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Optimal Design of Water Distribution Systems Based on Entropy and Topology

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  • Salah Saleh
  • Tiku Tanyimboh

Abstract

A new multi-objective evolutionary optimization approach for joint topology and pipe size design of water distribution systems is presented. The algorithm proposed considers simultaneously the adequacy of flow and pressure at the demand nodes; the initial construction cost; the network topology; and a measure of hydraulic capacity reliability. The optimization procedure is based on a general measure of hydraulic performance that combines statistical entropy, network connectivity and hydraulic feasibility. The topological properties of the solutions are accounted for and arbitrary assumptions regarding the quality of infeasible solutions are not applied. In other words, both feasible and infeasible solutions participate in the evolutionary processes; solutions survive and reproduce or perish strictly according to their Pareto-optimality. Removing artificial barriers in this way frees the algorithm to evolve optimal solutions quickly. Furthermore, any redundant binary codes that result from crossover or mutation are eliminated gradually in a seamless and generic way that avoids the arbitrary loss of potentially useful genetic material and preserves the quality of the information that is transmitted from one generation to the next. The approach proposed is entirely generic: we have not introduced any additional parameters that require calibration on a case-by-case basis. Detailed and extensive results for two test problems are included that suggest the approach is highly effective. In general, the frontier-optimal solutions achieved include topologies that are fully branched, partially- and fully-looped and, for networks with multiple sources, completely separate sub-networks. Copyright The Author(s) 2014

Suggested Citation

  • Salah Saleh & Tiku Tanyimboh, 2014. "Optimal Design of Water Distribution Systems Based on Entropy and Topology," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3555-3575, September.
    • Handle: RePEc:spr:waterr:v:28:y:2014:i:11:p:3555-3575
    DOI: 10.1007/s11269-014-0687-y
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    References listed on IDEAS

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    1. Salah Saleh & Tiku Tanyimboh, 2013. "Coupled Topology and Pipe Size Optimization of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(14), pages 4795-4814, November.
    2. Ioannis Kougias & Nicolaos Theodossiou, 2013. "Multiobjective Pump Scheduling Optimization Using Harmony Search Algorithm (HSA) and Polyphonic HSA," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(5), pages 1249-1261, March.
    3. Calvin Siew & Tiku Tanyimboh, 2012. "Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(15), pages 4485-4507, December.
    4. Raúl Baños & Juan Reca & Juan Martínez & Consolación Gil & Antonio Márquez, 2011. "Resilience Indexes for Water Distribution Network Design: A Performance Analysis Under Demand Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(10), pages 2351-2366, August.
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    1. Tiku T. Tanyimboh & Anna M. Czajkowska, 2021. "Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions," Environment Systems and Decisions, Springer, vol. 41(2), pages 267-285, June.
    2. B. Sriman Pankaj & M. Naveen Naidu & A. Vasan & Murari RR Varma, 2020. "Self-Adaptive Cuckoo Search Algorithm for Optimal Design of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(10), pages 3129-3146, August.
    3. Salah Saleh & Tiku T. Tanyimboh, 2016. "Multi-Directional Maximum-Entropy Approach to the Evolutionary Design Optimization of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(6), pages 1885-1901, April.
    4. Tiku T. Tanyimboh, 2017. "Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(10), pages 3189-3204, August.
    5. Calvin Siew & Tiku T. Tanyimboh & Alemtsehay G. Seyoum, 2016. "Penalty-Free Multi-Objective Evolutionary Approach to Optimization of Anytown Water Distribution Network," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(11), pages 3671-3688, September.
    6. Upaka Rathnayake & Tiku Tanyimboh, 2015. "Evolutionary Multi-Objective Optimal Control of Combined Sewer Overflows," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2715-2731, June.
    7. Tiku T. Tanyimboh & Anna Czajkowska, 2018. "Self-Adaptive Solution-Space Reduction Algorithm for Multi-Objective Evolutionary Design Optimization of Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3337-3352, August.
    8. Mashor Housh & Alaa Jamal, 2022. "Utilizing Matrix Completion for Simulation and Optimization of Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(1), pages 1-20, January.
    9. Akbar Shirzad & Massoud Tabesh & Moharram Heidarzadeh, 2015. "A New Method for Quasi-Optimal Design of Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(14), pages 5295-5308, November.
    10. Tiku T. Tanyimboh & Calvin Siew & Salah Saleh & Anna Czajkowska, 2016. "Comparison of Surrogate Measures for the Reliability and Redundancy of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3535-3552, August.
    11. Yuehua Huang & Bailin Luo & Qi Wang & Qianqian Zhou & Zhiwei Zhao, 2024. "A Global Resilience Analysis-Based Benchmark Framework for Comparing Reliability Surrogate Measures of Water Distribution Systems," Sustainability, MDPI, vol. 16(19), pages 1-20, October.
    12. Alemtsehay G. Seyoum & Tiku T. Tanyimboh, 2016. "Investigation into the Pressure-Driven Extension of the EPANET Hydraulic Simulation Model for Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(14), pages 5351-5367, November.

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