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Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization

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  • A. Shibu
  • M. Reddy

Abstract

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • A. Shibu & M. Reddy, 2014. "Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 4075-4094, September.
    • Handle: RePEc:spr:waterr:v:28:y:2014:i:12:p:4075-4094
    DOI: 10.1007/s11269-014-0728-6
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    References listed on IDEAS

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    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    2. Huang, Tao & Zhao, Ruiqing & Tang, Wansheng, 2009. "Risk model with fuzzy random individual claim amount," European Journal of Operational Research, Elsevier, vol. 192(3), pages 879-890, February.
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    Cited by:

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    2. Hossein Fallah & Ozgur Kisi & Sungwon Kim & Mohammad Rezaie-Balf, 2019. "A New Optimization Approach for the Least-Cost Design of Water Distribution Networks: Improved Crow Search Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3595-3613, August.
    3. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    4. C. Dai & Y. Cai & Y. Liu & W. Wang & H. Guo, 2015. "A Generalized Interval Fuzzy Chance-Constrained Programming Method for Domestic Wastewater Management Under Uncertainty – A Case Study of Kunming, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3015-3036, July.
    5. Swati Sirsant & M. Janga Reddy, 2021. "Optimal Design of Pipe Networks Accounting for Future Demands and Phased Expansion using Integrated Dynamic Programming and Differential Evolution Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(4), pages 1231-1250, March.

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