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Problem-driven scenario clustering in stochastic optimization

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Abstract

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by finding a smaller subset of scenarios, reduce the numerical complexity while keeping the error at an acceptable level. In this paper we propose a novel and computationally efficient methodology to tackle the scenario reduction problem for two-stage problems when the error to be minimised is the implementation error, i.e. the error incurred by implementing the solution of the reduced problem in the original problem. Specifically, we develop a problem-driven scenario clustering method that produces a partition of the scenario set. Each cluster contains a representative scenario that best reflects the optimal value of the objective function in each cluster of the partition to be identified. We demonstrate the efficiency of our method by applying it to two challenging two-stage stochastic combinatorial optimization problems: the two-stage stochastic network design problem and the two-stage facility location problem. When compared to alternative clustering methods and Monte Carlo sampling, our method is shown to clearly outperform all other methods.

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Acknowledgements

This research was initiated when Julien Keutchayan was postdoctoral researcher at University of Montreal. Janosch Ortmann was partially supported by a NSERC Discovery Grant. While working on this paper, Walter Rei was the Canada Research Chair (CRC) in Stochastic Optimization of Transport and Logistics Systems. In addition, he was supported by the National Sciences and Engineering Research Council of Canada (NSERC) through the discovery grants program. He gratefully acknowledges all the support that is provided by the CRC and NSERC programs.

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Authors and Affiliations

  1. McGill University, Montreal, QC, Canada

    Julien Keutchayan

  2. Département AOTI, UQAM, Montreal, QC, Canada

    Janosch Ortmann & Walter Rei

  3. Centre de recherches mathématiques, Montreal, Canada

    Janosch Ortmann

  4. GERAD, Montreal, QC, Canada

    Janosch Ortmann

  5. CIRRELT, Montreal, QC, Canada

    Walter Rei

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  1. Julien Keutchayan
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  2. Janosch Ortmann
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  3. Walter Rei
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Correspondence to Julien Keutchayan, Janosch Ortmann or Walter Rei.

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Keutchayan, J., Ortmann, J. & Rei, W. Problem-driven scenario clustering in stochastic optimization. Comput Manag Sci 20, 13 (2023). https://doi.org/10.1007/s10287-023-00446-2

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