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Interval Tools in Branch-and-Bound Methods for Global Optimization

In: The Palgrave Handbook of Operations Research

Author

Listed:
  • José Fernández

    (University of Murcia)

  • Boglárka G.-Tóth

    (University of Szeged)

Abstract

Interval analysisInterval analysis has been applied with success at solving continuous nonlinear programming problems. In this chapter we review the most relevant research on interval branch-and-bound methods in the period 2011-2021, in particular, bounding rules, discarding/filtering methods, rules for the selection of the next box to be processed and subdivision strategies. No constraint programming techniques nor hybrid proposals are included in the review for the sake of brevity, although we do include a review of the available interval arithmetic libraries for different programming languages as well as software packages with implementations of interval branch-and-bound algorithms. Surprisingly, interval tools have been seldom applied to cope with mixed-integer nonlinear programming problemsMINLP. This chapter also reviews the proposals in the literature to use interval methods in this type of problems, and suggests how some of the techniques proposed for continuous problems can be adapted for mixed-integer problems.

Suggested Citation

  • José Fernández & Boglárka G.-Tóth, 2022. "Interval Tools in Branch-and-Bound Methods for Global Optimization," Springer Books, in: Saïd Salhi & John Boylan (ed.), The Palgrave Handbook of Operations Research, chapter 0, pages 237-267, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-96935-6_8
    DOI: 10.1007/978-3-030-96935-6_8
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