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Parallel Scenario Decomposition of Risk-Averse 0-1 Stochastic Programs

Author

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  • Yan Deng

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Shabbir Ahmed

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Siqian Shen

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

In this paper, we extend a recently proposed scenario decomposition algorithm for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider two-stage risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the considered problem. We then develop three variants of the scenario decomposition algorithm for this minimax formulation based on different relaxations of the nonanticipaticity constraints. The algorithms proceed by solving scenario subproblems to obtain candidate solutions and bounds and subsequently cutting off the candidate solutions from the search space to achieve convergence to an optimal solution. We design three parallelization schemes for implementing the algorithms with different tradeoffs between overhead time and computation time. Our computational results with risk-averse extensions of two standard stochastic 0-1 programming test instances demonstrate the scalability of the proposed decomposition and parallelization framework.

Suggested Citation

  • Yan Deng & Shabbir Ahmed & Siqian Shen, 2018. "Parallel Scenario Decomposition of Risk-Averse 0-1 Stochastic Programs," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 90-105, February.
  • Handle: RePEc:inm:orijoc:v:30:y:2018:i:1:p:90-105
    DOI: 10.1287/ijoc.2017.0767
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    References listed on IDEAS

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    8. Ricardo Collado & Dávid Papp & Andrzej Ruszczyński, 2012. "Scenario decomposition of risk-averse multistage stochastic programming problems," Annals of Operations Research, Springer, vol. 200(1), pages 147-170, November.
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    Cited by:

    1. Kevin Ryan & Shabbir Ahmed & Santanu S. Dey & Deepak Rajan & Amelia Musselman & Jean-Paul Watson, 2020. "Optimization-Driven Scenario Grouping," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 805-821, July.
    2. J. Cole Smith, 2019. "In Memoriam: Shabbir Ahmed (1969–2019)," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 633-635, October.

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