217. Low-Rank Multi-Objective Linear Programming
Invited abstract in session TC-5: Multiobjective Optimization 2: Continuous Problems, stream Decision Theory and Multi-criteria Decision Making.
Thursday, 11:45-13:15Room: H7
Authors (first author is the speaker)
| 1. | Pascal Zillmann
|
| Faculty of Mathematics and Computer Science, Institute of Mathematics, Friedrich Schiller University Jena | |
| 2. | Andreas Löhne
|
| Institut für Mathematik, FSU Jena |
Abstract
When solving multi-objective programs, the number of objectives essentially determines the computing time. This can even lead to practically unsolvable problems. Consequently, it is worthwhile to reduce the number of objectives without losing information. In this article, we introduce a method to transform a multi-objective linear program (MOLP) into an equivalent vector linear program (VLP) with merely as many objectives as the rank of the original objective matrix. To this end, only an LU decomposition of this matrix is needed to be calculated. One of the factors then forms a new ordering cone, while the other factor remains as the objective matrix. Through several series of numerical experiments, we will show that this approach indeed leads to a significant speedup of computing time, and therefore provides a powerful technique for MOLP solving in practical concerns. As there are fewer objectives to consider, the approach additionally helps decision makers to get a better visualization as well as understanding of the actual problem. Moreover, we will point out that the equivalence of the MOLP and the corresponding VLP can be used to derive statements about the concept of nonessential objectives. Finally, we will present an idea for reducing the rank of a high-rank objective matrix by deleting the smallest singular values.
Keywords
- Multi-Objective Programming
- Multi-Objective Decision Making
- Computational Experiments
Status: accepted
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