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Multi-dimensional pruning from the Baumann point in an Interval Global Optimization Algorithm

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Abstract

A new pruning method for interval branch and bound algorithms is presented. In reliable global optimization methods there are several approaches to make the algorithms faster. In minimization problems, interval B&B methods use a good upper bound of the function at the global minimum and good lower bounds of the function at the subproblems to discard most of them, but they need efficient pruning methods to discard regions of the subproblems that do not contain global minimizer points. The new pruning method presented here is based on the application of derivative information from the Baumann point. Numerical results were obtained by incorporating this new technique into a basic Interval B&B Algorithm in order to evaluate the achieved improvements.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Murcia, Campus Universitario de Espinardo, Murcia, 30100, Spain

    Boglárka Tóth

  2. Departamento de Arquitectura de Computadores y Electrónica, Universidad de Almería, Crta. Sacramento s/u, Almería, 04120, Spain

    Leocadio G. Casado

Authors
  1. Boglárka Tóth
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  2. Leocadio G. Casado
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Correspondence to Boglárka Tóth.

Additional information

This work has been supported by the Ministry of Education and Science of Spain through grants TIC 2002-00228, TIN2005-00447, and research project SEJ2005-06273 and by the Integral Action between Spain and Hungary by grant HH2004-0014.

Boglárka Tóth: On leave from the Research Group on Artificial Intelligence of the Hungarian Academy of Sciences and the University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1., Hungary.

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Tóth, B., Casado, L.G. Multi-dimensional pruning from the Baumann point in an Interval Global Optimization Algorithm. J Glob Optim 38, 215–236 (2007). https://doi.org/10.1007/s10898-006-9072-6

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  • DOI: https://doi.org/10.1007/s10898-006-9072-6

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