Journal of Global Optimization

, Volume 56, Issue 3, pp 1101–1121

On interval branch-and-bound for additively separable functions with common variables

  • J. L. Berenguel
  • L. G. Casado
  • I. García
  • E. M. T. Hendrix
  • F. Messine
Open AccessArticle

DOI: 10.1007/s10898-012-9928-x

Cite this article as:
Berenguel, J.L., Casado, L.G., García, I. et al. J Glob Optim (2013) 56: 1101. doi:10.1007/s10898-012-9928-x
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Abstract

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis.

Keywords

Branch-and-boundInterval arithmeticSeparable functions
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© The Author(s) 2012

Authors and Affiliations

  • J. L. Berenguel
    • 1
  • L. G. Casado
    • 2
  • I. García
    • 3
  • E. M. T. Hendrix
    • 3
    • 4
  • F. Messine
    • 5
  1. 1.TIC 146: “Supercomputing-Algorithms” Research GroupUniversity of AlmeríaAlmeríaSpain
  2. 2.Department of Computer Architecture and ElectronicsUniversity of AlmeríaAlmeríaSpain
  3. 3.Department of Computer ArchitectureUniversity of MálagaMálagaSpain
  4. 4.Operations Research and LogisticsWageningen UniversityWageningenThe Netherlands
  5. 5.ENSEEIHT-IRIT UMR-CNRS-5505University of ToulouseToulouseFrance