Finding an optimal design for hydraulic structures and devices, which work together in irrigation networks, can be formulated as a multi-objective optimization problem. In this paper, a novel framework is proposed for simultaneous optimization of an open channel section and a labyrinth weir geometry. A recently proposed optimizer called Multi-Objective Multi-Verse Optimization (MOMVO) algorithm is employed and its results are compared with Pareto Envelope-based Selection Algorithm II (PESA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) using five metrics, including spacing (SP), Maximum Spread (MS), Non-uniformity of Pareto Front (NPF), Mean Ideal Distance (MID), and Coverage Measure (CM). The first objective function is defined to minimize the construction costs per unit length of the open channel, and the second one is to minimize total concrete volume of the labyrinth weir. The results showed significant differences between MOMVO Pareto optimal solutions and the other two algorithms. The least values of SP, NPF, and MID metrics were provided by MOMVO, which meant its solutions had better conditions regarding uniformity and the closeness to the ideal point. To optimize irrigation network as a system, penalty functions were applied to satisfy hydraulic conditions (flow velocity, Froude number, and nappe interference). Results showed that if the proposed model had been employed in Isfahan Irrigation Networks (IINs) design, it would have reduced the construction costs of open channel and labyrinth weir approximately 11% and 74%, respectively. It can be reported that the most cost-effective design has the least channel wetted perimeter, channel cross-section top width, cross-sectional area, and labyrinth apex length; and the highest channel depth, and weir sidewall angles.

寻找在灌溉网络中协同工作的水力结构和设备的最佳设计，可以表述为一个多目标优化问题。在本文中，提出了一种新颖的框架，用于同时优化明渠截面和迷宫堰几何形状。采用了最近提出的称为多目标多节优化 (MOMVO) 算法的优化器，并将其结果与基于帕累托包络的选择算法 II (PESA-II) 和非支配排序遗传算法 II (NSGA-II) 进行比较，使用五个度量，包括间距 (SP)、最大传播 (MS)、帕累托前沿的非均匀性 (NPF)、平均理想距离 (MID) 和覆盖度量 (CM)。定义第一个目标函数以最小化明渠单位长度的建设成本，二是尽量减少迷宫堰的总混凝土体积。结果表明，MOMVO Pareto 最优解与其他两种算法存在显着差异。MOMVO 提供了 SP、NPF 和 MID 度量的最小值，这意味着其解决方案在均匀性和与理想点的接近度方面具有更好的条件。为了优化灌溉网络作为一个系统，应用惩罚函数来满足水力条件（流速、弗劳德数和推覆干扰）。结果表明，如果将所提出的模型用于伊斯法罕灌溉网络 (IIN) 的设计，它将分别降低明渠和迷宫堰的建设成本约 11% 和 74%。可以报​​告，最具成本效益的设计具有最少的通道润湿周长，通道横截面顶部宽度、横截面积和迷宫顶点长度；以及最高的通道深度和堰侧壁角度。