## 7 Simulation Result
### Performance Analysis and Discussion
In contrast, for math-related datasets, ICL, SSR, and ToT are the primary techniques, while for science-related datasets, RAG and SSR are more frequently employed. The emphasis on SSR in the math and science domains compared to the general domain is notable, as solving mathematical and scientific problems inherently demands step-by-step reasoning, which is crucial for handling complex problem-solving tasks. Additionally, while Qwen-2 consistently achieves the highest performance across most cases when no PES is applied, it is noteworthy that Phi-3.5 also emerges as a strong contender when Greedy PES is applied. More significantly, despite being the smallest model, Phi-3.5 exhibits substantial performance improvement when PES is applied, demonstrating the effectiveness of PE in enhancing MLLM performance. These findings suggest that Greedy PES has strong potential for MLLM model optimization, highlighting its applicability for further expansion and future advancements in multimodal AI research. A more detailed analysis of each dataset is now presented to examine the optimal MLLM and PES combinations for different multimodal tasks. The MSCOCO dataset is designed for image captioning, encompassing diverse scenes and objects. The optimal MLLM-PES combinations identified through Greedy PES are Phi-3.5 with RAG and Qwen-2 with ToT. The results indicate that Qwen-2 exhibits strong image captioning capabilities even without additional prompt engineering, suggesting that it is inherently well trained for general multimodal image-text alignment. In contrast, Phi-3.5, when integrated with RAG, demonstrates a more effective retrieval-based approach, allowing the model to extract relevant information from the image and generate high-quality captions. Flickr30k focuses on understanding relationships between people and objects within an image to generate relevant captions. The optimal MLLM-PES combination is Qwen-2 with ToT, reinforcing the finding that Qwen-2 is a strong candidate for text generation in general multimodal datasets. The results further suggest that the ToT-based approach facilitates enhanced logical reasoning, allowing the model to establish deeper semantic connections between elements in the image, ultimately producing more contextually relevant captions. The nocaps dataset is designed for open-domain image captioning, where models must generate captions that describe the main content of an image, even for unseen objects. As observed in prior datasets, the optimal MLLM-PES combination remains Qwen-2 with ToT, reinforcing its capability in open-domain captioning. Furthermore, in the baseline setting (B), Qwen-2 outperforms the other models, highlighting its robustness in unconstrained image captioning tasks. The ScienceQA dataset evaluates scientific reasoning and question answering, requiring the model to comprehend scientific concepts and principles. While Qwen-2 achieves the highest performance in the baseline setting (B), applying Greedy PES leads to optimal MLLM-PES combinations of Phi-3.5 with RAG or Phi-3.5 with ICL and SSR. This suggests that RAG and structured step-by-step reasoning (ICL, SSR) are the most effective strategies for solving scientific problems, as they facilitate information retrieval, logical deduction, and structured reasoning.