A general branch-and-bound framework for continuous global multiobjective optimization

Gabriele Eichfelder, Peter Kirst, Laura Meng, Oliver Stein*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and by the corresponding termination criteria and node selection steps. In particular, our branch-and-bound concept employs a new enclosure of the set of nondominated points by a union of boxes. On this occasion we also suggest a new discarding test based on a linearization technique. We provide a convergence proof for our general branch-and-bound framework and illustrate the results with numerical examples.

Original languageEnglish
JournalJournal of Global Optimization
DOIs
Publication statusE-pub ahead of print - 19 Jan 2021

Keywords

  • Branch-and-bound algorithm
  • Enclosure
  • Global optimization
  • Multiobjective optimization
  • Nonconvex optimization

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