## 7 Simulation Result
### CVBench  
As observed in Tables 14 and 15, the base performance (B) indicates that Qwen-2 demonstrates the highest overall performance, with Phi-3.5 also exhibiting comparable proficiency in understanding multimodal data. Specifically, Phi-3.5 achieves the highest scores in BLEU, ROUGE, and METEOR, while Qwen-2 records the best performance in S-BERT, MoverScore, and CIDEr. This suggests that responses generated by Qwen-2 are semantically more appropriate and natural compared to other models.  
When applying the Greedy PES, the optimal model \(m^{*}\) and prompt engineering strategy \(p^{*}\) are determined to be Phi-3.5 combined with the ICL technique. Furthermore, since ICL consistently emerges as the most effective prompt engineering method across various evaluation metrics for other MLLM models, this indicates that ICL is particularly advantageous for datasets such as CVBench, which require a fundamental yet comprehensive understanding of both text and image-based inputs.  
\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 B & 0.3874 & 0.1657 & 0.104 & 0.328 & 0.4066 & 0.2532 & 0.2208 & 0.3565 & 0.2583 & 0.0152 & 0 & 0.0546 \\ \hline I & **0.6916** & 0.5227 & 0.3874 & 0.1606 & **0.7134** & 0.4957 & 0.3767 & 0.2534 & 0.5 & **0.3297** & 0.0531 & 0 \\ \hline I, S & 0.6562 & 0.4991 & 0.39 & 0.1635 & 0.6246 & 0.4808 & 0.3775 & 0.2589 & **0.55** & 0.178 & 0.0653 & 0 \\ \hline I, T & 0.6069 & **0.5719** & 0.3865 & 0.1645 & 0.5291 & **0.5319** & 0.3798 & 0.2541 & 0.1389 & 0.2783 & 0.0426 & 0 \\ \hline C & 0.1318 & 0.2342 & 0.3457 & 0.362 & 0.2583 & 0.2872 & 0.3496 & 0.3959 & 0.0221 & 0.0325 & 0.1637 & 0.2179 \\ \hline C, I & 0.3895 & 0.2328 & 0.1445 & 0.1588 & 0.3761 & 0.2901 & 0.2527 & 0.2413 & 0.0227 & 0.0061 & 0.0001 & 0 \\ \hline C, S & 0.1711 & 0.1902 & 0.3319 & 0.3551 & 0.2848 & 0.2594 & 0.3428 & 0.4134 & 0.0221 & 0.0259 & 0.0869 & 0.2587 \\ \hline C, T & 0.3783 & 0.3004 & 0.4875 & 0.5079 & 0.4243 & 0.3117 & 0.5236 & 0.5509 & 0.1047 & 0.1104 & 0.3688 & 0.4693 \\ \hline S & 0.5498 & 0.3405 & **0.5052** & **0.5993** & 0.5191 & 0.3492 & 0.5388 & **0.6311** & 0.2349 & 0.121 & 0.3349 & 0.6106 \\ \hline T & 0.518 & 0.4316 & 0.4997 & 0.5751 & 0.4652 & 0.3944 & **0.5534** & 0.6072 & 0.2349 & 0.1765 & **0.3969** & **0.8036** \\ \hline R(B) & 0.6665 & 0.3318 & 0.3333 & 0.1889 & 0.6528 & 0.3427 & 0.314 & 0.2617 & 0.5 & 0.1967 & 0.0455 & 0 \\ \hline R(C) & 0.3092 & 0.1739 & 0.1603 & 0.2068 & 0.3408 & 0.2524 & 0.2464 & 0.2547 & 0.0227 & 0.0248 & 0.0038 & 0 \\ \hline R(S) & 0.2421 & 0.2087 & 0.2273 & 0.2153 & 0.3038 & 0.274 & 0.2718 & 0.2692 & 0.0728 & 0.0146 & 0.0045 & 0.0008 \\ \hline R(T) & 0.3814 & 0.1972 & 0.1016 & 0.2023 & 0.3855 & 0.2719 & 0.2317 & 0.2608 & 0.1189 & 0.0764 & 0 & 0.0182 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Performances of S-BERT, MoverScore, and CIDEr according to MLLM models and prompt engineering techniques on the MathVista dataset (The boldfaced numbers indicate the highest performance for each language model across different PES variants).