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An exact algorithm for solving large-scale two-stage stochastic mixed-integer problems: Some theoretical and experimental aspects

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  • Escudero, L.F.
  • Garín, M.A.
  • Merino, M.
  • Pérez, G.

Abstract

We present an algorithmic framework, so-called BFC-TSMIP, for solving two-stage stochastic mixed 0-1 problems. The constraints in the Deterministic Equivalent Model have 0-1 variables and continuous variables at any stage. The approach uses the Twin Node Family (TNF) concept within an adaptation of the algorithmic framework so-called Branch-and-Fix Coordination for satisfying the nonanticipativity constraints for the first stage 0-1 variables. Jointly we solve the mixed 0-1 submodels defined at each TNF integer set for satisfying the nonanticipativity constraints for the first stage continuous variables. In these submodels the only integer variables are the second stage 0-1 variables. A numerical example and some theoretical and computational results are presented to show the performance of the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:1:p:105-116
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    References listed on IDEAS

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    1. Alonso-Ayuso, A. & Escudero, L. F. & Garín, A. & Ortuño, M. T. & Pérez, G., 2005. "On the product selection and plant dimensioning problem under uncertainty," Omega, Elsevier, vol. 33(4), pages 307-318, August.
    2. Rafael Andrade & Abdel Lisser & Nelson Maculan & Gérard Plateau, 2006. "Enhancing a Branch-and-Bound Algorithm for Two-Stage Stochastic Integer Network Design-Based Models," Management Science, INFORMS, vol. 52(9), pages 1450-1455, September.
    3. Willem Klein Haneveld & Maarten van der Vlerk, 1999. "Stochastic integer programming:General models and algorithms," Annals of Operations Research, Springer, vol. 85(0), pages 39-57, January.
    4. Laureano Escudero & Araceli Garín & María Merino & Gloria Pérez, 2009. "On multistage Stochastic Integer Programming for incorporating logical constraints in asset and liability management under uncertainty," Computational Management Science, Springer, vol. 6(3), pages 307-327, August.
    5. Yang Yuan & Suvrajeet Sen, 2009. "Enhanced Cut Generation Methods for Decomposition-Based Branch and Cut for Two-Stage Stochastic Mixed-Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 480-487, August.
    6. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Teresa Ortuno, M., 2003. "BFC, A branch-and-fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0-1 programs," European Journal of Operational Research, Elsevier, vol. 151(3), pages 503-519, December.
    7. L. Escudero & A. Garín & M. Merino & G. Pérez, 2007. "A two-stage stochastic integer programming approach as a mixture of Branch-and-Fix Coordination and Benders Decomposition schemes," Annals of Operations Research, Springer, vol. 152(1), pages 395-420, July.
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    Cited by:

    1. Unai Aldasoro & Laureano Escudero & María Merino & Juan Monge & Gloria Pérez, 2015. "On parallelization of a stochastic dynamic programming algorithm for solving large-scale mixed 0–1 problems under uncertainty," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 703-742, October.
    2. Schwarz, Hannes & Bertsch, Valentin & Fichtner, Wolf, 2015. "Two-stage stochastic, large-scale optimization of a decentralized energy system - a residential quarter as case study," Working Paper Series in Production and Energy 10, Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP).
    3. E. Mijangos, 2015. "An algorithm for two-stage stochastic mixed-integer nonlinear convex problems," Annals of Operations Research, Springer, vol. 235(1), pages 581-598, December.
    4. Pagès-Bernaus, Adela & Pérez-Valdés, Gerardo & Tomasgard, Asgeir, 2015. "A parallelised distributed implementation of a Branch and Fix Coordination algorithm," European Journal of Operational Research, Elsevier, vol. 244(1), pages 77-85.
    5. 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).
    6. L. Aranburu & L. Escudero & M. Garín & G. Pérez, 2012. "A so-called Cluster Benders Decomposition approach for solving two-stage stochastic linear 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 279-295, July.
    7. Diego Ruiz-Hernández & David Delgado-Gómez, 2016. "The stochastic capacitated branch restructuring problem," Annals of Operations Research, Springer, vol. 246(1), pages 77-100, November.
    8. 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).
    9. 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.
    10. Osmani, Atif & Zhang, Jun, 2014. "Economic and environmental optimization of a large scale sustainable dual feedstock lignocellulosic-based bioethanol supply chain in a stochastic environment," Applied Energy, Elsevier, vol. 114(C), pages 572-587.

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