Sequential stopping rules for the multistart algorithm in global optimisation

Abstract

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.

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Betrò, B., Schoen, F. Sequential stopping rules for the multistart algorithm in global optimisation. Mathematical Programming 38, 271–286 (1987). https://doi.org/10.1007/BF02592015

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Key words

  • Global optimisation
  • Monte Carlo method
  • stopping rules
  • Multistart algorithm
  • Bayes methods