This paper puts forward a new automatic clustering algorithm based on Multi-Objective Particle Swarm Optimization and Simulated Annealing, "MOPSOSA". The proposed algorithm is capable of automatic clustering which is appropriate for partitioning datasets to a suitable number of clusters. MOPSOSA combines the features of the multi-objective based particle swarm optimization (PSO) and the Multi-Objective Simulated Annealing (MOSA). Three cluster validity indices were optimized simultaneously to establish the suitable number of clusters and the appropriate clustering for a dataset. The first cluster validity index is centred on Euclidean distance, the second on the point symmetry distance, and the last cluster validity index is based on short distance. A number of algorithms have been compared with the MOPSOSA algorithm in resolving clustering problems by determining the actual number of clusters and optimal clustering. Computational experiments were carried out to study fourteen artificial and five real life datasets.