Water Resources Management

, Volume 33, Issue 13, pp 4583–4598 | Cite as

A Depth-First Search Algorithm for Optimizing the Gravity Pipe Networks Layout

  • Gustavo Paiva Weyne RodriguesEmail author
  • Luis Henrique Magalhães Costa
  • Guilherme Marques Farias
  • Marco Aurélio Holanda de Castro


The layout is displayed in one of the most complex tasks in the gravity pipe network project because there are several factors to consider and often a choice of unassociated or smaller layout. Currently, the designer’s experience is needed so different layout alternatives be analyzed to reduce the depths of the network. Generally, this operation is manual and does not ensure the best result. For this research, a depth-first search algorithm was presented, which allows the optimization of the layout of a gravity pipe network, assessing the topographic conditions of the manholes (nodes), leading to a layout that has the sum of lower unfavorable slopes. A hypothetical and a real network were used. The computational time required was considered negligible. The results showed a robust model, which works for the complete layout of any network, of any size, resulting in the lowest possible depths.


Gravity Pipe networks Optimal layout Depth-first search algorithm Search algorithms 



  1. Afshar MH (2006) Application of a genetic algorithm to storm sewer network optimization. Sci Iran 13(3):234–244Google Scholar
  2. Boaventura Netto PO, Jurkiewicz S (2009) Grafos: introdução e prática. Blucher, São PauloGoogle Scholar
  3. Cormen TH (2013) Algorithms unlocked. MIT Press, CambridgeGoogle Scholar
  4. Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithm. MIT Press, CambridgeGoogle Scholar
  5. Dajani JS (1971) Network evaluation of wastewater collection economics. PhD thesis. Northwestern UniversityGoogle Scholar
  6. Dajani JS, Gemmel RS, Morlok EK (1972) Optimal design of urban wastewater collection networks. J Sanit Eng Div Am Soc Civ Eng 98(6):853–867Google Scholar
  7. Dasgupta S, Papadimitriou CH, Vazirani U (2008) Algorithms. McGraw-Hill Higher Education, New YorkGoogle Scholar
  8. Deininger RA (1966) Computer aided design of waste collection and treatment systems. Proc., 2nd American Water Resource Conf., Univ. of Chicago, ChicagoGoogle Scholar
  9. Diogo AF, Graveto VM (2006) Optimal layout of sewer systems: a deterministic versus a stochastic model. J Water Res Plan Man 132(9):927–943Google Scholar
  10. Gameiro LFS (2003) Dimensionamento otimizado de redes de esgotos sanitários com a utilização de algoritmos genéticos. MSc dissertation. Mato Grosso do Sul Federal UniversityGoogle Scholar
  11. Haghighi A, Bakhshipour AE (2012) Optimization of sewer networks using an adaptive genetic algorithm. Water Resour Manag 26:3441–3456CrossRefGoogle Scholar
  12. Haith D (1966) Vertical alignment of sewers and drainage systems by dynamic programming. MSc dissertation. Massachusetts Institute of TechnologyGoogle Scholar
  13. Heaney JP, Pitt R, Field R (2000) Innovative urban wet-weather flow management systems. EPA/600/R-99/029, U.S. Environmental Protection Agency, Cincinnati, USAGoogle Scholar
  14. Holland ME (1966) Computer models of wastewater collection systems. PhD thesis. Harvard University, CambridgeGoogle Scholar
  15. Kulkarni VS, Khanna P (1985) Pumped wastewater collection systems optimization. J Environ Eng Div (Am Soc Civ Eng) 111(5):589–601CrossRefGoogle Scholar
  16. Liebman JC (1967) A heuristic aid for the design of sewer networks. J Sanit Eng Div Am Soc Civ Eng 93(4):81–90Google Scholar
  17. Mai SW, Evans DJ (1984) A parallel algorithm for the enumeration of the spanning trees of a graph. Parallel Comput 1:275–286CrossRefGoogle Scholar
  18. Mays LW, Yen BC (1975) Optimal design of branched sewer system. Water Resour Res 11(1):37–47CrossRefGoogle Scholar
  19. Moeini R, Afshar MH (2017) Arc based ant colony optimization algorithm for optimal design of gravitational sewer networks. Ain Shams Engineering J 8(2):207–223. CrossRefGoogle Scholar
  20. Nzewi EU, Gray DD, Houck MH (1985) Optimal design program for gravity sanitary sewers. Civ Eng Syst 2:132–141CrossRefGoogle Scholar
  21. Pan TC, Kao JJ (2009) GA-QP model to optimize sewer system design. J Environ Eng 135(1):17–24CrossRefGoogle Scholar
  22. Russell SJ, Norvig P (2010) Artificial intelligence: a modern approach, 3rd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  23. Steele JC, Mahoney K, Karovic O, Mays LW (2016) Heuristic optimization model for the optmial laytou and pipe design of sewer systems. Water Resour Manag 30:1605–1620CrossRefGoogle Scholar
  24. Velon JP (1971) Sewer cost – estimation model: an aplication. MSc dissertation. Northwestern UniversityGoogle Scholar
  25. Villas MV, Ferreira AGM, Leroy PG (1993) Estruturas de dados: conceitos e técnicas de implementação. Ed. Campus, Rio de JaneiroGoogle Scholar
  26. Walsh S, Brown LC (1973) Least cost method for sewer design. J Environ Eng Div 99(3):333–345Google Scholar
  27. Walters GA, Lohbeck T (1993) Optimal layout of tree networks using genetic algorithms. Eng Optim 22(1):27–48CrossRefGoogle Scholar
  28. Walters GA, Smith DK (1995) Evolutionary design algorithm for optimal layout of tree networks. Eng Optim 24(4):261–281CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringVale do Acaraú State UniversitySobralBrazil
  2. 2.Department of Civil Engineering, Federal Institute of EducationScience and Technology of CearáFortalezaBrazil
  3. 3.Department of Civil EngineeringFederal University of CearáFortalezaBrazil

Personalised recommendations