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Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions

Author

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  • Tiku T. Tanyimboh

    (University of the Witwatersrand
    University of Strathclyde Glasgow)

  • Anna M. Czajkowska

    (University of Strathclyde Glasgow
    RPS Group)

Abstract

The informational entropy model for flow networks was formulated over 30 years ago by Tanyimboh and Templeman (University of Liverpool, UK) for a single discrete operating condition that typically comprises the maximum daily demands and was undefined for water distribution networks (WDNs) under multiple operating conditions. Its extension to include multiple independent discrete operating conditions was investigated experimentally herein considering the relationships between flow entropy and hydraulic capacity reliability and redundancy. A novel penalty-free multi-objective genetic algorithm was developed to minimize the initial construction cost and maximize the flow entropy subject to the design constraints. Furthermore, optimized designs derived from the maximum daily demands as a single discrete operating condition were compared to those derived from a combination of discrete operating conditions. Optimized designs from a combination of discrete operating conditions outperformed those from a single operating condition in terms of performance and initial construction cost. The best results overall were achieved by maximizing the sum of the flow entropies of the discrete operating conditions. The logical inference from the results is that the flow entropy of multiple discrete operating conditions is the sum of their respective entropies. In addition, a crucial property of the resulting flow entropy model is that it is bias free with respect to the individual operating conditions; hitherto a fundamental weakness concerning the practical application of the flow entropy model to WDNs is thus addressed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:envsyd:v:41:y:2021:i:2:d:10.1007_s10669-021-09807-1
    DOI: 10.1007/s10669-021-09807-1
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    References listed on IDEAS

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    1. Tiku T. Tanyimboh & Anna M. Czajkowska, 2018. "Joint Entropy Based Multi-Objective Evolutionary 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(8), pages 2569-2584, June.
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    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. 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.
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    6. 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.
    7. 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.
    8. 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.
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    11. Calvin Siew & Tiku Tanyimboh & Alemtsehay Seyoum, 2014. "Assessment of Penalty-Free Multi-Objective Evolutionary Optimization Approach for the Design and Rehabilitation 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. 28(2), pages 373-389, January.
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    14. Yu. Kovalenko & N. Gorev & I. Kodzhespirova & E. Prokhorov & G. Trapaga, 2014. "Convergence of a Hydraulic Solver with Pressure-Dependent Demands," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(4), pages 1013-1031, March.
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    16. 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.
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    18. 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.
    19. Manuel Herrera & Edo Abraham & Ivan Stoianov, 2016. "A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(5), pages 1685-1699, March.
    20. Carlo Ciaponi & Luigi Franchioli & Enrico Murari & Sergio Papiri, 2015. "Procedure for Defining a Pressure-Outflow Relationship Regarding Indoor Demands in Pressure-Driven Analysis 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(3), pages 817-832, February.
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    22. E. Creaco & M. Franchini & S. Alvisi, 2012. "Evaluating Water Demand Shortfalls in Segment Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(8), pages 2301-2321, June.
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