Annals of Operations Research

, Volume 219, Issue 1, pp 141–167 | Cite as

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

  • Graça Marques Gonçalves
  • Luís Gouveia
  • Margarida Vaz Pato
Article

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. Al-Khayyal, F. A., & Falk, J. E. (1983). Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2), 273–286. CrossRefGoogle Scholar
  2. Alperovits, E., & Shamir, U. (1977). Design of optimal water distribution systems. Water Resources Research, 13(6), 885–900. CrossRefGoogle 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. Google Scholar
  4. CPLEX Optimization (2007). ©ILOG USA. Google Scholar
  5. GAMS: The Solver Manuals (2004). ©GAMS Development Corporation. Google Scholar
  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. CrossRefGoogle 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. Google Scholar
  8. Hansen, C. T., Madsen, K., & Nielsen, H. B. (1991). Optimization of pipe networks. Mathematical Programming, 52, 45–58. CrossRefGoogle 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. CrossRefGoogle Scholar
  13. Knowles, T., Gupta, I., & Hassan, M. (1976). Decomposition of water distribution networks. AIIE Transactions, 8(4), 443–448. CrossRefGoogle 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. CrossRefGoogle Scholar
  16. McCormick, G. P. (1976). Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Mathematical Programming, 10, 147–175. CrossRefGoogle 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. CrossRefGoogle 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. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Graça Marques Gonçalves
    • 1
    • 2
  • Luís Gouveia
    • 2
    • 3
  • Margarida Vaz Pato
    • 2
    • 4
  1. 1.Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaMonte da CaparicaPortugal
  2. 2.Centro de Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  3. 3.Departamento de Estatística e Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  4. 4.Departamento de Matemática, Instituto Superior de Economia e GestãoUniversidade Técnica de LisboaLisboaPortugal

Personalised recommendations