IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v338y2024i2d10.1007_s10479-024-05947-0.html
   My bibliography  Save this article

Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models

Author

Listed:
  • Jinxiang Wei

    (Tongji University)

  • Zhaolin Hu

    (Tongji University)

  • Jun Luo

    (Shanghai Jiao Tong University)

  • Shushang Zhu

    (Sun Yat-Sen University)

Abstract

We study a class of chance constrained programs (CCPs) where the underlying distribution is modeled by a Gaussian mixture model. As the original work, Hu et al. (IISE Trans 54(12):1117–1130, 2022. https://doi.org/10.1080/24725854.2021.2001608 ) developed a spatial branch-and-bound (B &B) algorithm to solve the problems. In this paper, we propose an enhanced procedure to speed up the computation of B &B algorithm. We design an enhanced pruning strategy that explores high-potential domains and an augmented branching strategy that prevents redundant computations. We integrate the new strategies into original framework to develop an enhanced B &B algorithm, and illustrate how the enhanced algorithm improves on the original approach. Furthermore, we extend the enhanced B &B framework to handle the CCPs with multiple chance constraints, which is not considered in the previous work. We evaluate the performance of our new algorithm through extensive numerical experiments and apply it to solve a real-world portfolio selection problem.

Suggested Citation

  • Jinxiang Wei & Zhaolin Hu & Jun Luo & Shushang Zhu, 2024. "Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models," Annals of Operations Research, Springer, vol. 338(2), pages 1283-1315, July.
    • Handle: RePEc:spr:annopr:v:338:y:2024:i:2:d:10.1007_s10479-024-05947-0
    DOI: 10.1007/s10479-024-05947-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-024-05947-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-024-05947-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    2. Shanshan Wang & Jinlin Li & Sanjay Mehrotra, 2021. "Chance-Constrained Multiple Bin Packing Problem with an Application to Operating Room Planning," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1661-1677, October.
    3. Zhiping Chen & Shen Peng & Jia Liu, 2018. "Data-Driven Robust Chance Constrained Problems: A Mixture Model Approach," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1065-1085, December.
    4. Juan Pablo Vielma & Shabbir Ahmed & George L. Nemhauser, 2008. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 438-450, August.
    5. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
    6. Anis, Hassan T. & Kwon, Roy H., 2022. "Cardinality-constrained risk parity portfolios," European Journal of Operational Research, Elsevier, vol. 302(1), pages 392-402.
    7. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    8. I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    9. Zhiping Chen & Shen Peng & Abdel Lisser, 2020. "A sparse chance constrained portfolio selection model with multiple constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 825-852, August.
    10. René Henrion & Andris Möller, 2012. "A Gradient Formula for Linear Chance Constraints Under Gaussian Distribution," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 475-488, August.
    11. Meryem Masmoudi & Fouad Ben Abdelaziz, 2017. "A chance constrained recourse approach for the portfolio selection problem," Annals of Operations Research, Springer, vol. 251(1), pages 243-254, April.
    12. Zhaolin Hu & Wenjie Sun & Shushang Zhu, 2022. "Chance constrained programs with Gaussian mixture models," IISE Transactions, Taylor & Francis Journals, vol. 54(12), pages 1117-1130, September.
    13. N. H. Agnew & R. A. Agnew & J. Rasmussen & K. R. Smith, 1969. "An Application of Chance Constrained Programming to Portfolio Selection in a Casualty Insurance Firm," Management Science, INFORMS, vol. 15(10), pages 512-520, June.
    14. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    2. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    3. Ümit Sakallı & Ömer Baykoç & Burak Birgören, 2011. "Stochastic optimization for blending problem in brass casting industry," Annals of Operations Research, Springer, vol. 186(1), pages 141-157, June.
    4. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Other publications TiSEM ab77f6f2-248a-42f1-bde1-0, Tilburg University, School of Economics and Management.
    5. Jiang, Jie & Peng, Shen, 2024. "Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation," European Journal of Operational Research, Elsevier, vol. 313(2), pages 616-627.
    6. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Discussion Paper 2011-137, Tilburg University, Center for Economic Research.
    7. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    8. Maji, Chandi Charan, 1975. "Intertemporal allocation of irrigation water in the Mayurakshi Project (India): an application of deterministic and chance-constrained linear programming," ISU General Staff Papers 197501010800006381, Iowa State University, Department of Economics.
    9. İhsan Yanıkoğlu & Dick den Hertog, 2013. "Safe Approximations of Ambiguous Chance Constraints Using Historical Data," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 666-681, November.
    10. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    11. Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Tan, Zhijia, 2013. "Risk management in liner ship fleet deployment: A joint chance constrained programming model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 1-12.
    12. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    13. Wu, Desheng (Dash) & Lee, Chi-Guhn, 2010. "Stochastic DEA with ordinal data applied to a multi-attribute pricing problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1679-1688, December.
    14. Patrice Gaillardetz & Saeb Hachem, 2019. "Risk-Control Strategies," Papers 1908.02228, arXiv.org.
    15. Giada Spaccapanico Proietti & Mariagiulia Matteucci & Stefania Mignani & Bernard P. Veldkamp, 2024. "Chance-Constrained Automated Test Assembly," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 92-120, February.
    16. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    17. Bilsel, R. Ufuk & Ravindran, A., 2011. "A multiobjective chance constrained programming model for supplier selection under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1284-1300, September.
    18. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    19. Cooper, W. W. & Hemphill, H. & Huang, Z. & Li, S. & Lelas, V. & Sullivan, D. W., 1997. "Survey of mathematical programming models in air pollution management," European Journal of Operational Research, Elsevier, vol. 96(1), pages 1-35, January.
    20. Nemirovski, Arkadi, 2012. "On safe tractable approximations of chance constraints," European Journal of Operational Research, Elsevier, vol. 219(3), pages 707-718.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:338:y:2024:i:2:d:10.1007_s10479-024-05947-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.