Robust optimization for water distribution systems least cost design

Lina Perelman, Mashor Housh, Avi Ostfeld

Research output: Contribution to journalArticlepeer-review


The objective of the least cost design problem of a water distribution system is to find its minimum cost with discrete diameters as decision variables and hydraulic controls as constraints. The goal of a robust least cost design is to find solutions which guarantee its feasibility independent of the data (i.e., under model uncertainty). A robust counterpart approach for linear uncertain problems is adopted in this study, which represents the uncertain stochastic problem as its deterministic equivalent. Robustness is controlled by a single parameter providing a trade-off between the probability of constraint violation and the objective cost. Two principal models are developed: uncorrelated uncertainty model with implicit design reliability, and correlated uncertainty model with explicit design reliability. The models are tested on three example applications and compared for uncertainty in consumers' demands. The main contribution of this study is the inclusion of the ability to explicitly account for different correlations between water distribution system demand nodes. In particular, it is shown that including correlation information in the design phase has a substantial advantage in seeking more efficient robust solutions. Key Points Uncertainty inclusion in robust least cost design of water networks Model development for uncertainty insertion with implicit design reliability Methodology for head loss linearization for robust counterpart modeling

Original languageEnglish
Pages (from-to)6795-6809
Number of pages15
JournalWater Resources Research
Issue number10
StatePublished - Oct 2013
Externally publishedYes


  • design
  • reliability
  • robust optimization
  • uncertainty
  • water distribution systems

ASJC Scopus subject areas

  • Water Science and Technology


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