Stochastic methods for global optimization

SYNOPTIC ABSTRACTThe most efficient methods for finding the global minimum of an objective function (not necessarily convex) are those that embody stochastic elements. In this survey, we focus on methods that are based on a random sample of points and that use a combination of clustering and local search to identify all the local optima that are potentially global. Special attention is paid to a proper termination criterion for the sequence of sampling, clustering and searching, and to the analysis of the result produced by the method.

[1]  H. Zimmermann.  Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[2]  B. Betrò.  Bayesian testing of nonparametric hypotheses and its application to global optimization , 1984 .

[3]  Antanas Zilinskas,et al.  Axiomatic approach to statistical models and their use in multimodal optimization theory , 1982, Math. Program..

[4]  Alexander H. G. Rinnooy Kan,et al.  A stochastic method for global optimization , 1982, Math. Program..

[5]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[6]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[7]  H. Kushner.  A versatile stochastic model of a function of unknown and time varying form , 1962 .

[8]  C. G. E. Boender,et al.  A Bayesian Analysis of the Number of Cells of a Multinomial Distribution , 1983 .

[9]  Alexander H. G. Rinnooy Kan,et al.  An efficient dynamic selection method , 1983, CACM.

[10]  Kenneth Steiglitz,et al.  Randomized Pattern Search , 1972, IEEE Transactions on Computers.

[11]  Günther F. Schrack,et al.  Optimized relative step size random searches , 1976, Math. Program..

[12]  Bruce W. Weide,et al.  Optimal Expected-Time Algorithms for Closest Point Problems , 1980, TOMS.

[13]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[14]  Luc Devroye,et al.  Progressive global random search of continuous functions , 1978, Math. Program..

[15]  Samuel H. Brooks.  A Discussion of Random Methods for Seeking Maxima , 1958 .

[16]  Ryszard Zieliński,et al.  A sequential Bayesian approach to estimating the dimension of a multinomial distribution , 1985 .

[17]  L. Shepp.  The joint density of the maximum and its location for a Wiener process with drift , 1979, Journal of Applied Probability.

[18]  L. Haan.  Estimation of the Minimum of a Function Using Order Statistics , 1980 .

[19]  T. Cacoullos.  Estimation of a multivariate density , 1966 .

[20]  J. K. Hartman.  Some experiments in global optimization , 1973 .

[21]  Ryszard Zielinski.  A statistical estimate of the structure of multi-extremal problems , 1981, Math. Program..

[22]  H. Bremermann.  A method of unconstrained global optimization , 1970 .

[23]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[24]  L. C. W. Dixon,et al.  Global Optima without Convexity , 1978 .