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A Novel and Efficient Mathematical Programming Approach for the Optimal Design of Rainwater Drainage Networks

Author

Listed:
  • Ana Paula Sene

    (State University of Maringá)

  • Jose A. Caballero

    (University of Alicante)

  • Mauro A. S. S. Ravagnani

    (State University of Maringá)

Abstract

Urban sanitation, especially in developing nations, relies on pipe networks, but determining flow in these networks is challenging. Rainwater Drainage Networks (RDNs) face high flow unpredictability due to extreme events and climate change. Optimization studies focused on RDNs frequently employ stochastic techniques due to these systems’ inherent complexities. This study aims to optimize RDNs design, reducing costs while adhering to standards, by selecting appropriate pipes, diameters, and inclinations using a deterministic method. Two mathematical models were developed and evaluated on three case studies exhibiting varying levels of complexity. A Rigorous Model provides a detailed and comprehensive approach to modeling the geometric dimensions of circular sections. However, its inherent non-linear and non-convex properties limit the model’s suitability to smaller-scale problems. The complex characteristics exhibited by larger-scale network surpass the capacities of the Rigorous Model. A Sequential Model is presented as a novel and effective formulation that replaces certain hydraulic equations with constraints, thus guaranteeing feasibility and an optimal network design without compromising the rigor. The model is formulated as a convex Mixed-Integer Quadratic Constrained Programming (MIQCP), solvable by advanced global optimum solvers. The Sequential Model, effectively and quickly, found optimal designs for all case studies, including a network with 160 nodes, offering a practical tool for engineers and urban planners in designing cost-effective RDNs.

Suggested Citation

  • Ana Paula Sene & Jose A. Caballero & Mauro A. S. S. Ravagnani, 2025. "A Novel and Efficient Mathematical Programming Approach for the Optimal Design of Rainwater Drainage Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 39(2), pages 883-905, January.
    • Handle: RePEc:spr:waterr:v:39:y:2025:i:2:d:10.1007_s11269-024-03998-3
    DOI: 10.1007/s11269-024-03998-3
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    References listed on IDEAS

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    1. Joshua Steele & Kurt Mahoney & Omer Karovic & Larry Mays, 2016. "Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(5), pages 1605-1620, March.
    2. Omid Seyedashraf, 2024. "Enhancing Decision-Making in Sustainable Urban Drainage System Optimization: A Novel Framework for Sparse Pareto-Fronts," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 38(15), pages 6157-6172, December.
    3. Joshua C. Steele & Kurt Mahoney & Omer Karovic & Larry W. Mays, 2016. "Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(5), pages 1605-1620, March.
    4. Faisal M. Alfaisal & Larry W. Mays, 2021. "Optimization Models for Layout and Pipe Design for Storm Sewer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4841-4854, November.
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    Cited by:

    1. Liqing Zhu & Chi Gao & Mianzhi Wu & Ruiming Zhu, 2025. "Integrating Blue–Green Infrastructure with Gray Infrastructure for Climate-Resilient Surface Water Flood Management in the Plain River Networks," Land, MDPI, vol. 14(3), pages 1-29, March.

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