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Top1. Introduction
Investigations and developments are made in recent decades to find optimal solutions for large and dynamic problems using nature-inspired algorithms (Chakraborty, Amrita, & Kumar Kar, 2017). This can be achieved by avoiding inefficient enumerating process. Many researchers have developed numerous optimization algorithms by looking into the nature, looking into the biology and tried to model some of the impressive and intellectual mechanisms (Pedrycz, & Witold, 2010) into new algorithms for different engineering applications (Bozorg-Haddad, & Omid, 2017).
Population based Meta-heuristic optimization algorithms have numerous engineering applications (Patnaik, Srikanta, Yang, & Nakamatsu, 2017). These kinds are popular in optimizing complex functions. Finding optimal structures of data is a challenging task in data mining (Özbakır, Lale, & Turna, 2017; Jain, 2010; Han, & Kamber, 2001). Cluster analysis is an unsupervised technique and one of the best way to find the structures of data. This clustering process discovers the natural grouping of data points according to the similarity of measured intrinsic characteristics (Gagliardi, & Francesco, 2012). For an instance, in the k-Means partitional clustering, the similarity function that should be minimize centroid distance to obtain good clusters. i.e. minimization of sum of squared Euclidean distance of objects from respective cluster means that is shown as fallows.
(1) Where
is the mean of
Table 1. Notations of Uni and Multimodal benchmark functions Where V_no = 30, fmin = 0
| Function name | Range |
F1(x) =  | [-100, 100] |
F2(x) =  | [-10, 10] |
F3(x) =  | [-100, 100] |
F4(x) = maxi { } | [-100, 100] |
F5(x) =  | [-30, 30] |
F6(x) =  | [-100, 100] |
F7(x) =  | [-1.28, 1.28] |