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

Gabriele Eichfelder (gabriele.eichfeldertu-ilmenau.de)
Peter Kirst (peter-kirstweb.de)
Laura Meng (laura.mengweb.de)
Oliver Stein (steinkit.edu)

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.

Keywords: Multiobjective Optimization; Nonconvex Optimization; Global Optimization; Branch-and-Bound Algorithm; Enclosure

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Global Optimization

Category 3: Nonlinear Optimization

Citation: Journal of Global Optimization, 2021

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Entry Submitted: 07/20/2020
Entry Accepted: 07/20/2020
Entry Last Modified: 01/19/2021

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