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.