Optimization and Engineering

, Volume 13, Issue 2, pp 219–246 | Cite as

On the optimal design of water distribution networks: a practical MINLP approach

  • Cristiana Bragalli
  • Claudia D’Ambrosio
  • Jon Lee
  • Andrea LodiEmail author
  • Paolo Toth


We propose a practical solution method for real-world instances of a water-network optimization problem with fixed topology using a nonconvex continuous NLP (NonLinear Programming) relaxation and a MINLP (Mixed Integer NonLinear Programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, with the goal of calculating only good feasible solutions, complicated algorithmics can be confined to the MINLP solver. We report successful computational experience using available open-source MINLP software on problems from the literature and on difficult real-world instances. An important contribution of this paper is that the solutions obtained, besides being low cost, are immediately usable in practice because they are characterized by an allocation of diameters to pipes that leads to a correct hydraulic operation of the network. This is not the case for most of the other methods presented in the literature.


Water network design Mixed-integer nonlinear programming Modeling Computation 


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  1. Artina S, Walker J (1983) Sull’uso della programmazione a valori misti nel dimensionamento di costo minimo di reti in pressione. Atti Accad Sci Ist Bologna, Serie III, vol 271(X) (in Italian) Google Scholar
  2. Beale E, Tomlin J (1970) Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence J (ed) Proc of the 5th int conf on operations research, pp 447–454 Google Scholar
  3. Bonami P, Lee J (2006) Bonmin users’ manual. Tech rep Google Scholar
  4. Bonami P, Biegler L, Conn A, Cornuéjols G, Grossmann C, Laird I, Lee J, Lodi A, Margot F, Sawaya N, Wächter A (2008) An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optim 5:186–204 MathSciNetzbMATHCrossRefGoogle Scholar
  5. Bragalli C, D’Ambrosio C, Lee J, Lodi A, Toth P (2006) An MINLP solution method for a water network problem. In: Azar Y, Erlebach T (eds) Algorithms—ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, pp 696–707 CrossRefGoogle Scholar
  6. Cunha M, Sousa J (1999) Water distribution network design optimization: simulated annealing approach. J Water Resour Plan Manag, Div Soc Civ Eng 125:215–221 CrossRefGoogle Scholar
  7. Dandy G, Simpson A, Murphy L (1996) An improved genetic algorithm for pipe network optimization. Water Resour Res 32:449–458 CrossRefGoogle Scholar
  8. Eiger G, Shamir U, Ben-Tal A (1994) Optimal design of water distribution networks. Water Resour Res 30:2637–2646 CrossRefGoogle Scholar
  9. Fourer R, Gay D, Kernighan B (2003) AMPL: a modeling language for mathematical programming, 2nd edn. Duxbury Press/Brooks/Cole Publishing Co., N. Scituate Google Scholar
  10. Fujiwara O, Khang D (1990) A two-phase decomposition method for optimal design of looped water distribution networks. Water Resour Res 26:539–549 CrossRefGoogle Scholar
  11. Ilog-Cplex (v. 10.1)
  12. Lansey K, Mays L (1989) Optimization model for water distribution system design. J Hydraul Eng 115:1401–1418 CrossRefGoogle Scholar
  13. Leyffer S (April 1998; revised March 1999) User manual for MINLP_BB. Tech rep, University of Dundee Google Scholar
  14. Sahinidis NV, Tawarmalani M (2005) BARON 7.2.5: global optimization of mixed-integer nonlinear programs, User’s Manual Google Scholar
  15. Savic DA, Walters GA (1997) Genetic algorithms for the least-cost design of water distribution networks. J Water Resour Plan Manag 123:67–77 CrossRefGoogle Scholar
  16. Schaake JCJ, Lai D (1969) Liner programming and dynamic programming application to water distribution network design. Report 116, Hydrodynamics Laboratory, Department of Civil Engineering, School of Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts Google Scholar
  17. Sherali HD, Subramanian S, Loganathan GV (2001) Effective relaxation and partitioning schemes for solving water distribution network design problems to global optimality. J Glob Optim 19:1–26 MathSciNetzbMATHCrossRefGoogle Scholar
  18. Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math Program 99:563–591 MathSciNetzbMATHCrossRefGoogle Scholar
  19. Van Den Boomen M, Mazijk AV, Beuken R (2004) First evaluation of new design concepts for self-cleaning distribution networks. J Water Supply, Res Technol, AQUA 53(1):43–50 Google Scholar
  20. Walski T (1984) Analysis of water distribution systems. Van Nostrand Reinhold Company, New York Google Scholar
  21. Walski T, Chase D, Savic D (2001) Water distribution modeling. Haestad Methods, Waterbury Google Scholar
  22. Xu C, Goulter I (1999) Reliability-based optimal design of water distribution networks. J Water Resour Plan Manag 125:352–362 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Cristiana Bragalli
    • 1
  • Claudia D’Ambrosio
    • 2
  • Jon Lee
    • 3
  • Andrea Lodi
    • 2
    Email author
  • Paolo Toth
    • 2
  1. 1.DISTARTUniversity of BolognaBolognaItaly
  2. 2.DEISUniversity of BolognaBolognaItaly
  3. 3.IBM T.J. Watson Research CenterYorktown HeightsUSA

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