Abstract
Recently, simulated annealing methods have proven to be a valuable tool for global optimization. We propose a new stochastic method for locating the global optimum of a function. The proposed method begins with the subjective specification of a probing distribution. The objective function is evaluated at a few points sampled from this distribution, which is then updated using the collected information. The updating mechanism is based on the entropy of a move selecting distribution and is loosely connected to some notions in statistical thermodynamics. Examples of the use of the proposed method are presented. These indicate its superior performance as compared with simulated annealing. Preliminary considerations in applying the method to discrete problems are discussed.
Similar content being viewed by others
References
Aarts, E. and J., Korst (1989) Simulated Annealing and Boltzmann Machines, New York: John Wiley.
Bélisle, C. J. P., H. E., Romeijn and R. L., Smith (1990), Hide-and-Seek: A Simulated Annealing Algorithm for Constrained Global Optimization, Technical Report 176, Department of Statistics, The University of Michigan, Ann Arbor, Michigan, U.S.A.
Bohachevsky, I., M. E., Johnson and M. L., Stein (1986), Generalized Simulated Annealing for Function Optimization, Technometrics 28, 209–217.
Cerny, V. (1985), Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm, Journal of Optimization Theory and Applications 45, 41–51.
Geman, S. and D., Geman (1984), Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Proc. Pattern Analysis and Machine Intelligence 6, 721–741.
Geman S. and D. E. McClure (1985), Bayesian Image Analysis: An Application to Single Photon Emission Tomography, Proc. American Statistical Association, Statistical Computing Section, 12–18.
Haines, L. M. (1987), The Application of the Annealing Algorithm to the Construction of Exact Optimal Designs for Linear-Regression Models, Technometrics 29, 439–448.
Kirkpatrick, S., C. D., Gelatt and M. P., Vecchi (1983), Optimization by Simulated Annealing, Science 220, 671–680.
Johnson, M. E. (1987), Multivariate Statistical Simulation, New York: John Wiley.
Laarhoven, P. J. M.van, and E. H. L., Aarts (1987), Simulated Annealing: Theory and Applications, Dordrecht: Reidel.
Mockus, J. (1989), Bayesian Approach to Global Optimization, Dordrecht: Kluwer Academic Publishers.
Pincus, M. (1970), A Monte-Carlo Method for the Approximate Solution of Certain Types of Constrained Optimization Problems, Operations Research 18, 1225–1228.
Pronzato, L., E., Walter, A., Zenot and J. F., LeBruchec (1984), General Purpose Global Optimizer, Mathematics and Computers in Simulation 26, 412–422.
Rinnoy Kan, A. H. G., C. G. E., Boender and G. Th., Timmer (1985), A Stochastic Approach to Global Optimization, in Computational Mathematical Programming, ed. K., Schittkowski, Berlin: Springer-Verlag, 281–308.
Ripley, B. D. (1987), Stochastic Simulation, New York: John Wiley.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laud, P.W., Berliner, L.M. & Goel, P.K. A stochastic probing algorithm for global optimization. J Glob Optim 2, 209–224 (1992). https://doi.org/10.1007/BF00122056
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00122056