## 3 Results
### Independent Validation  
The publicly available experimental data previously generated from the same location with same experimental design [54; 55; 56] were used to validate the GDM-DEA model. The yield data of three independent experiments were processed by min-max normalization. Lingo 18.0 was used to solve the CCR and GDM-DEA efficiency values of each cultivation measure in the three independent experiments. It was found that groups 12, 15, 19, and 35 met the criteria of CCR and GDM-DEA effectiveness. Among those, group 35 had the highest yield (Table S7 and Figure S1). The published results of the Anshun Pan experiment used the average yield of 36 groups (10,527.15 kg/ha) as the high-yield standard [54; 55]. Obviously, group 35 was the best cultivation measure, which met the standards of high performance and high yield. In the Anshun Pan experiments, the cultivation measures of groups 25-36 were the same. Except for groups 25 and 35, the efficiency value and GDM-DEA efficiency value of the other 10 groups were close to 1, and the yield was much higher than the standard high-yield value. The explanation for the differences between the Anshun Pan and JLASTU experiment in performance and yield may be that the effects of previously grown crops, environmental effects and/or the edge row could affect the experimental data. Groups 6, 12, 14, 16, 20, and 24 were CCR-effective only, and groups 15 and 35 were both CCR-effective and GDM-DEA-effective. Taking CCR and GDM-DEA effectiveness as the standard, the yield was reported as follows: 35 (13,502.1 kg/ha) > 15 (12,471.6 kg/ha). The experimental sites and design of the Anshun Tang experiment and the Anshun Pan experiment were the same, so the same cultivation measure in the two independent experiments had a similar performance and yield. This published research took 12,000 kg/ha as the high-yield standard of maize in the Anshun Tang experiment [54; 55]. Considering GDM-DEA efficiency and the yield, group 35 was the best cultivation measure in our analysis. The 12 th, 16 th, 18 th, and 20 th cultivation measures were all CCR-effective, while the CCR efficiency value of the 14 th, 22 nd, and 24 th cultivation measures were both CCR-effective and GDM-DEA-effective. The yield of the shared three groups was ranked as 22 (14,222.85 kg/ha) > 14 (13,147.05 kg/ha) > 24 (12,652.35 kg/ha). In contrast to the first two independent experiments, in the Chifeng Zheng experiment, we used DPS software to determine that the high-yield standard was 12,134.98 kg/ha. Groups 14, 22, and 24 all met the high-yield standard. The amount of nitrogen, phosphorus, and potassium fertilizer applied in group 22 was at level 0, and the planting density was level\(-\)2. The input of group 22 was lower than the other two groups, and the yield was larger than the other two groups, so it was the best cultivation measure. Here, the optimal cultivation measures from the GDM-DEA model and other statistical methods were compared (Table 4). The Anshun Pan experiment and Anshun Tang experiment used the high-yield frequency analysis method to obtain the optimal combination scheme of agronomic measures with a higher yield than the average yield. This scheme only determined the range of planting density, nitrogen application rate, potassium application rate, and phosphorus application rate, but did not give the best cultivation measure. In the Chifeng Zheng experiment, DPS was used to process the data and regression analysis results. Finally, the optimal solution of the quadratic regression model was obtained, and the highest yield cultivation measures were obtained at the theoretical level. In the Anshun Pan experiment and Anshun Tang experiment, the optimal cultivation measures selected by the GDM-DEA model Concorded with the range of optimal cultivation measures given in the experiment. The Chifeng Zheng experiment demonstrated the cultivation measures with the maximum theoretical yield.