Document Type : Research Paper


1 Department of Civil Engineering (Hydraulic Structures Engineering), Faculty of Engineering, Urmia University, Urmia, Iran

2 Department of Civil Engineering, Faculty of Engineering, Hydraulic Structure and River Mechanics Group, Urmia University, Urmia, Iran.


This paper applies an evolutionary algorithm, the particle swarm optimization (PSO), to design the optimum open channel section. Depth, channel side slope and bottom width are considered as the variables for rectangular, triangular and trapezoidal channels, respectively. The objective function is minimizing the construction cost of the channel section. MATLAB software is used for programming and doing the optimization process. Manning’s uniform flow formula has been used as a constraint for the optimization model. The cost function is included the cost of earthwork, the increment in the cost of earthwork with the depth below the ground surface and the cost of lining. Simple functions of unit cost terms have been used to express the optimum values of section variables. The optimum section variables are obtained for the case of minimum area or minimum wetted perimeter problems. The results of this study showed that the PSO is a robust algorithm to compute the optimum section variables in open channel design.


Main Subjects

Bhattacharjya, R. K., & Satish, M. G. (2007). Optimal design of a stable trapezoidal channel section using hybrid optimization techniques. Journal of irrigation and drainage engineering, 133(4), 323-329.
Bhattacharjya, R. K., (2012). Optimal design of open channel section considering freeboard. ISH Journal of Hydraulic Engineering, 141-151, Published online.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, New York.
Dong, L., Yuxiang, H., Qiang, F., Imran, K. M., Song, C., & Yinmao, Z. (2016). Optimizing channel cross section in irrigation area using improved cat swarm optimization algorithm. International Journal of Agricultural and Biological Engineering, 9(5), 76-82.
Easa, S. M., Vatankhah, A. R., & Halim, A. A. E. (2011). A simplified direct method for finding optimal stable trapezoidal channels. International journal of river basin management, 9(2), 85-92.
Froehlich, D. C. (1994). Width and depth-constrained best trapezoidal section. Journal of Irrigation and Drainage Engineering, 120(4), 828-835.
Guo, C. Y., & Hughes, W. C. (1984). Optimal channel cross section with freeboard. Journal of Irrigation and Drainage Engineering, 110(3), 304-314.
Kaveh, A., Talatahari,  S., & Azar, B. F., (2011). Optimum design of composite open channels using charged system search algorithm, Journal of Science and Technology. Transactions of Civil Engineering, 36(1), 67-77.
Kentli, A., & Mercan, O. (2014). Application of different algorithms to optimal design of canal sections. Journal of applied research and technology, 12(4), 762-768.
Kentli, A., & Mercan, O. (2014). Application of different algorithms to optimal design of canal sections. Journal of applied research and technology, 12(4), 762-768.
Loganathan, G. V. (1991). Optimal design of parabolic canals. Journal of Irrigation and Drainage Engineering, 117(5), 716-735.
Monadjemi, P. (1994). General formulation of best hydraulic channel section. Journal of Irrigation and Drainage Engineering, 120(1), 27-35.
Niazkar, M., & Afzali, S. H. (2015). Optimum design of lined channel sections. Water Resources Management, 29(6), 1921-1932.
Ruben, E. P., Kamran, B., (2007). Particle swarm optimization in structural design. NTECH Open Access Publisher.
Shi, Y., & Eberhart, R A., (1998). Modified particle swarm optimizer. In: IEEE international conference on evolutionary computation. IEEE Press, Piscataway, NJ, 1998, 69–73.
Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, 2(3), 221-248.
Swamee, P. K. (1995). Optimal irrigation canal sections. Journal of Irrigation and Drainage Engineering, 121(6), 467-469.
Swamee, P. K., Mishra, G. C., & Chahar, B. R. (2000). Minimum cost design of lined canal sections. Water Resources Management, 14(1), 1-12.
Tofiq, F. A., & Guven, A. (2015). Optimal design of trapezoidal lined channel with least cost: Semi-theoretical approach powered by genetic programming. Water SA, 41(4), 483-489.
Turan, M., & Yurdusev, M. (2011). Optimization of open canal cross sections by differential evolution algorithm. Mathematical and Computational Applications, 16(1), 77-86.
Zhang, J., Wu, Z., Cheng, C. T., & Zhang, S. Q. (2011). Improved particle swarm optimization algorithm for multi-reservoir system operation. Water Science and Engineering, 4(1), 61-73.
Zhang, Y., Wang, S., & Ji, G. (2015). A comprehensive survey on particle swarm optimization algorithm and its applications. Mathematical Problems in Engineering, 2015.