In cluster analysis, a fundamental problem is to determine the best estimate of the number of clusters; this is known as the automatic clustering problem. Because of lack of prior domain knowledge, it is difficult to choose an appropriate number of clusters, especially when the data have many dimensions, when clusters differ widely in shape, size, and density, and when overlapping exists among groups. In the late 1990s, the automatic clustering problem gave rise to a new era in cluster analysis with the application of nature-inspired metaheuristics. Since then, researchers have developed several new algorithms in this field. This paper presents an up-to-date review of all major nature-inspired metaheuristic algorithms used thus far for automatic clustering. Also, the main components involved during the formulation of metaheuristics for automatic clustering are presented, such as encoding schemes, validity indices, and proximity measures. A total of 65 automatic clustering approaches are reviewed, which are based on single-solution, single-objective, and multiobjective metaheuristics, whose usage percentages are 3%, 69%, and 28%, respectively. Single-objective clustering algorithms are adequate to efficiently group linearly separable clusters. However, a strong tendency in using multiobjective algorithms is found nowadays to address non-linearly separable problems. Finally, a discussion and some emerging research directions are presented. 
Automatic clustering using nature-inspired metaheuristics: A survey