## 3 Results and Discussion
Other algorithms predicted a total area close to 2010 Ha. However, slight differences were observed. Figure 11 displays the total revenue for the proposed cultivation pattern for the different algorithm. The price of the crops and the yield of each crop were considered based on the recommendations of the Department of Agriculture. To analyze the results, a decision-making system was needed. In fact, each algorithm performed differently in terms of nitrate concentration, cultivation pattern, total area, and revenue. Figure 8: Optimal nitrate concentration produced using the optimization model. Figure 9: Optimal cultivation pattern produced using the optimization model. Figure 12 displays vulnerability index of the nitrate concentration as well as total area. The weak performances of DE and IWO in terms of either the nitrate concentration or the total area can be observed clearly. Two tasks are essential in the FTOPSIS method: the rating of alternatives and the determination of the weights of importance. As presented in the previous section, three criteria were considered to prioritize the algorithms in the present study\" vulnerability indices for the nitrate concentration and total area and total revenue produced using the proposed cultivation pattern. The weights of importance for these criteria were considered as high, very high, and medium, respectively. The total area must be the same as the total available area, and it might be very important in terms of the social issues in the catchment. Hence, the total area was considered very high importance in the decision-making system. Moreover, the performance of the optimization model in minimizing the impacts of nitrate was considered high importance. The total revenue was considered medium importance because of being less important than the two other factors. The rating of the alternatives was carried out based on the computed vulnerability indices in Figure 12 and the assessed revenue in Figure 11 from very poor to very good, as proposed in the literature [8]. Figure 13 displays the final ranking produced with the FTOPSIS method. The highest CC demonstrates that the algorithm is the best one among all considered algorithms. The robustness of PSO and SCE was very close. Hence, these  
Figure 11: Total revenue for proposed cultivated pattern using different algorithms. Figure 10: Total cultivated area produced using the optimization model. algorithms were selected as the best algorithms to optimize cultivation patterns in the proposed method. We discussed the different aspects of the proposed method in this study. Previous studies optimized cropping patterns considering revenue or water consumption. However, environmental aspects should be highlighted for the future planning of farming. In fact, the destructive effect of agriculture on river ecosystems has been recognized in past decades. However, the previous methods for optimizing different aspects of agriculture are not able to take into account environmental degradation in their structure. Hence, developing new methods that are able to simulate environmental aspects in an integrated optimization system is necessary. This study developed an applicable method in this regard, in which the cultivation pattern was optimized considering the mitigation of the nitrate concentration in the aquatic habitats in the downstream river in a catchment. It opens a new window regarding the optimization process in agricultural engineering. One of the main reasons for achieving a successful solution for this problem was the application of the SWAT as a robust water quality model in the structure of the optimization model. Shifting from an optimization process to a simulation-optimization process is another necessity to handle environmental challenges in future studies. One of the key advantages of the proposed method is its low computational complexity, which makes the application of the method easier in actual projects. Computational complexity is defined as the time and memory required for the optimization algorithm.