The widespread application of clustering in various fields leads to the discovery of different clustering techniques in order to partition multidimensional data into separable clusters. Although there are various clustering approaches used in literature, optimized clustering techniques with multi-objective consideration are rare. This paper proposes a novel data clustering algorithm, Enhanced Kernel-based Exponential Grey Wolf Optimization (EKEGWO), handling two objectives. EKEGWO, which is the extension of KEGWO, adopts weight exponential functions to improve the searching process of clustering. Moreover, the fitness function of the algorithm includes intra-cluster distance and the inter-cluster distance as an objective to provide an optimum selection of cluster centroids. The performance of the proposed technique is evaluated by comparing with the existing approaches PSC, mPSC, GWO, and EGWO for two datasets: banknote authentication and iris. Four metrics, Mean Square Error (MSE), F-measure, rand and jaccord coefficient, estimates the clustering efficiency of the algorithm. The proposed EKEGWO algorithm can attain an MSE of 837, F-measure of 0.9657, rand coefficient of 0.8472, jaccord coefficient of 0.7812, for the banknote dataset.