## 5 Simulation Experiments
### Rationality of Using a GA to Identify Skyline Solutions
This demonstrates that a close relationship exists between the irrigated area and the agricultural economic benefits of vegetables. Finally, Figure 6d,g,i,j show that the irrigated areas of the three types of crops do not have a clear impact on the compensation for stopping irrigation. This is because, with such a small water supply, almost all of the farms must stop farming, resulting in little differences in the compensation. Next, we discuss the case of 25-50% water supply rates. From Figure 7a, we can see that the irrigated areas of rice and sugar cane do not significantly influence each other. However, Figure 7b,e show that any decrease in the irrigated areas of rice or sugar cane greatly increases the irrigated area of vegetables. Figure 7c,f,h similarly indicate a close relationship between the irrigated area and the agricultural economic benefits. However, in Figure 7d, the amount of compensation for stopping irrigation for rice, which was the highest among the three crops, dropped by approximately 16%; the proportion not requiring compensation unexpectedly increased. This means that with water supply rates of 25-50%, the strategy of reducing the irrigated area of the thirsty rice crop exerts varying degrees of positive influence on the irrigated areas of sugar cane and vegetables, agricultural economic benefits, and compensation for stopping irrigation. Lastly, there is the case of 50-75% water supply rates. Based on Figure 8, we arrive at the same conclusions that we did for Figure 7: reducing the irrigated areas of rice and sugar cane increases the irrigated area and agricultural economic performance of vegetables. These examples confirm that the skyline query concept introduced in this paper can find solutions when the objective values are conflicting (e.g., irrigated area and economic considerations), thereby overcoming the problems encountered by traditional top-\(k\) queries. They also show that the final result found by the proposed algorithm aligns with the intuitive choice. This verifies that the skyline query is often more suitable than the traditional top-\(k\) query. Figure 6: Comparisons of temporary skyline results obtained using the GA from different numbers of generations with water supply rates of 0–25%: (**a**) rice and sugar cane, (**b**) rice and vegetables, (**c**) rice and economic benefits, (**d**) rice and compensation, (**e**) sugar cane and vegetables, (**f**) sugar cane and economic benefits, (**g**) sugar cane and compensation, (**h**) vegetables and economic benefits, (**i**) vegetables and compensation, and (**j**) economic benefits and compensation. Figure 7: Comparisons of temporary skyline results obtained using the GA from different numbers of generations with water supply rates of 25–50%: (**a**) rice and sugar cane, (**b**) rice and vegetables, (**c**) rice and economic benefits, (**d**) rice and compensation, (**e**) sugar cane and vegetables, (**f**) sugar cane and economic benefits, (**g**) sugar cane and compensation, (**h**) vegetables and economic benefits, (**i**) vegetables and compensation, and (**j**) economic benefits and compensation. Figure 8: Comparisons of temporary skyline results obtained using GA from different numbers of generations with water supply rates of 50–75%: (**a**) rice and sugar cane, (**b**) rice and vegetables, (**c**) rice and economic benefits, (**d**) rice and compensation, (**e**) sugar cane and vegetables, (**f**) sugar cane and economic benefits, (**g**) sugar cane and compensation, (**h**) vegetables and economic benefits, (**i**) vegetables and compensation, and (**j**) economic benefits and compensation. We compiled statistics of the branches selected in all of the skyline solutions to understand the degree of importance of different branches in the irrigated region. Figure 9 displays the number of the branches and the number of times they are chosen under different water supply rates.