Joint entropy and multi-objective evolutionary optimization of water distribution networks

Tiku T. Tanyimboh, Anna M. Czajkowska

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
65 Downloads (Pure)


It is essential to consider resilience when designing any water distribution network and surrogate measures of resilience are used frequently as accurate measures often impose prohibitive computational demands in optimization algorithms. Previous design optimization algorithms based on flow entropy have essentially employed a single loading condition because the flow entropy concept formally has not been extended to multiple loading conditions in water distribution networks. However, in practice, water distribution networks must satisfy multiple loading conditions. The aim of the research was to close the gap
between the prevailing entropy-based design optimization approaches based on one loading condition essentially and water distribution practice that must address multiple loading conditions. A methodology was developed and applied to a real-world water distribution network in the literature, based on the concept of the joint entropy of independent probability schemes. The results demonstrated that the critical loading conditions were design specific. In other words, the critical loading and operating conditions cannot readily be determined
beforehand. Consequently, maximizing the joint entropy provided the most consistently competitive solutions in terms of the balance between cost and resilience. The results were derived using a penalty-free genetic algorithm with three objectives. Compared to previous research using flow entropy based on a single loading condition and two objectives, there was a substantial increase of 274% in the number of non-dominated solutions achieved.
Original languageEnglish
Number of pages16
JournalWater Resources Management
Early online date12 Apr 2018
Publication statusE-pub ahead of print - 12 Apr 2018


  • entropy vector for multiple operating conditions
  • genetic algorithm
  • infrastructure resilience
  • mechanical and hydraulic reliability
  • redundancy and failure tolerance
  • constrained evolutionary optimization


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