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Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm—Corrigenda for this article is available here
Open accessAbstract
A new global optimization algorithm for functions of continuous variables is presented, derived from the “Simulated Annealing” algorithm recently introduced in combinatorial optimization. The algorithm is essentially an iterative random search procedure with adaptive moves along the coordinate directions. It permits uphill moves under the control of a probabilistic criterion, thus tending to avoid the first local minima encountered. The algorithm has been tested against the Nelder and Mead simplex method and against a version of Adaptive Random Search. The test functions were Rosenbrock valleys and multiminima functions in 2,4, and 10 dimensions. The new method proved to be more reliable than the others, being always able to find the optimum, or at least a point very close to it. It is quite costly in term of function evaluations, but its cost can be predicted in advance, depending only slightly on the starting point.
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Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Cited by
Storn, R., & Price, K. (1997) · Journal of Global Optimization · doi:10.1023/a:1008202821328 · Cited by 29,569
Learning long-term dependencies with gradient descent is difficult
Bengio, Y., Simard, P., & Frasconi, P. (1994) · IEEE Transactions on Neural Networks · doi:10.1109/72.279181 · Cited by 8,542
Global Optimization of Statistical Functions with Simulated Annealing
Goffe, W. L., Ferrier, G. D., & Rogers, J. (1994) · Journal of Econometrics · doi:10.1016/0304-4076(94)90038-8 · Cited by 1,610
Pizzolato, C., Lloyd, D. G., Sartori, M., Ceseracciu, E., Besier, T. F., Fregly, B. J., & Reggiani, M. (2015) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2015.09.021 · Cited by 349
Sexton, R. S., Dorsey, R. E., & Johnson, J. D. (1999) · European Journal of Operational Research · doi:10.1016/s0377-2217(98)00114-3 · Cited by 235
Metadata
- Authors
- Corana, A., Marchesi, M., Martini, C., & Ridella, S.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 1987-09
- Volume
- 13
- Issue
- 3
- Pages
- 262-280
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W2088978850
- Cited by
- 1,531
- References
- 1
- FWCI
- 5.24
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Corana, A., Marchesi, M., Martini, C., & Ridella, S. (1987). Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm—Corrigenda for this article is available here. ACM Transactions on Mathematical Software. https://doi.org/10.1145/29380.29864
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
