Clustering or unsupervised classification techniques can be used to solve different types of classification problems of different domains. Symmetry is an important property for any real life object. Therefore, symmetry-based distance measurements play some important roles in identifying some patterns or clusters of real life datasets. In this paper, inspired by the symmetric property, we have proposed a point symmetry-based clustering algorithm which has been used to identify clusters of tissue samples from some real life cancer datasets. Our proposed algorithm is also multi-objective-optimisation (MOO) based, i.e., optimises more than one objectives simultaneously. We have also shown the superiority of our proposed algorithm with respect to some state-of-the-art clustering algorithms.