A cost model with several hydraulic constraints for optimizing in practice a trapezoidal cross section

Open channel structures are essential to infrastructure networks and expensive to manufacture. Optimizing the design of channel structures can reduce the total cost of a channel's length, including costs of lining, earthwork, and water lost through seepage and evaporation. The present research aims to present various optimization models towards the design of trapezoidal channel cross section. First, a general resistance equation was applied as a constraint. Next, a genetic algorithm (GA) was used to determine the optimal geometry of a trapezoidal channel section based on several parameters, i. e., depth, bottom width, and side slope. Eight different models were proposed and evaluated with no other constraint besides financial cost as well as with a normal depth, flow velocity, Froude number, top width, and by ignoring the cost of seepage. Numerical outcomes obtained by the GA are compared to previous studies in order to determine the most efficient model. Results from a single application indicate that the restriction of depth, velocity, and Froude number can increase the total cost, while restriction of the top width can decrease the cost of the construction. Also, the solution for various example problems incorporating different discharge values and bed slopes caused increase and decrease in cost, respectively.