Abstract
Many combinatorial optimization problems can be described as finding the global minimum of a certain function U(•) over a finite state space S, say, {l, 2,…, N}. A commonly used approach is the gradient method. It takes “downhill” movements only. This guarantees a fast convergence. But it usually ends up with a local minimum, which might depend on the initial state.
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References
E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines, Wiley, New York, 1989.
Y. Amit and U. Grenander, Compare sweeping strategies for stochastic relaxation, Preprint, Brown Univ, 1989.
R. Azencott, Simulated Annealing, Seminaire Bourbaki, 1987–88, no. 697.
P. Barone and A. Frigessi, Improving stochastic relaxation for Gaussian random fields, Preprint, IAC, Roma, 1988.
O. Catoni, Applications of sharp lare deviations estimates to optimal cooling schedules, Preprint, Ecole Normale Superieure, 1990.
V. Cerny, Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm, J. Opt. Theory Appl. 45 (1985), 41–51.
T. S. Chiang and Y. Chow, On the convergence rate of annealing processes, SIAM J. Control Optim. 26 (1988), 1455–1470.
T. S. Chiang and Y. Chow, A limit theorem for a class of inhomogeneous Markov processes, Ann. Probab. 17 (1989), 1483–1502.
T. S. Chiang and Y. Chow, The asymptotic behavior of simulated annealing process with absorption, Preprint, 1989.
T. S. Chiang, C. R. Hwang and S. J. Sheu, Diffusion for global optimization in Rn, SIAM J. Control Optim. 25 (1987), 737–753.
T. S. Chiang and Y. Chow, Asymptotic behavior of eigenvalues and random updating schemes, Preprint, 1990.
Y. Chow and J. Hsieh, On occupation times of annealing processes, Preprint, 1990.
D. P. Connors and P. R. Kumar, Simulated annealing type Markov chains and their order balance equations, SIAM J. Control Optim. 27 (1989), 1440–1461.
L. Davis, Genetic Algorithm and Simulated Annealing, Pitman. London, 1987.
M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, Springer, Berlin, 1984.
A. Frigessi, C.R. Hwang, S.J. Sheu, P. Stefano, On the Gibbs sampler, the Metropolis algorithm and other single-site updating dynamics, Preprint, 1990.
A. Frigessi, C.R. Hwang and L. Younis, Optimal spectral structure of reversible stochastic matrices, Monte Carlo methods and the simulation of Markov random fields, Preprint, 1990.
N. Gantert, Laws of large numbers for the annealing algorithm, Preprint, Universitat Bonn, 1989.
D. Geman, Random fields and inverse problems in imaging, in Lecture Notes in Mathematics 1427, Springer-Verlag, 1990.
S. Geman and D. Geman, Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images, IEEE PAMI 6 (1984), 721–741.
S. Geman and C. R. Hwang, Diffusions for global optimization, SIAM J. Control Optim. 24 (1986), 1031–1043.
B. Gidas, Global optimization via the Langevin equation, Proc. 24th IEEE Conf. Decision and Control, Fort Lauderdale, Florida, 1985, 774–778.
B. Hajek, Cooling schedules for optimal annealing, Math. Oper. Res. 13 (1988), 311–329.
R. Holley and D. Stroock, Simulated annealing via Sobolev inequalities, Commun. Math. Phys. 115 (1988), 553–569.
C.R. Hwang and S.J. Sheu, Large time behaviors of perturbed diffusion Markov processes with applications III: Simulated annealing, Preprint, 1986.
C.R. Hwang and S.J. Sheu, Singular perturbed Markov chains and exact behaviors of simulated annealing process, Preprint, 1988.
S. Kirkpatrick, C. Gebatt and M. Vecchi, Optimizations by simulated annealing, Science 220 (1983), 671–680.
P. J. M. van Laarhoven and E. Aarts, Simulated Annealing: Theory and Applications, Reidel, Dordrecht, 1987.
D. Mitra, F. Romeo and A. Sangiovanni-Vincentelli, Convergence and finite time behavior of simulated annealing, Adv. Appl. Prob. 18 (1986), 747–771.
A. D. Sokal, Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms, Preprint, 1989.
J. N. Tsitsiklis, Markov chains with rare transitions and simulated annealing, Math. Oper. Res. 14 (1989), 70–90.
A. D. Ventcel, On the asymptotics of eigenvalues of matrices with elements of order exp(-V;•/2f2), Soviet Math. Dokl. 13 (1972), 65–68.
G. Winkler, An ergodic L2-theorem for simulated annealing in Bayesian image reconstruction, J. Appl. Prob. 27 (1990), 779–791.
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© 1992 Springer-Verlag Berlin Heidelberg
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Chiang, T.S., Chow, Y., Hsieh, J. (1992). Some Limit Theorems on Simulated Annealing. In: Barone, P., Frigessi, A., Piccioni, M. (eds) Stochastic Models, Statistical Methods, and Algorithms in Image Analysis. Lecture Notes in Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2920-9_8
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DOI: https://doi.org/10.1007/978-1-4612-2920-9_8
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