GA-QP Model to Optimize Sewer System Design
Publication: Journal of Environmental Engineering
Volume 135, Issue 1
Abstract
Sanitary sewer systems are fundamental and expensive facilities for controlling water pollution. Optimizing sewer design is a difficult task due to its associated hydraulic and mathematical complexities. Therefore, a genetic algorithm (GA) based approach has been developed. A set of diameters for all pipe segments in a sewer system is regarded as a chromosome for the proposed GA model. Hydraulic and topographical constraints are adopted in order to eliminate inappropriate chromosomes, thereby improving computational efficiency. To improve the solvability of the proposed model, the nonlinear cost optimization model is approximated and transformed into a quadratic programming (QP) model. The system cost, pipe slopes, and pipe buried depths of each generated chromosome are determined using the QP model. A sewer design problem cited in literature has been solved using the GA-QP model. The solution obtained from the GA model is comparable to that produced by the discrete differential dynamic programming approach. Finally, several near-optimum designs produced using the modeling to generate alternative approach are discussed and compared for improving the final design decision.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers would like to thank the National Science Council, R.O.C., for providing partial financial support of this research under Grant No. UNSPECIFIEDNSC94-2211-E-009-010.
References
Afshar, M. H., Afshar, A., Marino, M. A., and Darbandi, A. A. S. (2006). “Hydrograph-based storm sewer design optimization by genetic algorithm.” Can. J. Civ. Eng., 33(3), 310–325.
Argaman, Y., Shamir, U., and Spivak, E. (1973). “Design of optimal sewerage systems.” J. Envir. Engrg. Div., 99(5), 703–716.
Babayan, A., Kapelan, Z., Savic, D., and Walters, G. (2005). “Least-cost design of water distribution networks under demand uncertainty.” J. Water Resour. Plann. Manage., 131(5), 375–382.
Berry, L. T. M., Murtagh, B. A., McMahon, G., Sugden, S., and Welling, L. (1999). “An integrated GA-LP approach to communication network design.” Telecommun. Syst., 12, 265–280.
Cai, X., McKinney, D. C., and Lasdon, L. S. (2001). “Solving nonlinear water management models using a combined genetic algorithm and linear programming approach.” Adv. Water Resour., 24, 667–676.
Chang, S. Y., and Brill, E. D. (1982). “Use of mathematical models to generate alternative solutions to water resources planning problems.” Water Resour. Res., 18(1), 58–64.
Chang, S. Y., and Liaw, S. L. (1985). “Generating design for wastewater system.” J. Environ. Eng., 111(5), 665–679.
Dandy, G. C., and Engelhardt, M. (2001). “Optimal scheduling of water pipe replacement using genetic alogrithms.” J. Water Resour. Plann. Manage., 127(4), 214–223.
El-Araby, E. E., Yorino, N., and Sasaki, H. (2003). “A two level hybrid GA/SLP for FACTS allocation problem considering voltage security.” Int. J. Electr. Power Energy Syst., 25, 327–335.
Elimam, A. A., Charalambous, C., and Ghobrial, F. H. (1989). “Optimum design of large sewer networks.” J. Environ. Eng., 115(6), 1171–1190.
Goldberg, D. E. (1989). “A genetle introduction to genetic algorithms.” Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading, Mass., 1–27.
Goldberg, D. E., and Kuo, C. H. (1987). “Genetic algorithms in pipeline optimization.” J. Comput. Civ. Eng., 1(2), 128–141.
Gupta, A., Kripakaran, P., Mahinthakumar, G., and Baugh, J. W. (2005). “Genetic algorithm-based decision support for optimizing seismic response of piping systems.” J. Struct. Eng., 131(3), 389–398.
Heidari, M., Chow, V. T., Kokotović, P. V., and Meredith, D. D. (1971). “Discrete differential dynamic programming approach to water resources system optimization.” Water Resour. Res., 7(2), 273–282.
ILOG Inc. (2002). ILOG Cplex8.0, Gentilly, France.
Kamphausen, S. (2003). “Simple generalized GA.” Tellumar Kampiva, ⟨http://www.skamphausen.de/software⟩ (Dec. 20, 2003).
Kulkarni, V. S., and Khanna, P. (1985). “Pumped wastewater collection systems optimization.” J. Environ. Eng., 111(5), 589–601.
Li, G., and Matthew, R. G. S. (1990). “New approach for optimization of urban drainage system.” J. Environ. Eng., 116(5), 927–944.
Liang, L. Y., Thompson, R. G., and Young, D. M. (2004). “Optimising the design of sewer networks using genetic algorithms and tabu search.” Eng., Constr., Archit. Manage., 11(2), 101–112.
Liebman, J. C. (1967). “A heuristic aid for the design of sewer networks.” J. Sanit. Engrg. Div., 93(4), 81–90.
Lippai, I., Heaney, J. P., and Laguna, M. (1999). “Robust water system design with commercial intelligent search optimizers.” J. Comput. Civ. Eng., 13(3), 135–143.
Mays, L. W., and Wenzel, H. G. (1976). “Optimal design of multilevel branching sewer system.” Water Resour. Res., 12(5), 913–917.
Mays, L. W., Wenzel, H. G., and Liebman, J. C. (1976). “Model for layout and design of sewer systems.” J. Water Resour. Plng. and Mgmt. Div., 102(2), 385–405.
Mays, L. W., and Yen, B. C. (1975). “Optimal cost design of branched sewer system.” Water Resour. Res., 11(1), 37–47.
Simpson, A. R., Dandy, G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.” J. Water Resour. Plann. Manage., 120(4), 423–443.
Swamee, P. K. (2001). “Design of sewer line.” J. Environ. Eng., 127(9), 776–781.
Walsh, S., and Brown, L. C. (1973). “Least cost method for sewer design.” J. Envir. Engrg. Div., 99(3), 333–345.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Aug 20, 2007
Accepted: Jun 20, 2008
Published online: Jan 1, 2009
Published in print: Jan 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.