Cuckoo Search via Lévy Flight Applied to Optimal Water Supply System Design

  • Ricardo SotoEmail author
  • Broderick CrawfordEmail author
  • Rodrigo OlivaresEmail author
  • Carlos CastroEmail author
  • Pía Escárate
  • Steve Calderón
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10868)


Designing optimal water supply systems is an important purpose of any urban system that involves relevant installation, operation and maintenance costs. However, achieving the optimal design is known to be a complex task, indeed the corresponding mathematical model for this problem leads to a non-linear and non-convex problem classified as NP-hard. In this paper, we propose using the cuckoo search algorithm which a modern bio-inspired metaheuristic based on the obligate brood parasitic behavior of cuckoo birds. This behavior is combined with the interesting Lévy flight, which mimic the exploration of some birds and flies, that move by combining straight flights and ninety degrees turns. The proposed approach results in a fast convergence algorithm able to noticeably reduce the number of objective function evaluations needed to solve this problem.


Optimal water supply system design Cuckoo search algorithm Metaheuristics 



Ricardo Soto is supported by Grant CONICYT/FONDECYT/REGULAR/1160455. Broderick Crawford is supported by Grant CONICYT/FONDECYT/REGULAR/1171243. Rodrigo Olivares is supported by CONICYT/FONDEF/IDeA/ID16I10449, FONDECYT/STIC-AMSU/17STIC-03, FONDECYT/MEC/MEC80170097, and Postgraduate Grant Pontificia Universidad Católica de Valparaíso (INF - PUCV 2015–2018).


  1. 1.
    Reynolds, A.M., Frye, M.A.: Free-flight odor tracking in drosophila is consistent with an optimal intermittent scale-free search. PLoS ONE 2(4), e354 (2007)CrossRefGoogle Scholar
  2. 2.
    Baños, R., Gil, C., Reca, J., Montoya, F.G.: A memetic algorithm applied to the design of water distribution networks. Appl. Soft Comput. 10(1), 261–266 (2010)CrossRefGoogle Scholar
  3. 3.
    Crawford, B., Soto, R., Monfroy, E., Palma, W., Castro, C., Paredes, F.: Parameter tuning of a choice-function based hyperheuristic using particle swarm optimization. Expert Syst. Appl. 40(5), 1690–1695 (2013)CrossRefGoogle Scholar
  4. 4.
    Cunha, M., Sousa, J.: Water distribution network design optimization: simulated annealing approach. J. Water Resour. Plann. Manage. 125(4), 215–221 (1999)CrossRefGoogle Scholar
  5. 5.
    Dandy, G., Simpson, A., Murphy, L.: An improved genetic algorithm for pipe network optimization. Water Resour. Res. 32(2), 449–458 (1996)CrossRefGoogle Scholar
  6. 6.
    Eusuff, M., Lansey, K.: Optimization of water distribution network design using the shuffled frog leaping algorithm. J. Water Resour. Plan. Manage. ASCE 129(3), 210–225 (2003)CrossRefGoogle Scholar
  7. 7.
    Geem, Z.W.: Optimal cost design of water distribution networks using harmony search. Eng. Optim. 38(3), 259–277 (2006)CrossRefGoogle Scholar
  8. 8.
    Gupta, I., Gupta, A., Khanna, P.: Genetic algorithm for optimization of water distribution systems. Environ. Modell. Softw. 14(5), 437–446 (1999)CrossRefGoogle Scholar
  9. 9.
    Halhal, D., Walters, G., Ouazar, D., Savic, D.: Water network rehabilitation with structured messy genetic algorithms. J. Water Resour. Plan. Manage. 123(3), 137–146 (1997)CrossRefGoogle Scholar
  10. 10.
    Jacoby, S.L.S.: Design of optimal hydraulic networks. J. Hydraul. Div. 94(3), 641–661 (1968)Google Scholar
  11. 11.
    Keedwell, E., Khu, S.-T.: A hybrid genetic algorithm for the design of water distribution networks. Eng. Appl. AI 18(4), 461–472 (2005)Google Scholar
  12. 12.
    Lin, M., Liu, Y., Liu, G., Chu, C.: Scatter search heuristic for least-cost design of water distribution networks. Eng. Optim. 39(7), 857–876 (2007)CrossRefGoogle Scholar
  13. 13.
    Maier, H., Simpsom, A., Zecchin, A., Foong, W., Phang, K., Seah, H., Tan, C.: Ant colony optimization for the design of water distribution systems. J. Water Resour. Plan. Manage. ASCE 129(3), 200–209 (2003)CrossRefGoogle Scholar
  14. 14.
    Monfroy, E., Castro, C., Crawford, B., Soto, R., Paredes, F., Figueroa, C.: A reactive and hybrid constraint solver. J. Exp. Theoret. Artif. Intell. 25(1), 1–22 (2013)CrossRefGoogle Scholar
  15. 15.
    Montalvo, I., Izquierdo, J., Pérez, R., Tung, M.M.: Particle swarm optimization applied to the design of water supply systems. Comput. Math. Appl. 56(3), 769–776 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Montalvo, I., Izquierdo, J., Pérez-García, R., Herrera, M.: Improved performance of PSO with self-adaptive parameters for computing the optimal design of water supply systems. Eng. Appl. AI 23(5), 727–735 (2010)Google Scholar
  17. 17.
    Ostfeld, A., Tubaltzev, A.: Ant colony optimization for least cost design and operation of pumping and operation of pumping water distribution systems. J. Water Resour. Plann. Manage. 134(2), 107–118 (2008)CrossRefGoogle Scholar
  18. 18.
    Pavlyukevich, I.: Lévy flights, non-local search and simulated annealing. J. Comput. Phys. 226, 1830–1844 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Pitchai, R.: A model for designing water distribution pipe networks. Ph.D. thesis, Harvard University (1966)Google Scholar
  20. 20.
    Prasad, D., Park, N.: Multiobjective genetic algorithms for design of water distribution networks. J. Water Resour. Plan. Manage. 130(1), 73–82 (2004)CrossRefGoogle Scholar
  21. 21.
    Quindry, G., Brill, E., Lienman, J.: Water distribution system design criteria. Technical report, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL (1979)Google Scholar
  22. 22.
    Savic, D., Walters, G.: Genetic algorithms for least-cost design of water distribution networks. J. Water Resour. Plan. Manage. ASCE 123(2), 67–77 (1997)CrossRefGoogle Scholar
  23. 23.
    Schaake, J., Lai, D.: Linear programming and dynamic programming applications to water distribution network design. Technical report 116, Hydrodynamics Laboratory, MIT, Cambridge, MA (1969)Google Scholar
  24. 24.
    Sedki, A., Ouazar, D.: Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems. Adv. Eng. Inf. 26(3), 582–591 (2012)CrossRefGoogle Scholar
  25. 25.
    Shamir, U., Alperovits, E.: Design of optimal water distribution systems. Water Resour. Res. 13(6), 885–900 (1977)CrossRefGoogle Scholar
  26. 26.
    Shlesinger, M.F.: Search research. Nature 443, 281–282 (2006)CrossRefGoogle Scholar
  27. 27.
    Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds.): Lévy Flights and Related Topics in Phyics. Springer, Heidelberg (2007)Google Scholar
  28. 28.
    Simpson, A., Murphy, L., Dandy, G.: Genetic algorithms compared to other techniques for pipe optimisation. J. Water Resour. Plan. Manage. ASCE 120(4), 423–443 (1994)CrossRefGoogle Scholar
  29. 29.
    Soto, R., Crawford, B., Galleguillos, C., Monfroy, E., Paredes, F.: A pre-filtered cuckoo search algorithm with geometric operators for solving sudoku problems. Sci. World J. 2014, 12 (2014). Article ID 465359CrossRefGoogle Scholar
  30. 30.
    Suribabu, C.R.: Differential evolution algorithm for optimal design of water distribution networks. J. Hydroinf. 12(1), 66–82 (2010)CrossRefGoogle Scholar
  31. 31.
    Suribabu, C.R., Neelakantan, T.R.: Design of water distribution networks using particle swarm optimization. J. Urban Water 3(2), 111–120 (2006)CrossRefGoogle Scholar
  32. 32.
    Vairavamoorthy, K., Ali, M.: Water network rehabilitation with structured messy genetic algorithms. Comput. Aided Civil Infrastruct. Eng. 15(5), 374–382 (2000)CrossRefGoogle Scholar
  33. 33.
    Yang, X.-S., Deb, S.: Cuckoo search via lévy flights. In: World Congress on Nature & Biologically Inspired Computing (NaBIC), pp. 210–214. IEEE (2009)Google Scholar
  34. 34.
    Yates, D.F., Templeman, A.B., Boffey, T.B.: The computational complexity of the problem of determining least capital cost designs for water supply networks. Eng. Optim. 7(2), 143–155 (1984)CrossRefGoogle Scholar
  35. 35.
    Zecchin, A.C., Simpson, A.R., Maier, H.R., Leonard, M., Roberts, A.J., Berrisford, M.J.: Application of two ant colony optimisation algorithms to water distribution system optimisation. Math. Comput. Modell. 44(5–6), 451–468 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Pontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Universidad de ValparaísoValparaísoChile
  3. 3.Universidad Técnica Federico Santa MaríaValparaísoChile

Personalised recommendations