University of Wuppertal –
Multi-objective optimization methods often proceed by iteratively producing new solutions. For this purpose it is important to determine and update the search region efficiently. It corresponds to the part of the objective space where new nondominated points could lie and can be described by a set of so-called local upper bounds whose components are defined by already known nondominated points. In the bi-objective case the update of the search region is easy since a new point can dominate only one local upper bound. Moreover, the local upper bounds as well as the nondominated points can be kept sorted increasingly with respect to one objective and decreasingly with respect to the other.
For more than two objectives these properties do no longer hold. In particular, several local upper bounds might have to be updated at once when a new nondominated point is inserted into the search region. In this talk we concentrate on how to design this update efficiently. Therefore we study a specific neighborhood structure among local upper bounds. Thanks to this structure we can quickly identify all local upper bounds that are affected by a new nondominated point, i.e. that have to be updated. We propose a new scheme to update the search region with respect to a new point more efficiently compared to existing approaches. Besides, the neighborhood structure provides new theoretical insight into the search region and the location of nondominated points for more than two objectives (cf. Dächert, K., Klamroth, K., Lacour, R., Vanderpooten, D.: Efficient computation of the search region in multi-objective optimization, European Journal of Operational Research 260(3):841–855, 2017).
Dr. Kerstin Dächert is a Research Associate (interim lecturer position) at the Department of Mathematics and Informatics, University of Wuppertal, Germany. Her interests include multicriteria optimization, combinatorial optimization and applications of operations research, e.g. in energy economics.
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