## 4 Results
### Sensitivity Analysis  
The DSSAT + GA framework demonstrated exceptional resilience to market volatility across all tested scenarios (Table 10). Under nitrogen cost fluctuations (\(\pm\)20%), the optimized strategy maintained relative profit gains of 10.99-11.04% over conventional practices (\(T_{3}\)), with absolute profitability shifts closely tracking external price variations. For instance, a 20% nitrogen price hike reduced \(T_{3}\)'s baseline profit by 0.29%, while DSSAT + GA retained 11.04% superiority (11,028 vs. 9932 USD ha\({}^{-1}\)), highlighting its capacity to buffer input cost escalations. Similarly, cotton price swings (\(\pm\)15%) amplified the framework's advantage: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Treatment** & **Seed Cotton** & **Lint Cotton** & **Fiber Quality** \\  & **(kg ha\({}^{-1}\))** & **(kg ha\({}^{-1}\))** & **(Unitless)** \\ \hline DSSAT + GA & 9687.8 \(\pm\) 320 \({}^{\text{a}}\) & 5025.6 \(\pm\) 210 *** & 0.51 \(\pm\) 0.03 ** \\
2023-Tr-1 & 7076.08 \(\pm\) 285 \({}^{\text{b}}\) & 3155.55 \(\pm\) 180 \({}^{\text{c}}\) & 0.45 \(\pm\) 0.02 \\
2023-Tr-2 & 7215.99 \(\pm\) 310 \({}^{\text{b}}\) & 3323.46 \(\pm\) 195 \({}^{\text{bc}}\) & 0.46 \(\pm\) 0.02 \\
2023-Tr-3 & 8014.9 \(\pm\) 335 \({}^{\text{ab}}\) & 3658.35 \(\pm\) 205 \({}^{\text{b}}\) & 0.46 \(\pm\) 0.03 \\
2024-Tr-1 & 7848.2 \(\pm\) 305 \({}^{\text{ab}}\) & 3620.59 \(\pm\) 190 \({}^{\text{b}}\) & 0.46 \(\pm\) 0.02 \\
2024-Tr-2 & 9756.09 \(\pm\) 345 \({}^{\text{a}}\) & 4487.8 \(\pm\) 225 \({}^{\text{a}}\) & 0.46 \(\pm\) 0.03 \\
2024-Tr-3 & 9712.74 \(\pm\) 330 \({}^{\text{a}}\) & 4531.17 \(\pm\) 215 \({}^{\text{a}}\) & 0.47 \(\pm\) 0.02 \\ \hline \hline \end{tabular} Data presented as mean \(\pm\) 95% confidence interval (n = 3 replicates). *** \(p<\) 0.001, ** \(p<\) 0.01 vs. 2023-Tr-1 control (Tukey’s HSD test). Different superscript letters indicate significant differences (\(p<\) 0.05) across treatments.  
\end{table} 
Table 8: Comparison of cotton quality metrics between optimized and experimental treatments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **DSSAT + GA** & **Tr1** & **Tr2** & **Tr3** \\ \hline Urea application & 372.83 \(\pm\) 18.7 \({}^{\text{a}}\) & 450 \(\pm\) 22.5 \({}^{\text{b}}\) & 405 \(\pm\) 20.3 \({}^{\text{ab}}\) & 360 \(\pm\) 17.9 \({}^{\text{a}}\) \\ NUE & 13.48 \(\pm\) 0.62 ** & 8.05 \(\pm\) 0.45 & 11.08 \(\pm\) 0.53 \({}^{\text{a}}\) & 12.59 \(\pm\) 0.58 \\ \hline \hline \end{tabular} Values represent mean \(\pm\) 95% CI derived from bootstrap resampling (1000 iterations). ** \(p=\) 0.003, \({}^{\text{a}}\) = 0.023 vs. Tr1 control (ANOVA with Dumnett’s correction). Common letters denote non-significant differences in urea application (\(p>\) 0.05).  
\end{table} 
Table 9: Comparative analysis of nitrogen use efficiency (NUE) across fertilization strategies. during a 15% price surge, DSSAT + GA achieved 27.9% absolute profit growth (12,739 vs. 11,476 USD ha\({}^{-1}\)) while preserving an 11% relative margin. Crucially, under combined stress (N cost +20% + cotton price \(-\)15%), the algorithm limited profit erosion to \(-\)6.16% versus baseline, outperforming \(T_{3}\)'s \(-\)15.51% decline. This robustness stems from the fitness function's explicit optimization of yield-to-fertilization ratios, which inherently prioritizes nitrogen use efficiency (NUE = 13.48 kg/kg) over input maximization. By decoupling economic gains from absolute input-output balances, the ratio-driven fitness metric enforces thermodynamic efficiency principles in fertilization scheduling. This design minimizes exposure to price volatility, as evidenced by the stable 10.99-11.06% relative profit margins across scenarios. Unlike conventional approaches that optimize yield or cost in isolation, DSSAT + GA's balanced objective function embeds risk mitigation into its decision logic.