## 5 Simulation Experiments
### Rationality of Using a GA to Identify Skyline Solutions
The black numbers are the numbers of the branches, and the numbers in other colors represent the number of times they appear in the skyline results under different water supply rates. For instance, Branch 2 in Figure 10 was chosen 9, 95, and 484 times under the water supply rates of 0-25%, 25-50%, and 50-75%, respectively. From Table 2, we can see that there were 10, 171, and 484 skyline solutions under these conditions; this means that Branch 2, being a crucial branch, was almost always chosen in the shown experiments. Under the 50-75% water supply rates, the algorithm chose to maintain irrigation to the three main branches (Branches 1, 22, and 38) and gradually reduce irrigation to the branches so as to ensure the most efficient allocation of water resources. Interestingly, over half of the solutions chosen by the target approach do not prioritize irrigation to the wider upstream branches but rather focus on the downstream branches as the main subjects of irrigation (Branches 23, 26, 27, 30, 39, 40, 41, 42, 45, 46, etc.). This contrasts strongly with traditional approaches to prioritize upstream over downstream to reduce water resource divergence. We did not input water resource divergence data, nor did we list it as an objective, so naturally, the algorithm did not take this into consideration. The result underlines the efficacy of the decision support provided by the algorithm, which objectively identified the most important branches and directed resources accordingly. Under the 25-50% water supply rates, the prioritization of downstream over upstream was even more apparent: except for the three main branches (Branches 1, 22, and 38), irrigation to almost all of the most upstream branches was stopped, a portion of the midstream branches were kept, and nine of the downstream branches (Branches 39, 40, 42, 46, 47, 48, 49, 50, and 52) were included in most of the solutions. Under the 0-25% water supply rates, the target algorithm suggested only supplying water to one main branch (Branch 1) and its branches downstream. Under these very low supply rates, irrigation to most of the downstream branches was not possible; thus, most of the objectives were not met. Under these conditions, the target algorithm recommended reserving most of the water resources for the first main branch to achieve the objectives as much as possible. Based on these experiment results, we observed three phenomena: (1) the traditional approach of prioritizing irrigation based on branch width and upstream/downstream position made it almost impossible to obtain optimal solutions, (2) the imbalance of the selected irrigation branches in the skyline solutions shows that the cultivation areas of the three crop types upstream and downstream are uneven, and (3) factors such as upstream/downstream position and crop type increased the risk of no irrigation in the event of water shortages. Figure 10: Results of the skyline and top-k queries for three water supply rates: (**a**) 0–25%, (**b**) 25–50%, and (**c**) 50–75%. Figure 9: Number of times branches are selected in skyline solutions under different water supply rates.