TITLE:
An Optimal Cooling Schedule Using a Simulated Annealing Based Approach
AUTHORS:
Alex Kwaku Peprah, Simon Kojo Appiah, Samuel Kwame Amponsah
KEYWORDS:
Simulated Annealing (SA), Variable Cooling Factor (VCF), Powell-Simulated Annealing (PSA), Global Minima, Rosenrock Functions, Android Smartphone Systems (ASS)
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
31,
2017
ABSTRACT: 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.