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Optimal Localization of Pressure Reducing Valves in Water Distribution Systems by a Reformulation Approach

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  • Pham Dai
  • Pu Li

Abstract

Leakage reduction represents one of the most challenging tasks in managing water distribution systems (WDSs). An effective way to leakage reduction is to carry out network operational pressure management through optimizing locations and regulations for pressure reducing valves (PRVs) and system pressures. This leads to a mixed-integer nonlinear program (MINLP) with a large number of binary variables which make it difficult to solve by an available software package. In this study, instead of directly solving the MINLP problem, we reformulate it to a mathematical program with complementarity constraints which can be efficiently solved by available NLP algorithms. The binary variables are replaced by continuous ones with complementarity constraints to be satisfied by a penalization scheme. To improve the quality of the solution and also to accelerate the convergence, in each relaxed NLP the results of the binary variables are rounded to binary values with which the NLP problem is solved again to achieve a MINLP solution. The final solution will be determined by the best one among the MINLP solutions. The results from two case studies reveal new and better combinations of PRVs as compared with those given in the literature. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Pham Dai & Pu Li, 2014. "Optimal Localization of Pressure Reducing Valves in Water Distribution Systems by a Reformulation Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 3057-3074, August.
    • Handle: RePEc:spr:waterr:v:28:y:2014:i:10:p:3057-3074
    DOI: 10.1007/s11269-014-0655-6
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    References listed on IDEAS

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    1. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
    2. L. Araujo & H. Ramos & S. Coelho, 2006. "Pressure Control for Leakage Minimisation in Water Distribution Systems Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 20(1), pages 133-149, February.
    3. S. Liberatore & G. Sechi, 2009. "Location and Calibration of Valves in Water Distribution Networks Using a Scatter-Search Meta-heuristic Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(8), pages 1479-1495, June.
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    Cited by:

    1. Aditya Gupta & K. D. Kulat, 2018. "A Selective Literature Review on Leak Management Techniques for Water Distribution System," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3247-3269, August.
    2. Pham Duc Dai & Pu Li, 2016. "Optimal Pressure Regulation in Water Distribution Systems Based on an Extended Model for Pressure Reducing Valves," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(3), pages 1239-1254, February.
    3. Filippo Pecci & Edo Abraham & Ivan Stoianov, 2017. "Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks," Computational Optimization and Applications, Springer, vol. 67(1), pages 201-223, May.
    4. Kristina Korder & Hao Cao & Elad Salomons & Avi Ostfeld & Pu Li, 2024. "Simultaneous Minimization of Water Age and Pressure in Water Distribution Systems by Pressure Reducing Valves," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 38(10), pages 3561-3579, August.
    5. Aditya Gupta & Neeraj Bokde & K. D. Kulat, 2018. "Hybrid Leakage Management for Water Network Using PSF Algorithm and Soft Computing Techniques," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(3), pages 1133-1151, February.
    6. Aditya Gupta & Neeraj Bokde & Kishore Kulat & Zaher Mundher Yaseen, 2020. "Nodal Matrix Analysis for Optimal Pressure-Reducing Valve Localization in a Water Distribution System," Energies, MDPI, vol. 13(8), pages 1-17, April.

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