## 3 Dataset and Calculation of Objective Values
### Calculation of Objective Values  
We consider five objective values: rice yield, sugar cane yield, vegetable yield, overall agricultural economic benefits, and compensation for stopping irrigation. For convenience  
Figure 1: Irrigation diagrams of the Jhuoshuei River region in the Chiayi-Tainan Plain of Taiwan.  
in interpretation, we converted the objective values into percentages and considered the proportion of farmers not requiring compensation to make all objective values follow the larger-the-better criterion. We use these five relatively intuitive target values to create a simple model for the first stage, as our focus lies on the development of the second stage of decision support. The proposed algorithm accepts the output of the first stage as input, so more sophisticated models could be substituted for the first stage without any change to the performance of our filtering approach. The five selected objective values are calculated as follows.  
1. Total cultivation area of each crop is calculated as follows: \[O_{i}=\sum_{j=1}^{M}\left(A_{i}^{j}\times C^{j}\right),\] (1) where \(i\) and \(j\) indicate crop type and serial number of irrigated areas, respectively; \(O_{i}\) denotes the total cultivation area of crop \(i\) in the current solution; \(M\) represents the total number of irrigated areas; \(A_{i}\) is the cultivation area of crop \(i\) along irrigated area \(j\); and \(C^{j}\) indicates whether irrigated area \(j\) is selected in the current solution, equaling 1 if it is selected and 0 if it is not.
2. Total yield of each crop is \(P_{i}=O_{i}\times U_{i}\), where \(i\) indicates the crop type; \(P_{i}\) is the total yield of crop \(i\) in the current solution; \(O_{i}\) denotes the total cultivation area of crop \(i\) in the current solution, and \(U_{i}\) is the average yield of crop \(i\) per unit of area based on agronomic standards.
3. Total output value of each crop is \(V_{i}=P_{i}\times W_{i}\), where \(i\) indicates the crop type; \(V_{i}\) is the total output value of crop \(i\) in the current solution; \(P_{i}\) is the total yield of crop \(i\) in the current solution; and \(W_{i}\) denotes the average output value of crop \(i\) per unit of weight recorded in agronomic standards.  
While directly using agronomic standards for the second and third objectives may not be the most accurate approach, it is beyond the scope of this study. If the readers need accurate, objective values, other approaches may be applied to predict relevant values without any adverse impact on the proposed algorithm.  
1. Total compensation for stopping irrigation is calculated as follows: \[T=\sum_{i=1}^{N}\left(\left(\sum_{j=1}^{M}A_{i}^{j}\right)-O_{i}\right)\times Q _{i},\] (2) where \(i\) and \(j\) indicate crop type and a serial number of irrigated area, respectively; \(T\) denotes the total compensation for stopping irrigation under the current solution; \(N\) represents the number of crop types; \(M\) represents the total number of irrigated areas; \(A_{i}^{j}\) is the cultivation area of crop \(i\) along irrigated area \(j\); \(O_{i}\) denotes the total cultivation area of crop \(i\) in the current solution; and \(Q_{i}\) is the compensation for stopping irrigation for crop \(i\) per unit of area.
2. Total demand of irrigation water resources is calculated as follows: \[S=\left(\sum_{i=1}^{N}O_{i}\times R_{i}\right)+\sum_{j=1}^{M}D^{j},\] (3) where \(i\) and \(j\) indicate crop type and serial number of irrigated area, respectively; \(S\) denotes the total demand of water resources under the current solution; \(N\) represents the number of crop types; \(M\) represents the total number of irrigated areas; \(O_{i}\) denotes the total cultivation area of crop \(i\) in the current solution; \(R_{i}\) is the demand of water resources of crop \(i\) per unit of area; and \(D^{j}\) is the amount of water resources wasted by each area.