Optimization Online


Limit sets in continuous global multiobjective optimization

Gabriele Eichfelder (Gabriele.Eichfelder***at***tu-ilmenau.de)
Oliver Stein (stein***at***kit.edu)

Abstract: For the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein, A general branch-and-bound framework for continuous global multiobjective optimization, Journal of Global Optimization (2021), DOI: 10.1007/s10898-020-00984-y, we study in which sense the generated terminal enclosure and the terminal provisional nondominated set approximate the nondominated set when the termination accuracy is driven to zero. Our convergence analysis of the enclosures is tightly connected to the constructions from the above paper, but self-contained. The analysis for the provisional nondominated set is based on general convergence properties of the epsilon-nondominated set, and hence it is also applicable to other algorithms which generate such points. Furthermore, we discuss post processing steps for the terminal enclosure and provide numerical illustrations for the cases of two and three objective functions.

Keywords: Enclosure; nondominated set; approximation; branch-and-bound; truncation

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Global Optimization (Theory )

Citation: Optimization Online, Preprint ID 2021-04-8353, 2021

Download: [PDF]

Entry Submitted: 04/23/2021
Entry Accepted: 04/23/2021
Entry Last Modified: 04/23/2021

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