EURO 2024 Copenhagen
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1952. Dimension reduction in multiobjective optimization

Invited abstract in session TA-37: Objective Space-Based Approaches in Multiobjective Optimization, stream Multiobjective Optimization.

Tuesday, 8:30-10:00
Room: 33 (building: 306)

Authors (first author is the speaker)

1. Ina Lammel
Optimization, Fraunhofer ITWM
2. Volker Maag
Optimization, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik

Abstract

Many real-world optimization problems depend on several criteria. The computational effort of approximating the nondominated set of these multiobjective optimization problems increases quickly with the number of objectives. For a large number of objectives, computing a good approximation of the nondominated set may exceed the available computation budget.

To compute approximations of high-dimensional nondominated sets, we incorporate dimension reduction techniques into the approximation process. We analyze the problem to identify strongly-correlated directions of the nondominated set and reduce the objective space dimension accordingly. After computing an approximation in the lower-dimensional space, we project the approximation back to the original full-dimensional space.
We relate the approximation of the nondominated set constructed by this algorithm to the approximation of the full-dimensional set and develop criteria under which the approximation in lower-dimensional space still yields a good approximation when projected back to the full-dimensional space.

Finally, we demonstrate the usefulness of the method on examples from different fields of application.

Keywords

Status: accepted

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