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Robust multiobjective optimization with application to Internet routing

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Abstract

Robust optimization addressing decision making under uncertainty has been very well developed for problems with a single objective function and applied to areas of human activity such as portfolio selection, investment decisions, signal processing, and telecommunication-network planning. As these decision problems typically have several decisions or goals, we extend robust single objective optimization to the multiobjective case. The column-wise uncertainty model can be carried over to the multiobjective case without any additional assumptions. For the row-wise uncertainty model, we show under additional assumptions that robust efficient solutions are efficient to specific instance problems and can be found as the efficient solutions of another deterministic problem. Being motivated by the fact that Internet traffic must be maintained in a reliable yet affordable manner in situations of complex and dynamic usage, we apply the row-wise model to an intradomain multiobjective routing problem with polyhedral traffic uncertainty. We consider traditional objective functions corresponding to link utilizations and implement the biobjective case using the parametric simplex algorithm to compute robust efficient routings. We also present computational results for the Abilene network and analyze their meaning in the context of the application.

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Notes

  1. Optical Carrier with a data rate of 9953.28 Mbit/s, that is, 10 Gbit/s.

  2. Optical Carrier with a data rate of 2488.32 Mbit/s, that is, 2.5 Gbit/s.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their thorough and helpful reviews which significantly improved the quality of the paper. The second author recognizes partial support from Clemson University through Grant URGC 2009/2010. The third author recognizes partial support from the Office of Naval Research through Grant Number N00014-16-1-2725.

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  1. Hervé L. M. Kerivin

    Present address: Institute for Computer Science, LIMOS CNRS UMR 6158, University Clermont Auvergne, Clermont-Ferrand, France

Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Erin K. Doolittle, Hervé L. M. Kerivin & Margaret M. Wiecek

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  1. Erin K. Doolittle
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Correspondence to Margaret M. Wiecek.

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Doolittle, E.K., Kerivin, H.L.M. & Wiecek, M.M. Robust multiobjective optimization with application to Internet routing. Ann Oper Res 271, 487–525 (2018). https://doi.org/10.1007/s10479-017-2751-5

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