Informational entropy: a failure tolerance and reliability surrogate for water distribution networks

Tiku T. Tanyimboh

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)
42 Downloads (Pure)


Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.
Original languageEnglish
Pages (from-to)3189–3204
Number of pages16
JournalWater Resources Management
Issue number10
Early online date19 May 2017
Publication statusPublished - 31 Aug 2017


  • water distribution systems
  • resilience
  • discrete penalty-free constrained evolutionary optimization
  • maximum entropy formalism
  • uncertainty
  • hydraulic reliability
  • optimisation
  • optimization algorithms
  • multi-objective genetic algorithm


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