The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Cooling Schedules for Optimal Annealing
Abstract
A Monte Carlo optimization technique called “simulated annealing” is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima. The level of randomization is determined by a control parameter T, called temperature, which tends to zero according to a deterministic “cooling schedule.” We give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states. In the special case that the cooling schedule has parametric form T(t) = c/log(1 + t), the condition for convergence is that c be greater than or equal to the depth, suitably defined, of the deepest local minimum which is not a global minimum state.
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Citations
Cites
Optimization by Simulated Annealing
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983) · Science · doi:10.1126/science.220.4598.671 · Cited by 45,134
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
Černý, V. (1985) · Journal of Optimization Theory and Applications · doi:10.1007/bf00940812 · Cited by 3,436
Diffusions for Global Optimization
Geman, S., & Hwang, C.-R. (1986) · SIAM Journal on Control and Optimization · doi:10.1137/0324060 · Cited by 313
Nonstationary Markov chains and convergence of the annealing algorithm
Gidas, B. (1985) · Journal of Statistical Physics · doi:10.1007/bf01007975 · Cited by 248
Cited by
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS
Sambridge, M., & Mosegaard, K. (2002) · Reviews of Geophysics · doi:10.1029/2000rg000089 · Cited by 829
Simulated annealing: A tool for operational research
Eglese, R. W. (1990) · European Journal of Operational Research · doi:10.1016/0377-2217(90)90001-r · Cited by 801
Simulated annealing for permutation flow-shop scheduling
Osman, I., & Potts, C. (1989) · Omega · doi:10.1016/0305-0483(89)90059-5 · Cited by 614
Schmitt, L. M. (2001) · Theoretical Computer Science · doi:10.1016/s0304-3975(00)00406-0 · Cited by 512
Minimization of $\ell_{1-2}$ for Compressed Sensing
Yin, P., Lou, Y., He, Q., & Xin, J. (2015) · SIAM Journal on Scientific Computing · doi:10.1137/140952363 · Cited by 473
Metadata
- Authors
- Hajek, B.
- Venue
- Mathematics of Operations Research
- Published
- 1988-05
- Volume
- 13
- Issue
- 2
- Pages
- 311-329
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2005228957
- Cited by
- 1,246
- References
- 5
- FWCI
- 28.99
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hajek, B. (1988). Cooling Schedules for Optimal Annealing. Mathematics of Operations Research. https://doi.org/10.1287/moor.13.2.311
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