Bed sills are a kind of grade control structure built at the same level as the river bed to protect it against erosion and to reduce the longitudinal slope of the channel. The aim of the present research was to determine the optimal dimensions of the structure by devising a new methodology to minimize cost and maximize stability, based on the optimization model of the multi-objective non-dominated sorting genetic algorithm (NSGA-II). This is achieved by calculating the width, height and distance between bed sills with these stability and cost objectives in mind. The NSGA-II algorithm is applied to solve the problem, and a set of Pareto points is obtained. The results are verified by considering the bed sills of the River Madarsoo in Iran and the River Plima in Italy, and comparing the results with those obtained using the Branch-and-Bound (B-and-B) algorithm. The results indicate that the cost and stability could respectively be improved by up to 18 and 20% in the River Madarsoo, and up to 18 and 26% in the River Plima, if the NSGA-II algorithm is used.

河床是一种坡度控制结构，与河床建在同一水平面上，以保护河床免受侵蚀，减少河道的纵向坡度。本研究的目的是基于多目标非支配排序遗传算法 (NSGA-II) 的优化模型，通过设计一种新的方法来最小化成本和最大化稳定性来确定结构的最佳尺寸。这是通过在考虑这些稳定性和成本目标的情况下计算床门槛之间的宽度、高度和距离来实现的。应用NSGA-II算法求解该问题，得到一组Pareto点。通过考虑伊朗 Madarsoo 河和意大利的 Plima 河的床台验证了结果，并将结果与​​使用分支定界 (B-and-B) 算法获得的结果进行比较。结果表明，如果使用NSGA-II算法，Madarsoo河的成本和稳定性分别提高了18%和20%，Plima河的成本和稳定性分别提高了18%和26%。