Very fast simulated re-annealing. (English) Zbl 0681.90091

Ingber, L.

Math. Comput. Modelling 12, No. 8, 967-973 (1989).

Summary: An algorithm is developed to statistically find the best global fit of a nonlinear nonconvex cost-function over a D-dimensional space. It is argued that this algorithm permits an annealing schedule for “temperature” T decreasing exponentially in annealing-time k, \(T=T_ 0\exp (-ck^{1/D})\). The introduction of re-annealing also permits to changing insensitivities in the multidimensional parameter-space. This annealing schedule is faster than fast Cauchy annealing, where \(T=T_ 0/k\), and much faster than Boltzmann annealing, where \(T=T_ 0/\ln k\). Applications are being made to fit empirical data to Lagrangians representing nonlinear Gaussian-Markovian systems.

MSC:

90C99	Mathematical programming
74A15	Thermodynamics in solid mechanics

Keywords:

best global fit; nonlinear nonconvex cost-function; annealing schedule; re-annealing

References:

[1]	Jammer, M., The Philosophy of Quantum Mechanics (1974), Wiley: Wiley New York
[2]	Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E., Equation of state calculations by fast computing machines, J. chem. Phys., 21, 1087-1092 (1953) · Zbl 1431.65006
[3]	Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P., Optimization by simulated annealing, Science, 220, 671-680 (1983) · Zbl 1225.90162
[4]	German, S.; Geman, D., Stochastic relaxation, Gibbs distribution and the Baysian restorations in images, IEEE Trans. Patt. Anan. Mac. Int., 6, 721-741 (1984)
[5]	Szu, H.; Hartley, R., Fast simulated annealing, Phys. Lett. A, 122, 157-162 (1987)
[6]	Langouch, F.; Roekaerts, D.; Tirapegui, E., Functional Integration and Semiclassical Expansions (1982), Reidel: Reidel Dordrecht · Zbl 0505.28009
[7]	Ingber, L., Statistical mechanics algorithm for response to targets (SMART), ((1985), AAAI-RCA: AAAI-RCA Melo Park, Calif), 258-264, Workshop on Uncertainty and Probability in Artificial Intelligence, UC Los Angeles, 14-16 August 1985
[8]	Ingber, L., Statistical mechanics of nonlinear nonequilibrium financial markets, Mathl Modelling, 5, 343-361 (1984) · Zbl 0562.90018
[9]	Ingber, L., \(C^3\) decision aids: statistical mechanics application of biological intelligence, (1987 Symposium on \(C^3\) Research. 1987 Symposium on \(C^3\) Research, National Defense University, Washington, D.C., 16-18 June 1987 (1987), National Defense University: National Defense University Washington, D.C), 49-57
[10]	Ingber, L., Mathematical comparison of computer-models to exercise data: comparison of JANUS(T) to National Training Center data, (1988 JDL \(C^2\) Symposium. 1988 JDL \(C^2\) Symposium, Naval Postgraduate School, Monterey, Calif., 7-9 June 1988 (1988), SAIC: SAIC McLean, Va), 541-549
[11]	Ingber, L., Riemannian contributions to short-ranged velocity-dependent nucleon-nucleoninteractions, Phys. Rev. D, 33, 3781-3784 (1986)
[12]	Ingber, L., Statistical mechanics of neocortical interactions. Dynamics of synaptic modification, Phys. rev. A, 28, 395-416 (1983)
[13]	Ingber, L., Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity, Phys. Rev. A, 29, 3346-3358 (1984)
[14]	Ingber, L., Statistical mechanics of neocortical interactions. EEG dispersion relations, IEEE Trans. Biomed. Engng, 32, 91-94 (1985)
[16]	Ingber, L., Noise-induced extrema in time-dependent Ginsburg-Landau systems, Mathl Modelling, 7, 525-528 (1986) · Zbl 0613.60075
[17]	Ingber, L., Mesoscales in neocortex and in command, control and communications \((C^3)\) systems, (Delacour, J.; Levy, J. C.S., Systems with Learning and Memory Abilities: Proceedings, University of Paris, 15-19 June 1987 (1988), Elsevier: Elsevier Amsterdam), 387-409
[18]	Nunez, P. L., Electric Fields of the Brain: The Neurophysics of EEG (1981), Oxford Univ. Press: Oxford Univ. Press New York
[19]	Wehner, M. F.; Wolfer, W. G., Numerical evaluation of path integral solutions to Fokker-Planck equations—III. Time and functionally dependent coefficients, Phys. Rev. A, 35, 1795-1801 (1987)