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Partial sample average approximation method for chance constrained problems

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Abstract

In this paper, we present a new scheme of a sampling-based method to solve chance constrained programs. The main advantage of our approach is that the approximation problem contains only continuous variables whilst the standard sample average approximation (SAA) formulation contains binary variables. Although our approach generates new chance constraints, we show that such constraints are tractable under certain conditions. Moreover, we prove that the proposed approach has the same convergence properties as the SAA approach. Finally, numerical experiments show that the proposed approach outperforms the SAA approach on a set of tested instances.

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Notes

  1. It is the empirical feasible probability of given optimal solution \(x^*\) attained from different approximation approaches with 100, 000 scenarios.

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Acknowledgements

This research benefited from the support of the “FMJH Program Gaspard Monge in Optimization and Operations Research”, and from the support to this program by EDF, Grant Number \(2012-042H\). This research has also been supported in part by the Bisgrove Scholars program (sponsored by Science Foundation Arizona).

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Authors and Affiliations

  1. Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Jianqiang Cheng

  2. Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Bât. 650, 91405, Orsay Cedex, France

    Céline Gicquel & Abdel Lisser

Authors
  1. Jianqiang Cheng
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  2. Céline Gicquel
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  3. Abdel Lisser
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Correspondence to Jianqiang Cheng.

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Cheng, J., Gicquel, C. & Lisser, A. Partial sample average approximation method for chance constrained problems. Optim Lett 13, 657–672 (2019). https://doi.org/10.1007/s11590-018-1300-8

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