Analytical Optimization Approach for Simultaneous Design and Operation of Water Distribution-Systems Optimization

Mengning Qiu, Mashor Housh, Avi Ostfeld

Research output: Contribution to journalArticlepeer-review


This paper presents an analytical algorithm for simultaneous least-cost design and operation of looped water distribution systems (WDSs). This method could be used to replace evolutionary methods (which are typically used to solve the design-operation problem), or it can be used in conjunction with evolutionary algorithms to enhance their performance (i.e., a hybrid approach). Unlike previous studies that propose analytical methods for split-pipe or continuous diameter design, the developed method addresses a more realistic case in which the pipe design is restricted to commercially available discrete diameters. The analytical approach consists of three stages. In the first stage, a reformulated linear programming (LP) method is used to find the least-cost design of a WDS for a given set of flow distribution while allowing a pipe-split in the solution. In the second stage, the equivalent pipe diameters of the split-pipe design are calculated and modified to discrete pipe diameters by applying a rounding-up strategy to the next commercially available pipe diameter. In the third stage, a nonlinear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the design of the second stage. It is shown in this study that the results produced by the analytical method outperform the results of evolutionary methods when compared to previously published studies. Moreover, when a hybrid approach is adapted, the analytical method can be used to initialize the evolutionary algorithm to gain enhanced performance. The results of the hybrid approach fine-tune those obtained from the analytical method and demonstrate a substantial improvement when compared to a standard evolutionary algorithm initialized with a randomly generated initial population.

Original languageEnglish
Article number06020014
Pages (from-to)1-8
JournalJournal of Water Resources Planning and Management - ASCE
Issue number3
StatePublished - 1 Mar 2021

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation (Grant No. 555/18) and the Israeli Water Authority (Grant No. 4501687498).

Publisher Copyright:
© 2020 American Society of Civil Engineers.


  • Hybrid genetic algorithm (GA)
  • Linear programming
  • Nonlinear programming
  • Water distribution system
  • Water distribution system design
  • Water distribution system operation

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geography, Planning and Development
  • Water Science and Technology
  • Management, Monitoring, Policy and Law


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