## 7 Simulation Result
### ScienceQA  
As observed in Tables 10 and 11, the baseline performance (B) analysis demonstrates that Qwen-2 achieves the highest performance across all evaluation metrics. Following Qwen-2, Phi-3.5, Llama 3.2, and Pixtral exhibit strong performance in descending order.  
Upon applying the greedy prompt engineering strategy (Greedy PES), the optimal model \(m^{*}\) and optimal prompt engineering strategy \(p^{*}\) are identified as Phi-3.5 with the base RAG technique. Additionally, Phi-3.5 with the ICL and SSR combination also demonstrates strong performance, albeit with a marginal difference. This result highlights the importance of knowledge expansion and step-by-step reasoning techniques, such as base RAG, ICL, and SSR, in scientific question-answering tasks, where structured reasoning and contextual information retrieval are crucial for generating accurate responses.  
Furthermore, after applying Greedy PES, the combination of Qwen-2 with SSR follows Phi-3.5 in terms of performance. Notably, Qwen-2 also exhibited strong performance in the baseline results, reinforcing its effectiveness in scientific-domain-specific response generation.  
\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{3}{c}{**S-BERT**} & \multicolumn{3}{c}{**MoverScore**} & \multicolumn{3}{c}{**CIDEr**} & \\ \hline B & 0.236 & 0.0935 & 0.0282 & 0.241 & 0.3317 & 0.262 & 0.2267 & 0.3512 & 0.3639 & 0.042 & 0 & 1.0446 \\ \hline I & 0.4667 & **0.3941** & 0.3925 & 0.0448 & 0.5129 & **0.4659** & 0.3326 & 0.2682 & 0.9533 & 0.6496 & 0.1269 & 0.0019 \\ \hline I, S & **0.519** & 0.3646 & 0.394 & 0.0265 & **0.5482** & 0.4293 & 0.3299 & 0.2651 & 0.9407 & 0.3114 & 0.1203 & 0.0208 \\ \hline I, T & 0.4826 & 0.3847 & 0.383 & 0.0105 & 0.484 & 0.4605 & 0.3297 & 0.2539 & 0.5228 & 0.4409 & 0.1233 & 0.0008 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Performances of S-BERT, MoverScore, and CIDEr according to MLLM models and prompt engineering techniques on the ScienceQA dataset (The boldfaced numbers indicate the highest performance for each language model across different PES variants).  
\begin{table}
\begin{tabular}{c 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{3}{c}{**S-BERT**} & \multicolumn{3}{c}{**MoverScore**} & \multicolumn{3}{c}{**CIDEr**} & \\ \hline B & 0.236 & 0.0935 & 0.0282 & 0.241 & 0.3317 & 0.262 & 0.2267 & 0.3512 & 0.3639 & 0.042 & 0 & 1.0446 \\ \hline I & 0.4667 & **0.3941** & 0.3925 & 0.0448 & 0.5129 & **0.4659** & 0.3326 & 0.2682 & 0.9533 & 0.6496 & 0.1269 & 0.0019 \\ \hline I, S & **0.519** & 0.3646 & 0.394 & 0.0265 & **0.5482** & 0.4293 & 0.3299 & 0.2651 & 0.9407 & 0.3114 & 0.1203 & 0.0208 \\ \hline I, T & 0.4826 & 0.3847 & 0.383 & 0.0105 & 0.484 & 0.4605 & 0.3297 & 0.2539 & 0.5228 & 0.4409 & 0.1233 & 0.0008 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Performances of BLEU, ROUGE, and METEOR according to MLLM models and prompt engineering techniques on the ScienceQA dataset (The boldfaced numbers indicate the highest performance for each language model across different PES variants).