Abstract
In this paper a brief survey of recent developments in the field of stochastic global optimization methods will be presented. Most methods discussed fall in the category of two-phase algorithms, consisting in a global or exploration phase, obtained through sampling in the feasible domain, and a second or local phase, consisting of refinement of local knowledge, obtained through classical descent routines. A new class of methods is also introduced, characterized by the fact that sampling is performed through deterministic, well distributed, sample points. It is argued that for moderately sized problems this approach might prove more efficient than those based upon uniform random samples.
Similar content being viewed by others
References
Bratley, P., Fox, B. L., and Niederreiter, H. (1994), Algorithm 738: Programs to generate Niederreiter's low-discrepancy sequences, ACM Transactions on Mathematical Software 20: 494–495.
Deheuvels, P. (1983), Strong bounds for multidimensional spacings, Z. Wahrsch. Verw. Geb. 64: 411–424.
Drmota, M. and Tichy, R. (1997), Sequences, discrepancies and applications, Vol. 1651 of Lecture Notes in Mathematics, eds., A. Dold, F. Takens, Springer Verlag, New York.
Halton, J. H. (1960), On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2: 84–90.
Locatelli, M. (1996), Convergence properties of simulated annealing for continuous global optimization, Journal of Applied Probability 33: 1127–1140.
Locatelli, M. and Schoen, F. (1996), Simple Linkage: Analysis of a threshold-accepting global optimization method, Journal of Global Optimization 9: 95–111.
Locatelli, M. and Schoen, F. (1998), Random Linkage: a family of acceptance/rejection algorithms for global optimisation, Mathematical Programming, to appear.
Neumaier, A. (1997), Molecular modeling of proteins and mathematical prediction of protein structure, SIAM Review 39: 407–460.
Niederreiter, H. (1992), Random number generation and quasi-Monte Carlo methods, SIAM
Ribenboim, P. (1995), The New book on Prime Number Records, 3rd edn, Springer Verlag. New York.
Rinnooy Kan, A. H. G. and Timmer, G. (1987a), Stochastic global optimization methods. Part I: Clustering methods, Mathematical Programming 39: 27–56.
Rinnooy Kan, A. H. G. and Timmer, G. (1987b), Stochastic global optimization methods. Part II: Multi level methods, Mathematical Programming 39: 57–78.
Schoen, F. (1997), Global optimization methods for high-dimensional problems, European Journal of Operations Research, submitted.
Schoen, F. (1998), Stochastic global optimization: Two phase methods, in C. Floudas and P. Pardalos (eds.), Encyclopedia of Optimization, to appear. Kluwer Academic Publishers, Dordrecht/Boston/London.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schoen, F. Random and Quasi-Random Linkage Methods in Global Optimization. Journal of Global Optimization 13, 445–454 (1998). https://doi.org/10.1023/A:1008354314309
Issue Date:
DOI: https://doi.org/10.1023/A:1008354314309