Abstract
Simulated Annealing is a randomized optimization method, which accepts deteriorations of the objective function with a probability depending on a control parameter, based on a physical analogy.
In the building of Simulated Annealing algorithms, the manner in which a set of parameters is defined (cooling strategy) specifies two distinct classes: Dynamic Algorithms, with adaptive parameters and Static Algorithms, when parameters are fixed a priori.
We believe that the direct thermodynamic analogy can effectively be used in the evaluation of dynamic annealing parameters. In this paper we show how the concept of entropy can be used to evaluated two of such parameters.
We present an account of the entropy concept, within the Information Theory and Thermodynamics contexts, and derive a method for thermal equilibrium identification. With basis on this result, we propose an adaptive annealing schedule and present a report of its application to a different combinatorial optimization problem.
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References
E.Bonomi, J. Lutton, The N-City Travelling Salesman Problem: Statistical Mechanics and the Metropolis Algorithm, Society for Industrial and Applied Mathematics, Vol. 26 N-4 October, 1984.
V. Cerny, Thermodynamical Approach to the Traveling Salesman Problem: an Efficient Simulation Algorithm, J. Opt. Theory Appl., Vol.n245 (1985) 41–45.
J. S. Dugdale, Entropy and Low Temperature Physics, Hutchinson University Library, London, 1966.
B. Hajek; Cooling Schedules for Optimal Annealing, Mathematical of Operational Research, Vol. 13, n22, May 1988.
E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, Vol. 106, n-4, May 15, 1987.
S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Optimization by Simulated Annealing, Science, Vol. 220, n-4598 13 May 1983.
P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, 1987.
M. P. McLaughlin, Simulated Annealing, Dr. Dobb’s Journal, September 1989.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H.Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, Vol. 21, n-6, June 1953.
L. J. Osborne, B. E. Gillett, A Comparison of Two Simulated Annealing Algorithms Applied to the Directed Steiner Problem on Networks, ORSA Journal of Computing, Vol.n23 Summer 1991.
F. Reif, Statistical Physics, Berkeley Physics Course, Vol. 5, McGraw-Hill, 1965.
J. Rose, W. Klebsch, J. Wolf, Temperature Measurement and Equilibrium Dynamics of Simulated Annealing Placements, IEEE Transactions on Computer Aided Design, Vol. 9, n-3, March 1990.
G. Sasaki, The Effect of the Density of States on the Metropolis Algorithm, Information Processing Letters, 37 (1991), 159–163, North-Holland.
C. E. Shannon, W. Weaver, The Mathematical Theory of Communication, University of Illinois Press, Urbana, 1949.
M. P. Vecchi, S. Kirkpatrick, Global Wiring by Simulated Annealing, IEEE Transactions on Computer Aided Design, Vol. CAD 2, n-4, October 1983.
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© 1993 Springer-Verlag Berlin Heidelberg
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Rodrigues, M.R.D., Anjo, A.J.B. (1993). On Simulating Thermodynamics. In: Vidal, R.V.V. (eds) Applied Simulated Annealing. Lecture Notes in Economics and Mathematical Systems, vol 396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46787-5_3
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DOI: https://doi.org/10.1007/978-3-642-46787-5_3
Publisher Name: Springer, Berlin, Heidelberg
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