## 3 Data Synthesis and Analysis
#### 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 [PERSON] 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. [PERSON] and [PERSON] [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. [PERSON], [PERSON], and [PERSON] [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. [PERSON] and [PERSON] [59] combined K-means and PSO to propose RVPSO-K for clustering Web Usage patterns achieving better stability. [PERSON], [PERSON], and [PERSON] [60] proposed K-NM-PSO, which hybridized PSO and Nelder-Mead simplex search with K-means clustering algorithm. [PERSON] and [PERSON] [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 [PERSON], [PERSON], and [PERSON] [62] to fully use the advantages of the two algorithms for better cluster analysis. [PERSON] and [PERSON] [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. [PERSON] and [PERSON] [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. [PERSON] and [PERSON] [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. [PERSON] and [PERSON] [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 [PERSON] 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. [PERSON] 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. [PERSON] [68] proposed an improvement on the regular hybridization of PSO and K-means clustering algorithm by applying mutation operation with PSO particles. [PERSON], [PERSON], and [PERSON] [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. [PERSON] and [PERSON] [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.