Annals of Operations Research

, Volume 1, Issue 2, pp 111–128 | Cite as

A Bayesian algorithm for global optimization

  • B. Betrò
  • R. Rotondi
Global Optimization

Abstract

A crucial step in global optimization algorithms based on random sampling in the search domain is decision about the achievement of a prescribed accuracy. In order to overcome the difficulties related to such a decision, the Bayesian Nonparametric Approach has been introduced. The aim of this paper is to show the effectiveness of the approach when an ad hoc clustering technique is used for obtaining promising starting points for a local search algorithm. Several test problems are considered.

Keywords and phrases

Global optimization Bayesian nonparametric inference random distributions cluster analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Archetti and B. Betrò, A priori analysis of deterministic strategies for global optimization, in: Towards Global Optimization 2, ed. C.W. Dixon and G.P. Szegó (North-Holland, Amsterdam, 1978).Google Scholar
  2. [2]
    F. Archetti and B. Betrò, A probabilistic algorithm for global optimization, Calcolo XVI (1979)335.Google Scholar
  3. [3]
    F. Archetti, B. Betrò and S. Steffe, A theoretical framework for global optimization via random sampling, Dipartimento di Recerca Operativa e Scienze Statistiche Universita di Pisa A25(1975).Google Scholar
  4. [4]
    F. Archetti and F. Schoen, A survey on the global optimization problem: general theory and computational approaches, Annals Oper. Res. 1(1984)87.Google Scholar
  5. [5]
    B. Betrò, Bayesian testing of nonparametric hypotheses and its application to global optimization, forthcoming in: J. of Optimization Theory and Applications 42(1982)1.Google Scholar
  6. [6]
    B. Betrò, A Bayesian nonparametric approach to global optimization, in: Methods of Operations Research, ed. P. Stáhly (Athenäum Verlag, 1983)45, 47.Google Scholar
  7. [7]
    C.G.E. Boender, A.H.F. Rinnooy Kan and G.T. Timmer, A stochastic method for global optimization, Math. Progr. 22(1982)125.Google Scholar
  8. [8]
    C.W. Dixon and G.P. Szegó, eds., Towards Global Optimization (North-Holland, Amsterdam, 1978).Google Scholar
  9. [9]
    K. Doksum, Tailfree and neutral random probabilities and their posterior distributions, The Annals of Probability 2(1974)183.Google Scholar
  10. [10]
    T.S. Ferguson, A Bayesian analysis of some nonparametric problems, The Annals of Statistics 1(1973)209.Google Scholar
  11. [11]
    J. Mockus, V. Tiesis and A. Žilinskas, The application of Bayesian methods for seeking the extremum, in: Towards Global Optimization 2, ed. C.W. Dixon and G.P. Szegó (North-Holland, Amsterdam, 1978).Google Scholar
  12. [12]
    A.A. Torn, Cluster analysis using seed points and density-determined hyperspheres as an aid to global optimization, IEEE Transactions on Systems, Man, and Cybernetics (1977) SMC-7, 610.Google Scholar
  13. [13]
    A. Žilinskas, Axiomatic approach to statistical models and their use in multimodal optimization theory, Math. Progr. 22(1982)104.Google Scholar
  14. [14]
    A. Žilinskas, On justification of use of stochastic functions for multimodal optimization models. Ann. of Oper. Res. 1(1984)129.Google Scholar

Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1984

Authors and Affiliations

  • B. Betrò
    • 1
  • R. Rotondi
    • 1
  1. 1.CNR-IAMIMilanoItaly

Personalised recommendations