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Computational experience with generalized simulated annealing over continuous variables. (English) Zbl 0684.65061
This paper reports computational results obtained using the generalized simulated annealing method (GSA), introduced by I. O. Bohachevsky, M. E. Johnson and M. L. Stein [Technometrics 28, 209–217 (1986; Zbl 0609.65045)] which uses the current function value to control the random process, on a set of seven standard global optimization test problems with continuous variables, and compares to those obtained using some well-known competing stochastic methods.
It seems that although GSA may be competitive with these methods when solving these test problems of the size, its performance on functions with continuous variables may be worse than that on functions with discrete variables. It is less attractive that application of GSA to functions of continuous variables increasing the complexity of the process, and the sensitivity of its performance to the parameters, such as S (step size), necessitates user interaction to “tune” the algorithm.
Reviewer: Pingqi Pan

65K05 Numerical mathematical programming methods
90C31 Sensitivity, stability, parametric optimization
90C15 Stochastic programming
Full Text: DOI
[1] Anily S., Journal of Applied Probability 24 pp 657– (1987) · Zbl 0628.60046
[2] Bohachevsky I.O., Technometrics 28 pp 209– (1986)
[3] Bonomi E., SIAM Review 26 pp 551– (1984) · Zbl 0551.90095
[4] Branin F., Numerical Methods of Nonlinear Optimization (1971)
[5] Bremmerman H., Mathematical Biosciences 9 pp 1– (1970) · Zbl 0212.51204
[6] De Biasi L., Towards Global Optimization 2 (1978)
[7] Dixon L., Towards Global Optimization 2 (1978)
[8] Eureka: The Solver (IBM version)
[9] Geman S., IEEE Transactions Pattern Analysis and Machine Intelligence (1984)
[10] Gidas B., Journal of Statistical Physics 39 pp 73– (1965) · Zbl 0642.60049
[11] Hajek B., Adaptive Statistical Procedures and Related Topics; IMS Lecture Notes (1986)
[12] Kirkpatrick S., Science 220 pp 671– (1983) · Zbl 1225.90162
[13] Lundy M., Mathematical Programming 34 pp 111– (1986) · Zbl 0581.90061
[14] Mockus J., Towards Global Optimization 2 (1978)
[15] Nelder J .A., The Computer Journal 7 pp 308– (1965) · Zbl 0229.65053
[16] Price W., Towards Global Optimization 2 (1978)
[17] Rinnooy, Kan A., American Journal of Mathematical and Management Sciences 4 pp 7– (1984)
[18] Rinnooy Kan A., Mathematical Programming 39 pp 57– (1987) · Zbl 0634.90067
[19] Torn A., ”Cluster Analysis Using Seed Points and Density Determined Hypersheres with an Application to Global Optimization” (1976)
[20] Vanderbilt D., Journal of Computational Physics 56 pp 259– (1984) · Zbl 0551.65045
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