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Solving Large Nonconvex Water Resources Management Models Using Generalized Benders Decomposition

Author

Listed:
  • Ximing Cai

    (International Food Policy Research Institute, 2033 K. Washington D.C., 20006)

  • Daene C. McKinney

    (Department of Civil Engineering, College of Engineering, The University of Texas at Austin, Austin, Texas 78712)

  • Leon S. Lasdon

    (Department of Management Science and Information Systems, Graduate School of Business, The University of Texas at Austin, Austin, Texas 78712)

  • David W. Watkins

    (Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, Michigan 49931)

Abstract

Nonconvex nonlinear programming (NLP) problems arise frequently in water resources management, e.g., reservoir operations, groundwater remediation, and integrated water quantity and quality management. Such problems are usually large and sparse. Existing software for global optimization cannot cope with problems of this size, while current local sparse NLP solvers, e.g., MINOS (Murtagh and Saunders 1987), or CONOPT (Drud 1994) cannot guarantee a global solution. In this paper, we apply the Generalized Benders Decomposition (GBD) algorithm to two large nonconvex water resources models involving reservoir operations and water allocation in a river basin, using an approximation to the GBD cuts proposed by Floudas et al. (1989) and Floudas (1995). To ensure feasibility of the GBD subproblem, we relax its constraints by introducing elastic slack variables, penalizing these slacks in the objective function. This approach leads to solutions with excellent objective values in run times much less than the GAMS NLP solvers MINOS5 and CONOPT2, if the complicating variables are carefully selected. Using these solutions as initial points for MINOS5 or CONOPT2 often leads to further improvements.

Suggested Citation

  • Ximing Cai & Daene C. McKinney & Leon S. Lasdon & David W. Watkins, 2001. "Solving Large Nonconvex Water Resources Management Models Using Generalized Benders Decomposition," Operations Research, INFORMS, vol. 49(2), pages 235-245, April.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:2:p:235-245
    DOI: 10.1287/opre.49.2.235.13537
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    References listed on IDEAS

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    1. Arne Stolbjerg Drud, 1994. "CONOPT—A Large-Scale GRG Code," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 207-216, May.
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    Cited by:

    1. Hu, Zhineng & Chen, Yazhen & Yao, Liming & Wei, Changting & Li, Chaozhi, 2016. "Optimal allocation of regional water resources: From a perspective of equity–efficiency tradeoff," Resources, Conservation & Recycling, Elsevier, vol. 109(C), pages 102-113.
    2. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    3. Zheng, Hao & Feng, Suzhen & Chen, Cheng & Wang, Jinwen, 2022. "A new three-triangle based method to linearly concave hydropower output in long-term reservoir operation," Energy, Elsevier, vol. 250(C).
    4. Roberto Mínguez & Antonio Conejo & Enrique Castillo, 2013. "Optimal engineering design via Benders’ decomposition," Annals of Operations Research, Springer, vol. 210(1), pages 273-293, November.
    5. Ruben Menke & Edo Abraham & Panos Parpas & Ivan Stoianov, 2016. "Exploring Optimal Pump Scheduling in Water Distribution Networks with Branch and Bound Methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(14), pages 5333-5349, November.
    6. Enrique Castillo & Roberto Mínguez & Antonio Conejo & Beatriz Pérez & Oscar Fontenla, 2013. "Estimating the parameters of a fatigue model using Benders’ decomposition," Annals of Operations Research, Springer, vol. 210(1), pages 309-331, November.
    7. Ricardo Saraiva de Camargo & Gilberto de Miranda & Henrique Pacca L. Luna, 2009. "Benders Decomposition for Hub Location Problems with Economies of Scale," Transportation Science, INFORMS, vol. 43(1), pages 86-97, February.
    8. Wen-jing Niu & Zhong-kai Feng & Yu-rong Li & Shuai Liu, 2021. "Cooperation Search Algorithm for Power Generation Production Operation Optimization of Cascade Hydropower Reservoirs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(8), pages 2465-2485, June.
    9. Ratha, Anubhav & Pinson, Pierre & Le Cadre, Hélène & Virag, Ana & Kazempour, Jalal, 2023. "Moving from linear to conic markets for electricity," European Journal of Operational Research, Elsevier, vol. 309(2), pages 762-783.
    10. Andrzej Karbowski, 2021. "Generalized Benders Decomposition Method to Solve Big Mixed-Integer Nonlinear Optimization Problems with Convex Objective and Constraints Functions," Energies, MDPI, vol. 14(20), pages 1-18, October.

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