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Open AccessFeature PaperArticle

Symmetry Detection for Quadratic Optimization Using Binary Layered Graphs

Department of Computing, Imperial College London, London SW7 2AZ, UK
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Current address: Schlumberger Cambridge Research.
Processes 2019, 7(11), 838; https://doi.org/10.3390/pr7110838
Received: 16 May 2019 / Revised: 24 October 2019 / Accepted: 5 November 2019 / Published: 9 November 2019
Symmetry in mathematical optimization may create multiple, equivalent solutions. In nonconvex optimization, symmetry can negatively affect algorithm performance, e.g., of branch-and-bound when symmetry induces many equivalent branches. This paper develops detection methods for symmetry groups in quadratically-constrained quadratic optimization problems. Representing the optimization problem with adjacency matrices, we use graph theory to transform the adjacency matrices into binary layered graphs. We enter the binary layered graphs into the software package nauty that generates important symmetric properties of the original problem. Symmetry pattern knowledge motivates a discretization pattern that we use to reduce computation time for an approximation of the point packing problem. This paper highlights the importance of detecting and classifying symmetry and shows that knowledge of this symmetry enables quick approximation of a highly symmetric optimization problem. View Full-Text
Keywords: symmetry; quadratic optimization; quadratically-constrained quadratic optimization symmetry; quadratic optimization; quadratically-constrained quadratic optimization
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Kouyialis, G.; Wang, X.; Misener, R. Symmetry Detection for Quadratic Optimization Using Binary Layered Graphs. Processes 2019, 7, 838.

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