Optimal Design of Composite Channels Using Genetic Algorithm
Publication: Journal of Irrigation and Drainage Engineering
Volume 130, Issue 4
Abstract
In the past, studies involving optimal design of composite channels have employed Horton’s equivalent roughness coefficient, which uses a lumped approach in assuming constant velocity across a composite channel cross section. In this paper, a new nonlinear optimization program (NLOP) is proposed based on a distributed approach that is equivalent to Lotter’s observations, which allows spatial variations in velocity across a composite channel cross section. The proposed NLOP, which consists of an objective function of minimizing total construction cost per unit length of a channel, is solved using genetic algorithm (GA). Several scenarios are evaluated, including no restrictions, restricted top width, and restricted channel side slopes, to account for certain site conditions. In addition, the proposed NLOP is modified to include constraints on maximum permissible velocities corresponding to different lining materials of the composite channel cross section, probably for the first time. The proposed methodology is applied to trapezoidal and triangular channel cross sections but can be easily extended to other shapes or compound channels. Optimal design graphs are presented to determine the channel dimensions of a composite trapezoidal channel cross section. The results obtained in this study indicate that cost savings up to 35% can be achieved for the unconstrained velocity case and up to 55% for the limiting velocity case when the proposed NLOP is solved using GA as compared with the existing NLOP solved using either the classical optimization solution technique or GA.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aly, A. H., and Peralta, R. C.(1999). “Optimal design of aquifer cleanup systems under uncertainty using a neural network and genetic algorithm.” Water Resour. Res., 35(8), 2523–2532.
Axelrod, R. (1987). “The evolution of strategies in the iterated prisoner’s dilemma.” Genetic algorithm and simulated annealing, L. Davis, ed., Pitman, London, 32–41.
Belegundu, A. D., and Chandrarupalta, T. R. (2002). Optimization concepts and applications in engineering, Pearson Education, Delhi, India.
Cieniawski, S. E., Eheart, J. W., and Ranjithan, S.(1995). “Using genetic algorithm to solve a multiobjective groundwater monitoring problem.” Water Resour. Res., 31(2), 399–409.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, New York.
Das, A.(2000). “Optimal channel cross section with composite roughness.” J. Irrig. Drain. Eng., 126(1), 68–72.
Davis, L., and Coombs, S. (1987). “Genetic algorithms and communication link speed design: theoretical considerations.” Genetic Algorithms and Its Applications; Proc., 2nd Int. Conf. on Genetic Algorithm, 252–256.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms, Wiley, West Sussex, U.K.
Duan, Q. Y., Gupta, V. K., and Sorooshian, S.(1993). “Shuffled complex evolution approach for effective and efficient global optimization.” J. Optim. Theory Appl., 76(3), 501–521.
Einstein, H. A., and Barbarossa, N. L.(1952). “River channel roughness.” Trans. ASCE., 117, 1121–1146.
Froehlich, D. C.(1994). “Width and depth-constrained best trapezoidal section.” J. Irrig. Drain. Eng., 120(4), 828–835.
Gentry, R. W., Camp, C. V., and Anderson, J. L.(2001). “Use of GA to determine areas of accretion to semi-confined aquifer.” J. Hydraul. Eng., 127(9), 738–746.
Gillies, A. M. (1985). “Machine learning procedures for generating image domain feature detectors.” PhD thesis, Univ. of Michigan, Ann Arbor, Mich.
Goldberg, D. E. (2000). Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Bangalore, India.
Goldberg, D. E., and Smith, R. E. (1987). “Nonstationary function optimization using genetic algorithms with dominance and diploidy.” Genetic Algorithm and Its Applications; Proc., 2nd Int. Conf. on Genetic Algorithm, 59–68.
Guo, C. Y., and Hughes, W. C.(1984). “Optimal channel cross section with freeboard.” J. Irrig. Drain. Eng., 110(3), 304–314.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, Mich.
Horton, R. E. (1933). “Separate roughness coefficients for channel bottom and sides.” Eng. News Record, 111(22), 652–653.
Jain, A., and Srinivasulu, S.(2004), “Development of effective and efficient rainfall-runoff models using integration of deterministic, real-coded genetic algorithms, and artificial neural network techniques.” Water Resour. Res.,40(4), W04302.
Jain, A., Srinivasulu, S., and Bhattacharjya, R. (2004), “Deterimination of an optimal unit pulse response function using real-coded genetic algorithm,” J. Hydrol. (in press).
Krishnamurthy, M., and Christensen, B. A.(1972). “Equivalent roughness for shallow channel.” J. Hydraul. Div., Am. Soc. Civ. Eng., 98(12), 2257–2263.
Liong, S., Chan, W. T., and Shreeram, J.(1995). “Peak-flow forecasting with genetic algorithm and SWMM.” J. Hydraul. Div., Am. Soc. Civ. Eng., 121(8), 613–617.
Loganathan, G. V.(1991). “Optimal design of parabolic canals.” J. Irrig. Drain. Eng., 117(5), 716–735.
Lotter, G. K.(1933). “Considerations on hydraulic design of channels with different roughness of walls.” J All Union Sci. Res. Inst. Hydraul. Engg., 9, 238–241.
Monadjemi, P.(1994). “General formulations of best hydraulic channel section.” J. Irrig. Drain. Eng., 120(1), 27–35.
Raghavan, V. V., and Agarwal, B. (1987). “Optimal determination of user-oriented clusters: an application for the reproduction plan.” Genetic Algorithm and Its Applications; Proc., 2nd Int. Conf. on Genetic Algorithm, 241–246.
Sannier, A. V., II, and Goodman, E. D. (1987). “Genetic learning procedures in distributed environments.” Genetic Algorithm and Its Applications; Proc., 2nd Int. Conf. on Genetic Algorithm, 162–169.
Schaffer, J. D. (1985). “Multiple objective optimization with vector evaluated genetic algorithms.” Proc., Int. Conf. on Genetic Algorithms and Their Applications, 93–100.
Swamee, P. K., Mishra, G. C., and Chahar, B. R.(2000). “Design of minimum seepage loss canal sections.” J. Irrig. Drain. Eng., 126(1), 28–32.
Trout, T. J.(1982). “Channel design to minimize lining material costs.” J. Irrig. Drain. Eng., 108(4), 242–249.
Wang, Q. J.(1991). “The genetic algorithm and its application to calibrating conceptual rainfall-runoff models.” Water Resour. Res., 27(9), 246–271.
Yen, B. C. (1991). “Hydraulic resistance in open channels.” Channel flow resistance: centennial of Manning’s formula, B. C. Yen, ed., Water Resources Publications, Highlands Ranch, Colo., 1–135.
Yen, B. C.(2002). “Open channel flow resistance.” J. Hydraul. Eng., 128(1), 20–39.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 130 • Issue 4 • August 2004
Pages: 286 - 295
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Nov 20, 2002
Accepted: Oct 30, 2003
Published online: Jul 15, 2004
Published in print: Aug 2004
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.