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

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.

Automated summary

This paper introduces a new framework for multi-objective branch-and-bound, including constructions for partial lower bounds, overall upper bounds, and overall lower bounds along with node selection steps. Additionally, it proposes a new enclosure of non-dominated points by a union of boxes and suggests a discarding test based on linearization technique. The convergence proof for the general branch-and-bound framework is provided along with numerical examples to illustrate the results.