IDEAS home Printed from https://ideas.repec.org/p/ehu/biltok/31248.html
   My bibliography  Save this paper

Generating cluster submodels from two-stage stochastic mixed integer optimization models

Author

Listed:
  • Eguía Ribero, María Isabel
  • Garín Martín, María Araceli
  • Unzueta Inchaurbe, Aitziber

Abstract

Stochastic optimization problems of practical applications lead, in general, to some large models. The size of those models is linked to the number of scenarios that defines the scenario tree. This number of scenarios can be so large that decomposition strategies are required for problem solving in reasonable computing time. Methodologies such as Branch-and-Fix Coordination and Lagrangean Relaxation make use of these decomposition approaches, where independent scenario clusters are given. In this work, we present a technique to generate cluster submodel structures from the decomposition of a general two-stage stochastic mixed integer optimization model. Scenario cluster submodels are generated from the original stochastic problem by combining the compact and splitting variable representations in some of the variables related to the nodes that belong to the first stage. We consider a two-stage stochastic capacity expansion problem as illustrative example where several decompositions are provided.

Suggested Citation

  • Eguía Ribero, María Isabel & Garín Martín, María Araceli & Unzueta Inchaurbe, Aitziber, 2018. "Generating cluster submodels from two-stage stochastic mixed integer optimization models," BILTOKI 31248, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    • Handle: RePEc:ehu:biltok:31248
    as

    Download full text from publisher

    File URL: https://addi.ehu.es/handle/10810/31248
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    2. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    3. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, September.
    4. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    5. Guglielmo Lulli & Suvrajeet Sen, 2004. "A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems," Management Science, INFORMS, vol. 50(6), pages 786-796, June.
    6. Samer Takriti & John R. Birge, 2000. "Lagrangian Solution Techniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 91-98, February.
    7. Lulli, Guglielmo & Sen, Suvrajeet, 2006. "A heuristic procedure for stochastic integer programs with complete recourse," European Journal of Operational Research, Elsevier, vol. 171(3), pages 879-890, June.
    8. Escudero, L.F. & Garín, M.A. & Merino, M. & Pérez, G., 2010. "An exact algorithm for solving large-scale two-stage stochastic mixed-integer problems: Some theoretical and experimental aspects," European Journal of Operational Research, Elsevier, vol. 204(1), pages 105-116, July.
    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. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Pérez Sainz de Rozas, Gloria & Unzueta Inchaurbe, Aitziber, 2010. "Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    2. Aldasoro, Unai & Escudero, Laureano F. & Merino, María & Pérez, Gloria, 2017. "A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0–1 problems," European Journal of Operational Research, Elsevier, vol. 258(2), pages 590-606.
    3. Laureano F. Escudero & María Araceli Garín & Celeste Pizarro & Aitziber Unzueta, 2018. "On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 865-888, July.
    4. Escudero, Laureano F. & Landete, Mercedes & Rodríguez-Chía, Antonio M., 2011. "Stochastic set packing problem," European Journal of Operational Research, Elsevier, vol. 211(2), pages 232-240, June.
    5. Hannes Schwarz & Valentin Bertsch & Wolf Fichtner, 2018. "Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 265-310, January.
    6. L. Escudero & M. Garín & G. Pérez & A. Unzueta, 2012. "Lagrangian Decomposition for large-scale two-stage stochastic mixed 0-1 problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 347-374, July.
    7. Laureano Escudero, 2009. "On a mixture of the fix-and-relax coordination and Lagrangian substitution schemes for multistage stochastic mixed integer programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 5-29, July.
    8. Kazemi Zanjani, Masoumeh & Sanei Bajgiran, Omid & Nourelfath, Mustapha, 2016. "A hybrid scenario cluster decomposition algorithm for supply chain tactical planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 466-476.
    9. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Guignard, Monique & Weintraub, Andres, 2018. "Risk management for forestry planning under uncertainty in demand and prices," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1051-1074.
    10. Can Li & Ignacio E. Grossmann, 2019. "A finite $$\epsilon $$ϵ-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables," Journal of Global Optimization, Springer, vol. 75(4), pages 921-947, December.
    11. Giovanni Pantuso & Trine K. Boomsma, 2020. "On the number of stages in multistage stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 581-603, September.
    12. Huang, Zhouchun & Zheng, Qipeng Phil, 2020. "A multistage stochastic programming approach for preventive maintenance scheduling of GENCOs with natural gas contract," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1036-1051.
    13. Jean-Paul Watson & Roger J-B Wets & David L. Woodruff, 2010. "Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 543-554, November.
    14. Hossein Hashemi Doulabi & Shabbir Ahmed & George Nemhauser, 2022. "State-Variable Modeling for a Class of Two-Stage Stochastic Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 354-369, January.
    15. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Merino Maestre, María & Pérez Sainz de Rozas, Gloria, 2005. "A two-stage stochastic integer programming approach," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    16. Serhat Gul & Brian T. Denton & John W. Fowler, 2015. "A Progressive Hedging Approach for Surgery Planning Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 755-772, November.
    17. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    18. Torres-Rincón, Samuel & Sánchez-Silva, Mauricio & Bastidas-Arteaga, Emilio, 2021. "A multistage stochastic program for the design and management of flexible infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    19. Fernando Veliz & Jean-Paul Watson & Andres Weintraub & Roger Wets & David Woodruff, 2015. "Stochastic optimization models in forest planning: a progressive hedging solution approach," Annals of Operations Research, Springer, vol. 232(1), pages 259-274, September.

    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:ehu:biltok:31248. 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: Alcira Macías (email available below). General contact details of provider: https://edirc.repec.org/data/deehues.html .

    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.