In this article we would like to propose a modified simulated annealing procedure termed as adaptive mutation simulated annealing. In this, the parameters within the optimization scheme is dynamically updated keeping in view the requirements of the parameter values needed for efficient and unequivocal identification of the global minimum in a really rugged multiple minima surface. We apply this procedure to the problem of finding out the global minimum structures of pure Platinum and Palladium clusters as well as the mixed Pt-Pd ones (for cluster sizes upto 60), where the interactions among the constituents of the cluster are defined by the many body empirical Gupta potential. Once the structures are obtained, we try to find out the sizes for which the clusters possess greater stability. These so called magic numbers are compared with existing literature values. To test the efficiency of the proposed procedure we compare the results with conventional simulated annealing. We also analyse in detail and calculate various statistical properties and their evolution during the adaptive mutation simulated annealing run. This in-depth analysis gives an insight into why the current procedure outperforms the conventional simulated annealing. © 2013 Springer Science+Business Media New York.