# Comparison of Various Models for Optimal Water Distribution in Canal Systems
## 1 Introduction  
China's severe water shortage has significantly impacted the country's food security [1]. [PERSON] et al. forecast that, in the future, half of China's land area will experience serious water stress, affecting over 600 million people [2]. According to the Ministry of Water Resources' \"2021 Water Resources Bulletin\", agricultural water consumption accounts for 61.6% of total water usage, totaling 364.43 billion m\({}^{3}\)[3]. Furthermore, China's agricultural water shortage is projected to reach 90 billion m\({}^{3}\) in the coming years [4]. Therefore, improving the efficiency of agricultural water use through scientific management is crucial in alleviating water resource challenges [5, 6]. The optimized canal water distribution model ensures that water flow rates and distribution times are appropriately allocated to meet the water requirements of crops during their growth periods [7, 8]. However, the overflow capacity of the upper-level canal is insufficient to support simultaneous irrigation across all sections,necessitating the use of rotational irrigation. There are two primary types of rotational irrigation groupings: \"continuous irrigation within groups and rotational irrigation between groups\", and \"rotational irrigation within groups and continuous irrigation between groups\". [PERSON] and [PERSON] were the first to study the rotational irrigation grouping of irrigation canals using 0-1 models. They pioneered the transformation of the grouping problem into a mathematical formulation. By introducing the concept of flow pipes into irrigation scheduling, they proposed that water supply canals be composed of multiple hypothetical flow pipes, each with an equal flow rate. Instead of minimizing the number of pipes running simultaneously, their model focused on minimizing the total number of pipes in operation [9]. [PERSON] et al. identified and addressed this limitation by incorporating functions into the model. Since then, the 0-1 model for rotational irrigation grouping has been widely adopted [10]. [PERSON] and [PERSON] approached the irrigation scheduling problem by introducing a time module and a genetic algorithm, and demonstrated how to express the time-block model using this algorithm [11]. [PERSON] et al. developed a canal scheduling model aimed at reducing fluctuations in the upstream canal flow rate and minimizing leakage losses in the canals [12]. [PERSON] et al. developed a water distribution model with an unknown flow rate, taking various factors into account, and determined the optimal irrigation grouping [13]. [PERSON] et al. introduced a new method for canal network irrigation scheduling, and quantified the mutual influence among conflicting objectives [14]. The aforementioned water distribution models divide the canal into several distinct groups. In contrast, another model achieves the irrigation objective through the rational distribution of flow rates and times, without incorporating the concept of grouping. In this model, the irrigation time is generated randomly. [PERSON] and [PERSON] optimized canal system scheduling with a single-objective nonlinear model using a genetic algorithm [15]. [PERSON] et al. addressed the limitations of previous canal scheduling models by incorporating different irrigation indices, resulting in an improved model that more effectively achieved the water distribution target [16]. [PERSON] and [PERSON] et al. proposed an integrated stepwise approach that considered both farms and canals to solve the water allocation problem in irrigation systems [17]. [PERSON] et al. applied the MILP algorithm to reduce the start-up time of the model, bringing it closer to the planned irrigation time, while also aiming to minimize water loss and labor. [PERSON] also explored methods to optimize water allocation within a limited dispatch range, developing an approach that ensured different users were treated fairly [18]. [PERSON] et al.