Simulated annealing with noisy or imprecise energy measurements Contributed Papers DOI:
10.1007/BF00939629 Cite this article as: Gelfand, S.B. & Mitter, S.K. J Optim Theory Appl (1989) 62: 49. doi:10.1007/BF00939629 Abstract
The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.
Key Words Simulated annealing combinatorial optimization noisy measurements Markov chains
The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.
Kirkpatrick, S., Gelatt, C. D.
Optimization by Simulated Annealing
, Science, Vol. 220, pp. 621–680, 1983.
Cooling Schedules for Optimal Annealing
, Mathematics of Operations Research, Vol. 13, pp. 311–329, 1988.
A Thermodynamical Approach to the Travelling Statesman Problem: An Efficient Simulation Algorithm
, Journal of Optimization Theory and Applications, Vol. 45, pp. 41–51, 1985.
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-6, pp. 721–741, 1984.
Using Simulated Annealing to Solve Routing and Location Problems
, Naval Research Logistics Quarterly, Vol. 33, pp. 261–279, 1986.
Johnson, D. S., Aragon, C. R., McGeoch, L. A., and Schevon, C., Optimization by Simulated Annealing: An Experimental Evaluation, Preprint, 1985.
El Gamal, A., Hemachandra, L., Shperling, I.
Using Simulated Annealing to Design Good Codes
, IEEE Transactions on Information Theory, Vol. IT-33, pp. 116–123, 1987.
Nonstationary Markov Chains and Convergence of the Annealing Algorithm
, Journal of Statistical Physics, Vol. 39, pp. 73–131, 1985.
Mitra, D., Romeo, F.
Convergence and Finite-Time Behavior of Simulated Annealing
, Advances in Applied Probability, Vol. 18, pp. 747–771, 1986.
Markov Chains with Rare Transitions and Simulated Annealing
, Mathematics of Operations Research, Vol. 14, pp. 70–90, 1989.
Tsitsiklis, J., A Survey of Large Time Asymptotics of Simulated Annealing Algorithms, Massachusetts Institute of Technology, Laboratory for Information and Decision Systems, Report No. LIDS-P-1623, 1986.
Grover, L., Simulated Annealing Using Approximate Calculations, Preprint, 1986.
Probablity and Measure
, Wiley, New York, New York, 1978.
Goles, E., and Vichniac, G., Lyapunov Functions for Parallel Neural Networks, Proceedings of the AIP Conference on Neural Networks for Computing, Snowbird, Utah, pp. 165–181, 1986. Copyright information
© Plenum Publishing Corporation 1989