Abstract
Optimization models are developed for simultaneously determining the pipe layout and the pipe design for storm sewer systems. The pipe design process includes computation of commercial diameters, slopes, and crown elevations for the storm sewer pipes. The optimization models aim to minimize the total costs of the layout and the pipe design for most of system elements. The optimization models are formulated as a 0–1 Integer Nonlinear Programming problem and solved using the General Algebraic Modeling System without the use of heuristic models which were characteristic of all previous models for the simultaneous determine of the pipe layout and pipe design of sewer networks. The models are based upon two different optimization approaches: (1) considers one or more commercial diameters of pipe connecting two manholes and (2) considers only one commercial diameter in a pipe connecting two manholes. The commercial diameters, pipe slopes, crown elevations, and total costs of the storm sewer system were compared for the two approaches using an example that illustrates the savings in cost by allowing multiple pipe sizes. The two new optimization modeling approaches developed herein can simultaneously determine the minimum cost pipe design (commercial diameters, slopes, and crown elevations) and pipe layout of storm sewer systems and satisfy all design constraints.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
All data and models used in this study are available from the corresponding author by request.
Code Availability
The example system is available by request.
References
Afshar MH (2006) Application of a genetic algorithm to storm sewer network optimization. Sci Iran 13(3):234–244
Afshar MH (2010) A parameter free continuous Ant colony optimization algorithm for the optimal design of storm sewer networks. Adv Eng Softw 41:188–195. https://doi.org/10.1016/j.advengsoft.2009.09.009
Afshar MH, Afshar A, Mariño MA, Darbandi AAS (2006) Hydrograph-based storm sewer design optimization by genetic algorithm. Can J Civ Eng 33(3):319–325. https://doi.org/10.1139/l05-121
Argaman Y, Shamir U, Spivak E (1973) Design of optimal sewerage systems. J Environ Eng ASCE 99(5):703–716. https://doi.org/10.1061/JEEGAV.0000096
Cembrowicz RG, Krauter GE (1987) Design of cost optimal sewer networks. In: Gujer W. et al. (eds.) Proceedings of 4th International Conference on Urban Storm Drainage, Lausanne, Switzerland, pp 367–372
Dajani JS, Hasit Y (1974) Capital cost minimization of drainage networks. J Environ Eng-ASCE 100(2):325–337. https://doi.org/10.1061/JEEGAV.0000163
Dajani JS, Gemmell RS, Morlok EK (1972) Optimal design of urban wastewater collection networks. J Sanitary Eng Div 98(6):853–867. https://doi.org/10.1061/JSEDAI.0001502
Deininger RA (1966) Computer aided design of waste collection and treatment systems. In: Proceedings of the 2nd Annual Conference of American Water Resources, Chicago, USA, pp 247–258
Deininger RA (1970) Systems analysis for water supply and pollution control, natural resource systems models in decision making, Edited by GH Toebes, Water Resources Center, Purdue University
Diogo AF, Graveto VM (2006) Optimal layout of sewer systems: a deterministic versus a stochastic model. J Hydraul Eng-ASCE 132(9):927–943. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:9(927)
Farmani R, Savic DA,Walters GA (2006) A hybrid technique for optimization of branched urban water systems. In Proceedings of the 7th International Conference of Hydroinformatics Nice France 1:985–992
Guo Y, Walters GA, Khu ST, Keedwell EC (2007) A novel cellular automata based approach to storm sewer design. Eng Optim 39(3):345–364. https://doi.org/10.1080/03052150601128261
Guo Y, Walters GA, Savic D (2008) Optimal design of storm sewer networks: past, present and future. In Proceedings of the 11th international conference on urban drainage. Edinburgh, Scotland, UK
Haghighi A (2013) Loop-by-loop cutting algorithm to generate layouts for urban drainage systems. J Water Resour Plan Manag ASCE 139(6):693–703. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000294
Haghighi A, Bakhshipour AE (2012) Optimization of sewer networks using an adaptive genetic algorithm. Water Resour Manag 26:3441–3456. https://doi.org/10.1007/s11269-012-0084-3
Hassan WH, Jassem MH, Mohammed SS (2018) , SS (2018) A GA-HP Model for the optimal design of sewer networks. Water Resour Manag 32:865–879. https://doi.org/10.1007/s11269-017-1843-y
Holland ME (1966) Computer models of wastewater collection systems. PhD dissertation, Harvard University, Cambridge, Massachusetts, USA
Karovic O, Mays LW (2014) Sewer system design using simulated annealing in excel. Water Resour Manag 28:4551–4565. https://doi.org/10.1007/s11269-014-0750-8
Li GY (1986) The optimal design of sewer networks by DDDP. China Water Suppl Sewerage 2(2):18–23 (in Chinese)
Li GY, Matthew RGS (1990) New approach for optimization of urban drainage systems. J Environ Eng ASCE 116(5):927–944. https://doi.org/10.1061/(ASCE)0733-9372(1990)116:5(927)
Liang LY, Thompson RG, Young DM (2004) Optimizing the design of sewer networks using genetic algorithms and tabu search. J Eng Constr Archit Manag 11(2):101–112. https://doi.org/10.1108/09699980410527849
Mays LW (ed) (2001) Stormwater collection systems design handbook. McGraw-Hill Companies Inc, New York, USA
Mays LW (ed) (2004) Urban stormwater management tools. McGraw-Hill Companies Inc, New York, USA
Mays LW, Wenzel HG (1976) Optimal design of multi-level branching sewer systems. Water Resour Res 12(5):913–917. https://doi.org/10.1029/WR012i005p00913
Mays LW, Yen BC (1975) Optimal cost design of branched sewer systems. Water Resour Res 11(1):37–47. https://doi.org/10.1029/WR011i001p00037
Mays LW, Tang WH, Yen BC (1975) Optimal risk-based design of storm sewer networks. J Environ Eng Div ASCE 101(3):381–398. https://doi.org/10.1061/JEEGAV.0000347
Mays LW, Wenzel HG, Liebman JC (1976) Model for layout and design of sewer systems. J Water Resour Plan Manag Div ASCE 102(2):385–405. https://doi.org/10.1061/JWRDDC.0000030
Meredith DD (1971) Dynamic programming with case study on planning and design of urban water facilities, SEC. IX, Treatise on Urban Water Systems, Colorado State University, pp 590–652
Merritt LB, Bogan RH (1973) Computer-based optimal design of sewer systems. J Environ Eng Div 99(1):35–53. https://doi.org/10.1061/JEEGAV.0000009
Moeini R, Afshar MH (2012) Layout and size optimization of sanitary sewer network using intelligent ants. Adv Eng Softw 51:49–62. https://doi.org/10.1016/j.advengsoft.2012.05.003
Nzewi EU, Gray DD, Houck MH (1985) Optimal design program for gravity sanitary sewers. Civ Eng Syst 2:132–141. https://doi.org/10.1080/02630258508970397
Price RK (1978) Design of storm water sewers for minimum construction cost. In Proceedings of 1st international conference on storm drainage, Southampton, UK, pp 636–647
Steele JC, Mahoney K, Karovic O, Mays LW (2016) Heuristic optimization model for the optimal layout and pipe design of sewer systems. Water Resour Manag 30:1605–1620. https://doi.org/10.1007/s11269-015-1191-8
Tekeli S, Belkaya H (1986) Computerized layout generation for sanitary sewers. J Water Resour Plan Manag 112:500–515. https://doi.org/10.1061/(ASCE)0733-9496(1986)112:4(500)
Walters GA, Lohbeck T (1993) Optimal layout of tree networks using genetic algorithms. Eng Optim 22(1):27–48. https://doi.org/10.1080/03052159308941324
Walters GA, Smith DK (1995) Evolutionary design algorithm for optimal layout of tree networks. Eng Optim 24(4):261–281. https://doi.org/10.1080/03052159508941193
Walters GA, Templeman AB (1979) Non-optimal dynamic programming algorithms in the design of minimum cost drainage systems. Eng Optim 4:139–148. https://doi.org/10.1080/03052157908902416
Yen BC, Akan AO (1999) Hydraulic design of urban drainage systems. In: Mays LW (ed) Hydraulic design handbook. McGraw-Hill, New York
Yen BC, Wenzel HG, Mays LW, Tang WH (1976) Advanced methodologies for design of storm sewer systems, Research Report No. 112, Water Resources Center, University of Illinois, Urbana, Illinois
Acknowledgements
Authors would acknowledge the support from Researchers Supporting Project number (RSP-2021/297), King Saud University, Riyadh, Saudi Arabia.
Funding
This research is supported by the Researchers Supporting Project, King Saud University, Riyadh, Saudi Arabia.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [FMA],and [LWM]. The first draft of the manuscript was written by [FMA] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics Approval
Not applicable.
Informed Consent
All authors consent to participate in this research work.
Consent for Publication
All authors consent to publish this work.
Conflict of Interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Alfaisal, F.M., Mays, L.W. Optimization Models for Layout and Pipe Design for Storm Sewer Systems. Water Resour Manage 35, 4841–4854 (2021). https://doi.org/10.1007/s11269-021-02958-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-021-02958-5