## 7 Simulation Result
### MathVista  
As observed in Tables 12 and 13, the baseline performance (B) analysis demonstrates that Phi-3.5 outperforms all models across all evaluation metrics, followed by Qwen-2, Llama 3.2, and Pixtral in descending order. This result indicates that Phi-3.5 and Qwen-2 exhibit strong mathematical problem-solving and reasoning capabilities, whereas Pixtral demonstrates relatively lower performance in this domain. ### MathVista  
As observed in Tables 12 and 13, the baseline performance (B) analysis demonstrates that Phi-3.5 outperforms all models across all evaluation metrics, followed by Qwen-2, Llama 3.2, and Pixtral in descending order. This result indicates that Phi-3.5 and Qwen-2 exhibit strong mathematical problem-solving and reasoning capabilities, whereas Pixtral demonstrates relatively lower performance in this domain. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Method** & **Phi** & **Llama** & **Pixtral** & **Qwen** & **Phi** & **Llama** & **Pixtral** & **Qwen** & **Phi** & **Llama** & **Pixtral** & **Qwen** \\ \hline
**Metric** & \multicolumn{4}{c}{**S-BERT**} & \multicolumn{4}{c}{**MoverScore**} & \multicolumn{4}{c}{**CIDEr**} \\ \hline C & 0.1237 & 0.2108 & 0.3808 & 0.2485 & 0.3015 & 0.3171 & 0.4543 & 0.3559 & 0.05 & 0.2047 & 0.8835 & 0.8294 \\ \hline C, I & 0.4443 & 0.1819 & 0.1468 & 0.0365 & 0.447 & 0.3066 & 0.2632 & 0.2594 & 0.1142 & 0.0907 & 0.0264 & 0.001 \\ \hline C, S & 0.239 & 0.215 & 0.3352 & 0.206 & 0.3612 & 0.3162 & 0.4447 & 0.3295 & 0.15 & 0.2287 & 0.6745 & 0.3097 \\ \hline C, T & 0.3186 & 0.2346 & 0.4625 & 0.3151 & 0.427 & 0.3405 & 0.5154 & 0.4132 & 0.5348 & 0.1306 & 0.8801 & 0.7532 \\ \hline S & 0.4319 & 0.2622 & **0.4763** & **0.3892** & 0.4754 & 0.3513 & **0.5241** & 0.461 & 0.365 & 0.2754 & **0.896** & **1.4677** \\ \hline T & 0.3746 & 0.332 & 0.419 & 0.3498 & 0.4432 & 0.3878 & 0.4963 & 0.4164 & 0.3462 & 0.5067 & 0.8329 & 1.0355 \\ \hline R(B) & 0.4872 & 0.2374 & 0.2973 & 0.0839 & 0.5334 & 0.3451 & 0.3288 & 0.2736 & **1.7644** & **0.6944** & 0.1093 & 0.4706 \\ \hline R(C) & 0.3955 & 0.1331 & 0.1069 & 0.0981 & 0.4041 & 0.2945 & 0.2572 & 0.2828 & 0.2745 & 0.1218 & 0.0208 & 0.2322 \\ \hline R(S) & 0.4441 & 0.1652 & 0.2371 & 0.1033 & 0.4698 & 0.3016 & 0.3162 & 0.2783 & 0.8802 & 0.2335 & 0.0746 & 0.3806 \\ \hline R(T) & 0.3804 & 0.1852 & 0.0181 & 0.1006 & 0.4019 & 0.3128 & 0.2395 & 0.2775 & 0 & 0.3781 & 0 & 0.4826 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Method** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **Qwen** & **Phi** & **Llama** & **Pixtral** & **Qwen** & **Phi** & **[PERSON]** & **[PERSON]** & **[PERSON]** \\ \hline
**Metric** & \multicolumn{4}{c}{**BLEU**} & \multicolumn{4}{c}{**ROUGE**} & \multicolumn{4}{c}{**METEOR**} \\ \hline B & 0.6612 & 0.6143 & 0.126 & 0.6863 & 0.1408 & 0.033 & 0.0096 & 0.0618 & 0.0967 & 0.0406 & 0.0149 & 0.0782 \\ \hline I & 0.0918 & 0.6821 & 1.2592 & 0.0869 & 0.2276 & 0.2252 & 0.0693 & 0.0072 & 0.1256 & 0.1255 & 0.0837 & 0.0129 \\ \hline I, S & 0.2226 & 1.0011 & 1.5175 & 0.038 & **0.2462** & **0.2606** & 0.0819 & 0.0043 & **0.1371** & **0.1507** & 0.1003 & 0.0161 \\ \hline I, T & 0.5203 & 0.9322 & 1.1025 & 0.0762 & 0.0724 & 0.2099 & 0.066 & 0.005 & 0.0513 & 0.1245 & 0.0798 & 0.015 \\ \hline C & 0.4019 & 0.9774 & **1.8382** & **1.3637** & 0.019 & 0.0478 & 0.1725 & 0.1446 & 0.0149 & 0.0605 & 0.1101 & 0.1201 \\ \hline C, I & 0.5048 & 0.9231 & 0.505 & 0.0695 & 0.0292 & 0.0471 & 0.0314 & 0.0059 & 0.0276 & 0.0521 & 0.0461 & 0.0141 \\ \hline C, S & 0.406 & 0.952 Upon applying the greedy prompt engineering strategy (Greedy PES), the optimal model \(m^{*}\) and optimal prompt engineering strategy \(p^{*}\) are identified as Qwen-2 with the IoT approach. However, it is also notable that Phi-3.5 with the ICL approach achieves the best performance in the S-BERT and MoverScore metrics.