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Multiperiod Hypergraph Models for Water Systems Optimization

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  • Giovanni Sechi
  • Paola Zuddas

Abstract

Mathematical models describing water resources systems optimization are characterized by a large number of variables and constraints, which are needed to describe the physical components of the system, its functional ties, and its operating modalities. Some special algebraic structures allow its representation as a pure hypergraph flow problem. The hypergraph structure is derived from a multiperiod network describing the spatial and temporal structure of the physical system. As a crucial feature in modeling functional relations and in describing scenario changes in the system, with the hypergraph approach it is possible to reach a close correspondence between the components of the physical problem and those of the mathematical model. In this paper a water resources management model including a reservoir design problem is studied, and the methodology is tested by the hypergraph simplex algorithm on a real water resources system on the island of Sardinia (Italy) in a extended time horizon. The results obtained show that this technique is very competitive in this kind of problem. Copyright Springer Science+Business Media, Inc. 2008

Suggested Citation

  • Giovanni Sechi & Paola Zuddas, 2008. "Multiperiod Hypergraph Models for Water Systems Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(3), pages 307-320, March.
    • Handle: RePEc:spr:waterr:v:22:y:2008:i:3:p:307-320
    DOI: 10.1007/s11269-007-9163-2
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    References listed on IDEAS

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    1. Ravindra K. Ahuja & James B. Orlin & Giovanni M. Sechi & Paola Zuddas, 1999. "Algorithms for the Simple Equal Flow Problem," Management Science, INFORMS, vol. 45(10), pages 1440-1455, October.
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    Cited by:

    1. D. Haro & J. Paredes & A. Solera & J. Andreu, 2012. "A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4059-4071, November.
    2. Chih-Liang Kuo & Nien-Sheng Hsu, 2011. "An Optimization Model for Crucial Key Pipes and Mechanical Reliability: A Case Study on a Water Distribution System in Taiwan," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(2), pages 763-775, January.
    3. Jacopo Napolitano & Giovanni M. Sechi & Paola Zuddas, 2016. "Scenario Optimisation of Pumping Schedules in a Complex Water Supply System Considering a Cost–Risk Balancing Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(14), pages 5231-5246, November.
    4. Giovanni M. Sechi & Alexei A. Gaivoronski & Jacopo Napolitano, 2019. "Optimising Pumping Activation in Multi-Reservoir Water Supply Systems under Uncertainty with Stochastic Quasi-Gradient Methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(5), pages 1881-1895, March.
    5. Antonio Manca & Giovanni Sechi & Paola Zuddas, 2010. "Water Supply Network Optimisation Using Equal Flow Algorithms," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(13), pages 3665-3678, October.

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