Abstract
Simulated Annealing is a family of randomized algorithms for solving multivariate global optimization problems. Empirical results from the application of Simulated Annealing algorithms to certain hard problems including certain types of NP-complete problems demonstrate that these algorithms yield better results than known heuristic algorithms. But for the worst case input, the time bound can be exponential.
In this paper, for the first time, we show how to improve the performance of Simulated Annealing algorithms by exploiting some special properties of the cost function to be optimized. In particular, the cost functions we consider are small-separable, with parameter s(n). We develop an algorithm we call “Nested Annealing” which is a simple modification of simulated annealing where we assign different temperatures to different regions. Simulated Annealing can be shown to have expected run time 2Ω(n) whereas our improved algorithm has expected performance 2O(s(n)). Thus for example, in many vision and VLSI layout problems, for which \(s(n) = O(\sqrt n )\), our time bound is \(2^{O(\sqrt n )}\) rather than 2Ω(n).
Supported by NSF-DCR-85-03251 and ONR contract N00014-87-K-0310
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Brelaz, D., ‘New Methods to color the vertices of a graph,’ Comm. ACM 22, 1979, pp. 251–256.
Bonomi,E., and Lutton,J.L., 'simulated Annealing Algorithm for the Minimum Weighted Perfect Euclidean Matching Problem,’ R.A.I.R.O Operations Research, to appear.
Christofides, N., ‘Worst Case Analysis of a New Heuristic for the Travelling Salesman Problem', Abstract in Algorithms and Complexity (J. Traub, ed.). Academic Press 1976.
Dunlop, A.E., and Kernighan, B.W., ‘A Procedure for Placement of Standard-cell VLSI Circuits,’ IEEE Trans. Computer Aided Design 4, 1985, pp. 92–98.
ElGamal, A., and Shperling, I., ‘Design of Good Codes via Simulated Annealing,’ List of Abstracts, Workshop on Statistical Physics in Engineering and Biology, Yorktown Heights, NY, April 1984.
Golden, B.L., and Skiscim, C.C., ‘Using Simulated Annealing to solve Routing and Location Problems,’ Naval Research Logistics Quarterly, 33, 1986, pp. 261–279.
Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C., ‘Optimization by Simulated Annealing: An Experimental Evaluation (Part I),’ Preliminary Draft, AT&T Bell Labs., Murray Hill, NJ, 1987.
Karp, R.M., ‘Probabilistic Analysis of Partitioning Algorithms for the Travelling Salesman Problem in the Plane,’ Mathematics of Operations Research, vol.2, nO.3, 1977, pp. 209–224.
Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., ‘Optimization by Simulated Annealing,’ Science, May 1983.
Kirousis, L.M., Papadimitriou, C.H., ‘The Complexity of Recognizing Polyhedral Scenes,’ IEEE FOCS 1985. pp. 175–185.
Kasif, S., Reif, J.H., and Sherlekar, D.D., ‘Formula Dissection: A Divide and Conquer Algorithm for Satisfiability,’ Technical Report, Johns Hopkins University, 1985.
Lichtenstein, D., ‘Planar Formulae and their Uses,’ SIAM Journal of Computing, vol.11, no.2, 1982.
Lipton, R.J., and Tarjan, R.E., ‘Applications of a Planar Separator Theorem,’ SIAM Journal on Computing, vol.9, no.3, 1980.
Lipton, R.J., and Tarjan, R.E., ‘A Planar Separator Theorem,’ SIAM Journal on Applied Mathematics, vol.36, no.2, 1979.
Mitra, D.,Romeo, F., and Vincentelli, A.S., ‘Convergence and Finite-Time Behaviour of Simulated Annealing,’ Advances in Applied Probability, Sept. 1986.
Pan, V., and Reif, J.H., ‘Fast and Efficient Solutions of Linear Systems,’ Proc. 17th Annual Symposium on Theory Of Computing, 1985.
Rabin, M.O., ‘Probabilistic Algorithms,’ in: Traub, J.F., ed., Algorithms and Complexity, Academic Press, New York, 1976. pp. 21–36.
Solovay, R., and Strassen, V., ‘A Fast Monte-Carlo Test for Primality,’ SIAM Journal of Computing, vol.6, 1977, pp. 84–85.
Valiant, L.G., ‘A Theory of the Learnable,’ Communications of the ACM, vol.27, no. 11, Nov. 1984.
Vecchi, M.P., and Kirkpatrick, S., ‘Global Wiring by Simulated Annealing,’ Technical Report, IBM Thomas J. Watson Research Center, New York 10598.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rajasekaran, S., Reif, J.H. (1988). Nested annealing: A provable improvement to simulated annealing. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_134
Download citation
DOI: https://doi.org/10.1007/3-540-19488-6_134
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19488-0
Online ISBN: 978-3-540-39291-0
eBook Packages: Springer Book Archive