## 5 Simulation Experiments
### Influence of Objective Ranking on Skyline Solutions
This underlines the unevenness in crop distribution upstream and downstream. Furthermore, all six solutions tended to select the downstream branches for irrigation. In our second experiment, we sought to verify the relationship between economic benefits and vegetable yield when processing solutions with the same score. Thus, we raised the priority of economic benefits and vegetable yield; set lower objective yields for rice, sugar cane, and vegetables; and reduced the amount of compensation not needed. Finally, we set the limit of economic benefits close to the maximum so as to ensure that the ranking algorithm would encounter solutions with the same score. Table 5 displays a portion of the ranked results. As can be seen, the conditions of the top three solutions with the highest scores were all higher than the objective values. This means that the objective yield limits were too low, causing many of the skyline solutions to exceed the objective yield. We can, therefore, see that the three solutions have the same total priority scores. To rank these solutions, the algorithm used the original data to re-calculate the ranking scores to successfully separate them. This verifies that the proposed method can also rank solutions with the same score. Next, we relaxed only the limits of economic benefits, so crops whose yield increases by a greater degree are considered to be more strongly correlated with economic benefits. Under these conditions, the objective yield limits with regard to vegetables varied the most widely, thereby demonstrating that economic benefits are indeed associated with vegetable yield. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Solution** & **Rice Yield** & **Sugar Cane Yield** & **Vegetable Yield** & **Economic Benefits** & **Compensation for Stopping** & **Total Score without Expected Scores** & **Total Score with Expected Scores** \\ \hline
1 & 56.244 & 37.091 & 52.322 & 50.816 & 45.567 & 391.619 & 375.914 \\
2 & 53.782 & 39.783 & 49.234 & 48.784 & 45.703 & 384.633 & 373.912 \\
3 & 55.026 & 37.911 & 51.447 & 50.13 & 45.474 & 387.951 & 373.9 \\.................................... 105 & 48.663 & 37.333 & 73.72 & 62.233 & 46.833 & 403.441 & 353.655 \\......... &...... &...... &...... &... &... &... \\
169 & 65.529 & 48.903 & 6.017 & 26.425 & 47.067 & 373.902 & 335.442 \\
170 & 65.573 &  
We once again converted the first three solutions into branch maps to observe their selection strategies. The results are presented in Figure 12. The skyline solutions prioritizing economic benefits selected a large portion of the upstream branches for irrigation, and the upstream branches mainly serve vegetable production. In other words, economic benefits are indeed related to vegetable yields. In the third experiment, we sought to confirm the uneven distribution of the crops and verify whether the proposed algorithm can generate a reasonable ranking when crop yield limits exceed the maximum or fall below the minimum. We, thus, increased the priority of sugar cane yield and set lower objectives for rice yield, vegetable yield, economic benefits, and the amount of compensation not needed. The limit of sugar cane yield was set over the  
Figure 11: Numbers of times branches are selected in top-three and bottom-three skyline solutions using the first combination. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Solution** & **Rice Yield** & **Sugar Cane Yield** & **Vegetable** & **Economic** & **Compensation** & **Total Score** & **Total Score** \\
**Ranking** & **Rice Yield** & **Sugar Cane Yield** & **Vegetable** & **Economic** & **for Stopping** & **Expected** & **with Expected** \\  & & & & & **Irigation** & **Objective** & **Objective** \\  & & & & & **Scores** & **Scores** \\ \hline
1 & 47.907 & 35.105 & 77.396 & 63.961 & 46.032 & 492.262 & 360 \\
2 & 48.663 & 37.333 & 73.72 & 62.233 & 46.833 & 488.744 & 360 \\
3 & 44.161 & 35.397 & 74.077 & 61.115 & 44.472 & 470.085 & 360 \\... &... &... &... &... &... &... &... \\ \hline \hline \end{tabular}
\end{table}