	IEEE congress on evolutionary computation						13
Dai, Jiao & He [28]	IEEE	Int’l Conf on Intelligent Information Hiding & Multimedia Signal Proc						10
Das, Das & Dey [196]	Elsevier	Applied Soft Computing			√	√		25	6.725
Dasu, Reddy & Reddy [99]	Springer	Adv. in Cybernetics, Cognition, & Machine Learning for Comm Tech						1
Deepa, & Sumitra [121]	IOPScience	Int’l Conf on Mechanical, Electronics & Computer Engineering				√		0
Dhand & Sheoran [168]	Elsevier	Materials Today: Conf Proceeding			√	√		4	31.04
Djenouri, Belhadi & Belkebir [178]	Elsevier	Expert Systems with Appl	√	√	√	√		48	6.954
Djenouri, Habbas & Aggoune-Mtalaa [180]	SCITEPRESS	Int’l Conf on Agents & Artificial Intelligence						5
El-Shorbagy et al. [37]	Springer	Computational Statistics	√	√	√	√	√	14	1
Emami & Derakhshan [65]	Springer	Arabian Journal of Science & Engineering	√		√	√		28	2.334
Eshlaghy & Razi [42]	Inderscience	Int’l Journal of Business Systems			√	√		15	0.53
Eskandarzadehalamdary, Masoumi, & Sojodishijani [151]	IEEE	Iranian Conf on Elect Engineering						11
Fan et al. [134]	IEEE	Int’l Conf on Autonomic & Trusted Computing						2
Feng, Wang & Chen [154]	Springer	International Conf on Scalable Computing & Comms						0
Forsati et al. [141]	Elsevier	Neurocomputing		√	√	√		60	5.719
Forsati, Keikha & Shamsfard [197]	IEEE	IEEE/WIC/ACM Int’l Conf on Web Intelligence & Intelligent Agent Tech						69
Gan, & Lai [89]	IEEE	Int’l Conf on Automatic Control & Intelligent Systems (I2CACIS)						3
García, Yepes & Martí [118]	MDPI	Mathematics		√	√	√		21	2.258
Ghezelbash, Maghsoudi & Carranza [38]	Elsevier	Computer & Geoscience	√		√	√		23	3.372
Girsang, Yunanto & Aslamiah [113]	IEEE	Int’l Conf on Elect Engineering & Computer Science						6
Hassanzadeh & Meybodi [74]	IEEE	Int’l Conf on Elect Engineering & Computer Science						99
HimaBindu et al. [83]	Elsevier	Materials Today: Conf Proceeding			√	√		0	31.04
Hu et al. [128]	IEEE	Int’l Conf on Computer Science & Education (ICCSE)						11
Huang [100]	MDPI	Symmetry		√	√	√	√	1	2.713
Islam et al. [34]	Elsevier	Expert Systems with Appl	√	√	√	√		2	6.954
Jensi & Jiji [92]	arXiv Cornell Univerity	Advanced Computational Intelligence				√		37
Jiang et al. [174]	IEEE	IEEE Int’l Conf on Artificial Intelligence & Computer Appl						0
Jiang, Zang & Liu [155]	Springer	In Int’l Conf on Human Centered Computing						2
Jie & Yibo [71]	IEEE	Int’l Conf on Power & Renewable Energy						0
Jin, Lin & Zhang [98]	MDPI	Algorithms		√	√	√	√	0	2.27
Jitpakdee, Aimmanee & Uyyanonvara [79]	World Academy of Science, Engineering & Tech	Int’l Journal of Computer & Information Engineering						7
Kao & Lee [61]	Elsevier	Expert Systems with Appl	√	√	√	√		53	6.954
Kao, Zahara & Kao [60]	IEEE	Int’l Conf on Intelligent Computing & Intelligent Systems						400
Kapil, Chawla & Ansari [3]	IEEE	Int’l Conf on Parallel, Distributed & Grid Computing						67
Karegowda et al. [41]	Springer	Int’l Conf on Adv. in Computing						16
Karthik, Tamizhazhagan, & Narayana [185]	Elsevier	Materials Today: Conf Proceeding			√	√		0	31.04
Katarya & Verma [104]	Springer	Neural Computer & Appl	√		√	√	√	58	5.606
Kaur, Pal & Singh [81]	Springer	Int’l Journal of System Assurance Engineering & Mgt			√	√	√	15	1.72
Kim et al. [147]	IEEE	IEEE Annual Consumer Comms & Networking Conf						3
Korayem, Khorsid & Kassem [105]	IOP Publishing	IOP Conf series: materials science & engineering						44	0.51
Kumar, Reddy & Rao [164]	Elsevier	Journal of Computational Design & Engineering						4	6.6
Kumari, Rao & Rao [93]	Inderscience	Int’l Journal of Advanced Intelligence Paradigms			√	√	√	0	0.63
Kuo & Li [80]	Elsevier	Computers & Industrial Engineering	√		√	√		28	5.431
Kuo et al. [39]	Elsevier	Expert Systems with Appl	√	√	√	√		120	6.954
Kuo, Suryani & Yasid [126]	Springer	Institute of Industrial Engineers Asian Conf						16
Kwedlo [124]	Elsevier	Pattern Recognition Letters	√	√	√	√		128	3.756
Langari et al. [82]	Elsevier	Expert Systems with Appl	√	√	√	√		17	6.954
Lanying & Xiaolan [115]	ACM	Int’l Conf on Intelligent Information Proc						0
Lashkari & Moattar [202]	Iran Journals	Journal of AI & Data Mining				√		5	0.127
Laszlo & Mukherjee, [26]	IEEE	Transactions on pattern analysis & machine intelligence						153
Laszlo & Mukherjee, [27]	Elsevier	Pattern Recognition Letters	√	√	√	√		192
Li et al. [40]	IEEE	Int’l Conf on Digital Content, Multimedia Tech & its Appl						153
Lu et al. [43]	Springer	Int’l Conf on Bio-Inspired Computing: Theories & Appl						11
Mahdavi & Abolhassani [142]	Springer	Data Mining & Knowledge Discovery	√	√	√	√	√	168	3.67
Majhi & Biswal [164]	Elsevier	Karbala Int’l Journal of Modern Science						44	2.93
Manju & Fred [120]	Springer	Multimedia Tools & Appl	√		√	√	√	1	2.757
Mathew & Vijayakumar [75]	IEEE	Int’l Conf on High Performance Computing & Appl						15
Mohammadrezapou, Kisi & Pourahmadm [46]	Springer	Neural Computer & Appl	√		√	√	√	12	5.606
Mohammed et al. [107]	Emerald Publishing	World Journal of Engineering			√			0	1.2
Moorthy & Pabitha [109]	IEEE	Int’l Conf on High Performance Computing & Appl						3
Murugan & Baburaj [166]	IEEE	Int’l Conf on Smart Tech in Computing, Elect & Electronics						0
Mustafi & Sahoo [36]	Springer	Soft Computing	√		√	√	√	15	3.643
Naem & Ghali [167]	BEEI	Indonesia Journal			√	√		2
Nayak et al. [66]	Springer	Int’l Conf on Computer & Comm Tech						20
Nayak et al. [77]	Springer	Computational Intelligence in Data Mining						1
Nayak, Naik & Behera [79]	Springer	Adv. in Intelligent Systems & Computing						4
Nazeer, Sebastian & Kumar [145]	PMC	Bioinformatics		√	√	√		8	3.242
Niknam et al. [139]	Elsevier	Engineering Appl	√		√	√		244	6.212
Niknam, & Amiri [53]	Elsevier	Applied Soft Computing			√	√		476	6.725
Niu et al. [48]	Elsevier	Engineering Appl	√		√	√		22	6.212
Niu, Duan & Liang [201]	Springer	Int’l Conf on Intelligent Data Engineering & AutoLearning						6
Omran, Salman & Engelbrecht [58]	Springer	Pattern Analysis & Appl	√		√	√	√	325	2.58
Onan & Korukoglu [193]	ProQuest	Int’l Symposium on Computing in Science & Engineering						1
Pal & Pal [152]	Springer	Computational Intelligence in Data Mining						3
Pambudi, Badharudin & Wicaksono [106]	ICTACT	Journal on Soft computing						0	0.787
Pan et al. [135]	World Scientific	Int’l Journal of Pattern Recognition & Artificial Intelligence	√		√	√		18	1.375
Patel, Raghuwanshi & Jaiswal [200]	IEEE	IEEE Int’l Advance Computing Conf						13
Paul, De & Dey [70]	IEEE	Int’l Conf on Electronics, Computing & Comm Tech						11
Pavez, Altimiras, & Villavicencio [88]	Springer	Proc of the Computational Methods in Systems & Software
Prabha & Visalakshi [64]	IEEE	Int’l Conf on Intelligent Computing Appl						26
Rahman & Islam [32]	Elsevier	Knowledge-Based Systems	√	√	√	√		52	8.038
Ratanavilisagul [69]	IEEE	Int’l Conf on Computational Intelligence & Appl						1
Raval, Raval & Valiveti [146]	IEEE	Int’l Conf on Recent Trends in Information Tech						0
Razi [137]	Springer	Journal of Industrial Engineering Int’l						5	2.02
Revathi, Eswaramurthy, & Padmavathi [182]	IOP Publishing	In IOP Conf Series: Materials Science & Engineering						0	0.51
Saida, Kamel & Omar [112]	Springer	Recent Adv. on Soft Computing & Data Mining						11
Senthilkumar & Chitra [190]	IEEE	Int’l Conf on Smart Systems & Inventive Tech						0
Sharma & Patel [173]	ACADEMIA	Int’l Journal of Computer Science & Information Security (IJCSIS)	√	√		√		0	0.702
Sheng et al. [131]	IEEE	Transactions on Cybernetics						3	11.45
Sheng, Tucker & Liu, [30]	Springer	Soft Computing	√		√	√	√	2	3.643
Sierra, Cobos, & Corrales [127]	Springer	Ibero-American Conf on Artificial Intelligence						6
Silva et al. [130]	Springer	Int’l Conf on Green, Pervasive, & Cloud Computing						4
Singh & Solanki [116]	Springer	Emerging Research in Electronics, Computer Science & Tech						8
Sinha & Jana [33]	Springer	Journal of Supercomputing	√		√	√	√	21	2.474
Sood & Bansal [86]	Citeseer	Int’l Journal of Applied Information Systems				√		21
Tang et al. [194]	IEEE	Int’l Symposium on Distributed Computing & Appl						1
Tarkhaneh, Isazadeh & Khamnei [115]	Inderscience	Int’l Journal of Computer Appl			√	√	√	11	1.55
Teimoury et al. [187]	MDPI	Sensors		√	√	√	√	4	3.576
Thiruvenkatasuresh & Venkatachalam [171]	Inderscience	Int’l Journal of Biomedical Engineering & Tech			√	√		1	1.01
Tran et al. [96]	IEEE	Chinese Journal of Electronics	√	√	√	√		38	0.941
Tripathi, Sharma & Bala [87]	Springer	Int’l Journal of System Assurance Engineering & Mgt			√	√	√	32	1.72
Tsai & Kao [63]	IEEE	Int’l Conf on Systems, Man, & Cybernetics						91
Van der Merwe & Engelbrecht [49]	IEEE	Congress on Evolutionary Computation						953
Vijayakumari & Deepa [183]	Infokara							0
Wang et al. [101]	IEEE	Access						2	3.367
Wang et al. [176]	IEEE	Int’l Conf on Grey Systems & Intelligent Services						5
Wang [129]	IEEE	Adv. Infor Mgt, Comm, Electronic & Auto Control Conf						3
Wang, Liu & Xiang [160]	Taylor & Francis	Int’l Journal of Parallel, Emergent & Distributed Systems		√	√	√	√	2	1.51
Wang, Xiang & Liu [159]	IEEE	Int’l Conf on Intelligent Science & Big Data Engineering						0
Weisun & Liu [157]	WSEAS							0
Wu et al. [84]	Elsevier	Agricultural Water Mgt			√	√		6	4.516
Xiao, Yan, Zhang, & Tang [31]	Elsevier	Expert Systems with Appl	√	√	√	√		108	6.954
Xie et al. [74]	Elsevier	Applied Soft Computing			√	√		40	6.725
Yang, Sun & Zhang [62]	Elsevier	Expert Systems with Appl	√	√	√	√		228	6.954
Yang, & Sutrisno [198]	Elsevier	Applied Soft Computing			√	√		1	6.725
Ye et al. [111]	IEEE	Int’l Conf on Convergence & Hybrid Information Tech						10
Zhang & Zhou [35]	IEEE	Int’l Conf on Artificial Intelligence & Big Data						11
Zhang, Leung & Ye [199]	IEEE	Int’l Conf on Convergence & Hybrid Information Tech						26
Zhao & Liu [156]	Springer	Int’l Conf on Human Centered Computing						0
Zhao, Liu & Zhang [158]	TELKOMNIKA	Indonesian Journal of Elect Engineering,						5
Zhou et al. [192]		Guangxi Key Laboratory						19
Zhou et al. [45]	MDPI	ISPRS Int’l Journal of Geo-Information		√	√	√	√	20	2.899

4. Results and Discussions

4.1. Metrics

The articles that were selected for this study were based on metrics such as article publishers, journals, citation numbers, and the impact factors. Articles from conferences proceedings were also considered. The details of the articles selected are presented in Table 4. The largest number of articles were selected from IEEE with 46 articles, followed by Springer and Elsevier with 37 articles and 30 articles, respectively. Inderscience, MDPI, and IOP publishing, respectively, had six, five, and three articles each. PMC, ProQuest, and ScitePress have two articles each, while all other publishers have one each. Thirty-two of the articles were indexed in Science, twenty-four in WOS, sixty-one in Scopus, sixty-six in Google Scholar, and twenty-two in DBLP. All the articles were gathered between 19 May 2021 and 23 June 2021.

4.2. Strength of This Study

A comprehensive analysis of hybridization of K-means with nature-inspired metaheuristic optimization algorithms is presented in this study. It includes a hundred and forty-seven hybridized K-means with different MOA clustering algorithms. Recent publications from 2019, 2020, and 2021 are also considered. The role of K-means algorithms and the corresponding MOA in the hybridized algorithms were highlighted, including the dataset used for testing and the criteria for their performance measure. This detail is presented in Table 4. The algorithms that actually handled automatic clustering are also identified among the lot. The various automatic clustering approaches adopted in the reported automatic K-means hybridization are also identified and presented. Current challenges, as well as future directions, are also discussed.

4.3. Weakness of This Study

In order to incorporate details of the relevant manuscripts, a maximum effort has been expended, and most available articles in the last two decades were considered. Nevertheless, it is an impossible task to cover all the manuscripts in a single study. All non-English-based related manuscripts were not included in this study. Some other metaheuristic optimization algorithms were not considered as well.

4.4. Hybridization of K-Means with MOA

From this study, it can be observed that the K-means clustering algorithm has been widely hybridized with various MOA to improve the process of data clustering. The advantages of K-means in terms of simplicity and low computational complexity have been harnessed to improve the clustering capability of many of the MOA. The ability of many of the MOA in global optimum search enhanced the performance of K-means in escaping local optimal convergence leveraging on their optimization capability. Hybridizing K-means with MOA provides a balance between exploration and exploitation in the search algorithm to improve the quality of the final cluster result. There are noticeable improvements in general clustering performance and efficiency in relation to cluster results.

Specification of the number of clusters as a user parameter is a major challenge in cluster analysis. The various hybridization of nature-inspired meta-heuristics techniques with K-means clustering algorithms that handled automatic clustering problems were presented. From the study, it can be seen that only a few of the hybrid algorithms addressed the problem of automatic clustering. Different methods were adopted in estimating the optimal number of clusters in any given dataset. In most of the automatic hybrid algorithms, the correct number of clusters were optimized from the initial population, which were either randomly generated or deterministically selected from the data objects.

Automatic specification of cluster number in the K-means with MOA hybrid algorithm conspicuously enhanced the performance of the former algorithm by reducing the number of iteration operations required to obtain an optimal result compared with the traditional algorithm. Most initialization problems associated with traditional K-means, such as user-specified parameters of k and random selection of cluster centers, were resolved through the generation of optimized initial cluster centroids, which was made possible by the optimization process of the MOA. The number of optimum cluster centers invariably gives the number of clusters to be generated.

In some of the hybrid algorithms, parallelization of the K-means algorithm and quantum processing was made possible for faster convergence, handling distributed datasets, improved multidimensional datasets clustering, and reducing computational complexity. The issues of outlier detection, noise handling, discovering non-globular clusters, and non-linear partitioning were solved by some of the hybrid algorithms, as well as efficient clustering of large and high dimensional datasets.

Furthermore, the various hybridized algorithms were tested on either synthetically generated datasets, UCI datasets, or some real-life datasets. The datasets used with the corresponding hybrid algorithm can be found in Table 2. The performance of the hybridized algorithms was also measured using different cluster analysis performance metrics. This is also included in Table 2.

4.5. Impact of Automatic Hybridized K-Means with MOA

Hybridization of K-means with MOA for automatic clustering has been found to improve the performance of these algorithms in handling cluster analysis. Automatic determination of cluster numbers assists in avoiding the sensitivity of initial seeds in the initial population [45]. In most cases, it helps select near optimum initial cluster centroids for the clustering process instead of the usual random selection of the initial cluster centroids.

Determining the number of clusters automatically also enhances the convergence speed of the resultant hybridized clustering algorithm due to fewer iterations required to obtain the optimal cluster result. The impact of automatic hybridized algorithms is more pronounced when handling real-life datasets. An accurate guess of the correct number of clusters in real-life datasets is an assiduous task, if not impossible, due to its high dimensionality and density. Improving traditional K-means to solve real-life automatic clustering problems through hybridization is of great impact in cluster analysis.

4.6. Trending Areas of Application of Hybridized K-Means with MOA

The trending areas of application of K-means with MOA hybrid algorithms reported in the reviewed literature include cluster analysis optimization, image segmentation, social network community detection, localization and sizing of flexible AC transmission system, routing protocols, color quantization, forecasting models, image compression, satellite image classification, facility location, intrusion detection, document information retrieval, and cloud networks load balancing. A summarized list of all the application areas identified in the cause of the study that are associated with the hybrid K-means algorithms is listed in Table 1.

4.7. Research Implication and Future Directions

The major emphasis of this study is to identify the K-means hybrid developed for the purpose of automatic clustering. However, most of the reviewed articles concentrated efforts on finding solutions to the initial cluster centroid problems of the traditional K-means algorithm and the problem of local optimum convergence. In some other cases, the attention was not on improving the K-means clustering algorithm. Instead, the attention was on improving the performance of the corresponding MOA in handling the clustering problem. For the few that proposed improving the K-means clustering algorithm, their performances’ limitations, such as increased $d$ number of user-dependent variables and algorithm complexity, limit their performances. The same drawbacks also affect the hybridized algorithm extending the K-means algorithm for handling automatic clustering.

Moreover, the number of research papers on the hybridization of K-means with MOA is relatively small compared with the number of existing MOAs and still smaller when the issue of automatic clustering is considered. There is a need for further research on finding new K-means hybridization that will enhance its performance in handling automatic clustering for big data clustering while maintaining its desirable quality of linear order complexity. In most hybridized algorithms, a higher execution time is required to obtain higher quality clustering results. Further, they are more computationally expensive due to the increase in the necessary iteration operation to achieve convergence. A computationally less expensive hybridized K-means algorithm that can handle automatic clustering will be highly desirable.

5. Conclusions

In this study, hybridization of the K-means clustering algorithm with different MOAs has been presented. The primary objective of each hybridization was considered with the role of corresponding MOA and K-means in the resultant hybridized algorithm. The various dataset used for testing as well as the criteria used for performance evaluation were similarly extracted. The various existing MOA and hybrids used for comparison purposes for judging the performance of the hybridized algorithm were also presented. The publication rate of research on K-means hybridization with some MOA has also been presented as well as the normalized rate of the publications. The critical analysis of the findings from the study revealed the normalized publication rate of the different extracted articles on integrating K-means with MOAs. Five research questions were designed, and the corresponding answers were provided in this extensive literature analysis of the different hybridization methods incorporating the K-means clustering algorithm with MOA.

From the response to the first research question, twenty-nine metaheuristics optimization algorithm, most of which are nature-inspired, were considered with a hundred and forty-seven articles reviewed that reports the various hybridization with K-means clustering algorithm or any of its variants. In the provided answers to the second research question, the various articles whose primary objective was to solve the problem of automatic clustering were identified among the reviewed articles. These articles were relatively small compared with the total number of articles selected for the study. Various areas of application where these hybridized algorithms have been deployed are also listed. The reviewed hybridized algorithm’s various approaches to automatic clustering were discussed in response to the third research question. The response to the fifth question presented a thorough analysis of the publication trend with reference to K-means hybridization with MOA in the last two decades. A bifurcation presentation of the reviewed algorithms reveals that there is a generally low rate in research publication involving the hybridization of K-means with MOA in most of the reviewed literature. This indicates a great need for more attention in this area of research, most especially for handling automatic clustering problems. This was further verified by the graphical report obtained from the normalization of the publication rate. Finally, the study further reveals that the existing hybridized K-means algorithms with MOAs still require higher execution time when applied to the clustering of a big dataset to obtain higher quality clustering results.