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Simulated annealing (SA) has been a very useful stochastic method for solving problems of multidimensional global optimization that ensures convergence to a global optimum. This paper proposes a variable cooling factor (VCF) model for simulated annealing schedule as a new cooling scheme to determine an optimal annealing algorithm called the Powell-simulated annealing (PSA) algorithm. The PSA algorithm is aimed at speeding up the annealing process and also finding the global minima of test functions of several variables without calculating their derivatives. It has been applied and compared with the SA algorithm and Nelder and Mead Simplex (NMS) methods on Rosenbrock valleys in 2 dimensions and multiminima functions in 3, 4 and 8 dimensions. The PSA algorithm proves to be more reliable and always able to find the optimum or a point very close to it with minimal number of iterations and computational time. The VCF compares favourably with the Lundy and Mees, linear, exponential and geometric cooling schemes based on their relative cooling rates. The PSA algorithm has also been programmed to run on android smartphone systems (ASS) that facilitates the computation of combinatorial optimization problems.

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