An improved decomposition-based heuristic to design a water distribution network for an irrigation system


In this paper the authors address a pressurized water distribution network design problem for irrigation purposes. Two mixed binary nonlinear programming models are proposed for this NP-hard problem. Furthermore, a heuristic algorithm is presented for the problem, which considers a decomposition sequential scheme, based on linearization of the second model, coupled with constructive and local search procedures designed to achieve improved feasible solutions. To evaluate the robustness of the method we tested it on several instances generated from a real application. The best solutions obtained are finally compared with solutions provided by standard software. These computational experiments enable the authors to conclude that the decomposition sequential heuristic is a good approach to this difficult real problem.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Algorithm 1
Algorithm 2
Fig. 3
Fig. 4


  1. Al-Khayyal, F. A., & Falk, J. E. (1983). Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2), 273–286.

    Article  Google Scholar 

  2. Alperovits, E., & Shamir, U. (1977). Design of optimal water distribution systems. Water Resources Research, 13(6), 885–900.

    Article  Google Scholar 

  3. Bragalli, C., D’Ambrosio, C., Lee, J., Lodi, A., & Toth, P. (2006). An MINLP solution method for a water network problem (IBM Research Report, RC23893 (W0602-210)). February 28, pp. 1–17.

  4. CPLEX Optimization (2007). ©ILOG USA.

  5. GAMS: The Solver Manuals (2004). ©GAMS Development Corporation.

  6. Gonçalves, G. M., & Pato, M. V. (2000). A three-phase procedure for designing an irrigation system’s water distribution network. Annals of Operations Research, 94, 163–179.

    Article  Google Scholar 

  7. Gonçalves, G. M. (2008). Modelos de Optimização para o Desenho de uma Rede de Distribuição de Água sob Pressão em Sistemas de Rega. Ph.D. Dissertation, Lisboa.

  8. Hansen, C. T., Madsen, K., & Nielsen, H. B. (1991). Optimization of pipe networks. Mathematical Programming, 52, 45–58.

    Article  Google Scholar 

  9. Ionescu, V., Pantu, D., Berar, U., & Hutanu, V. (1981). Optimizing the dimensioning of a ramified network of pipe lines with flow variable in time. Economic Computation & Economic Cybernetics Studies & Research, 15(3), 41–49.

    Google Scholar 

  10. Karmeli, D., Gadish, Y., & Meyers, S. (1968). Design of optimal water distribution networks. Journal of the Pipeline Division, 94, 1–10.

    Google Scholar 

  11. Karp, R. M. (1972). In R. Miller & J. Thatcher (Eds.), Complexity of computer computations. New York: Plenum.

    Google Scholar 

  12. Kessler, A., & Shamir, U. (1991). Decomposition technique for optimal design of water supply networks. Engineering Optimization, 17, 1–19.

    Article  Google Scholar 

  13. Knowles, T., Gupta, I., & Hassan, M. (1976). Decomposition of water distribution networks. AIIE Transactions, 8(4), 443–448.

    Article  Google Scholar 

  14. Labye, Y., Olson, M., Galand, A., & Tsiourtis, N. (1988). FAO irrigation and drenage paper 44. Design and optimization of irrigation distribution networks. Rome: Food and Agriculture Organization of the United Nations.

    Google Scholar 

  15. Loganathan, G. V., Sherali, H. D., & Shah, M. P. (1990). A two-phase network design heuristic for minimum cost water distribution systems under a reliability constraint. Engineering Optimization, 15, 311–336.

    Article  Google Scholar 

  16. McCormick, G. P. (1976). Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Mathematical Programming, 10, 147–175.

    Article  Google Scholar 

  17. Sherali, H. D., & Smith, E. P. (1997). A global optimization approach to a water distribution network design problem. Journal of Global Optimization, 11, 107–132.

    Article  Google Scholar 

  18. Takahashi, H., & Matsuyama, A. (1980). An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24(6), 573–577.

    Google Scholar 

  19. Zhang, J., & Zhu, D. (1996). A bilevel programming method for pipe network optimization. SIAM Journal on Optimization, 6(3), 838–857.

    Article  Google Scholar 

Download references


This work is supported by Portuguese National Funding from FCT—Fundação para a Ciência e a Tecnologia, under the project: PEst-OE/MAT/UI0152.

The authors are grateful to the referees for the extensive suggestions that have considerably improved the paper.

Author information



Corresponding author

Correspondence to Graça Marques Gonçalves.

Appendix: Input data

Appendix: Input data

Table 8 Costs of the pipes commercially available (Cimianto, Sociedade Técnica de Hidráulica, S.A.)
Table 9 Bounds for the water speed on pipes (Labye et al. 1988)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gonçalves, G.M., Gouveia, L. & Pato, M.V. An improved decomposition-based heuristic to design a water distribution network for an irrigation system. Ann Oper Res 219, 141–167 (2014).

Download citation


  • Pressurized water distribution network design problem
  • Mixed binary nonlinear programming problem
  • Linearization
  • Heuristics