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Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction

Author

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  • Suvrajeet Sen

    (Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089)

  • Yifan Liu

    (Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089)

Abstract

Stochastic Programming (SP) has long been considered a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines so that statistically acceptable bounds can be obtained. In this paper we show that for a class of stochastic linear programming problems, an alternative approach known as Stochastic Decomposition (SD) can provide solutions of similar quality in far less computational time using ordinary desktop or laptop machines of today. In addition to these compelling computational results, we provide a stronger convergence result for SD, and introduce a new solution concept that we call the compromise decision. This new concept is attractive for algorithms that call for multiple replications in sampling-based convex optimization algorithms. For such replicated optimization, we show that the difference between an average solution and a compromise decision provides a natural stopping rule. We discuss three stopping criteria that enhance the reliability of the compromise decision, reducing bias and variance associated with the result. Finally our computational results cover a variety of instances from the literature, including a detailed study of SONET Switched Network (SSN), a network planning instance known to be more challenging than other test instances in the literature.

Suggested Citation

  • Suvrajeet Sen & Yifan Liu, 2016. "Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction," Operations Research, INFORMS, vol. 64(6), pages 1422-1437, December.
  • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1422-1437
    DOI: 10.1287/opre.2016.1526
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    References listed on IDEAS

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    1. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    2. Michael C. Fu, 2002. "Feature Article: Optimization for simulation: Theory vs. Practice," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 192-215, August.
    3. Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
    4. Julia Higle & Suvrajeet Sen, 1999. "Statistical approximations forstochastic linear programming problems," Annals of Operations Research, Springer, vol. 85(0), pages 173-193, January.
    5. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    6. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    7. Sujin Kim & Raghu Pasupathy & Shane G. Henderson, 2015. "A Guide to Sample Average Approximation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 207-243, Springer.
    8. Yehuda Bassok & Ravi Anupindi & Ram Akella, 1999. "Single-Period Multiproduct Inventory Models with Substitution," Operations Research, INFORMS, vol. 47(4), pages 632-642, August.
    9. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    10. Xin Chen & Melvyn Sim & Peng Sun & Jiawei Zhang, 2008. "A Linear Decision-Based Approximation Approach to Stochastic Programming," Operations Research, INFORMS, vol. 56(2), pages 344-357, April.
    11. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.
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    Cited by:

    1. Jangho Park & Rebecca Stockbridge & Güzin Bayraksan, 2021. "Variance reduction for sequential sampling in stochastic programming," Annals of Operations Research, Springer, vol. 300(1), pages 171-204, May.
    2. Jiajun Xu & Suvrajeet Sen, 2024. "Ensemble Variance Reduction Methods for Stochastic Mixed-Integer Programming and their Application to the Stochastic Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 587-599, March.
    3. Harsha Gangammanavar & Yifan Liu & Suvrajeet Sen, 2021. "Stochastic Decomposition for Two-Stage Stochastic Linear Programs with Random Cost Coefficients," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 51-71, January.
    4. Ward Romeijnders & David P. Morton & Maarten H. van der Vlerk, 2017. "Assessing the Quality of Convex Approximations for Two-Stage Totally Unimodular Integer Recourse Models," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 211-231, May.
    5. Clara Lage & Claudia Sagastizábal & Mikhail Solodov, 2020. "Multiplier Stabilization Applied to Two-Stage Stochastic Programs," Post-Print halshs-02900862, HAL.
    6. Clara Lage & Claudia Sagastizábal & Mikhail Solodov, 2020. "Multiplier Stabilization Applied to Two-Stage Stochastic Programs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02900862, HAL.
    7. Site Wang & Harsha Gangammanavar & Sandra Ekşioğlu & Scott J. Mason, 2020. "Statistical estimation of operating reserve requirements using rolling horizon stochastic optimization," Annals of Operations Research, Springer, vol. 292(1), pages 371-397, September.
    8. Clara Lage & Claudia Sagastizábal & Mikhail Solodov, 2020. "Multiplier Stabilization Applied to Two-Stage Stochastic Programs," Documents de travail du Centre d'Economie de la Sorbonne 20010, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Clara Lage & Claudia Sagastizábal & Mikhail Solodov, 2019. "Multiplier Stabilization Applied to Two-Stage Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 158-178, October.
    10. Postek, Krzysztof & Romeijnders, Ward & den Hertog, Dick & van der Vlerk, Maarten H., 2019. "An approximation framework for two-stage ambiguous stochastic integer programs under mean-MAD information," European Journal of Operational Research, Elsevier, vol. 274(2), pages 432-444.
    11. Atakan, Semih & Gangammanavar, Harsha & Sen, Suvrajeet, 2022. "Towards a sustainable power grid: Stochastic hierarchical planning for high renewable integration," European Journal of Operational Research, Elsevier, vol. 302(1), pages 381-391.
    12. Yunxiao Deng & Suvrajeet Sen, 2022. "Predictive stochastic programming," Computational Management Science, Springer, vol. 19(1), pages 65-98, January.

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