## 9 Conclusions  
This study investigated optimal PE strategies to mitigate one of the key limitations of MLLMs--the hallucination phenomenon. To achieve this, we analyzed representative multimodal PE techniques, including ICL, CoT, SSR, ToT, and RAG. These techniques were systematically applied across multiple datasets with distinct domain characteristics, allowing for a comprehensive performance evaluation.  
The primary contribution of this work is the proposal of the greedy prompt engineering strategy (Greedy PES), a methodology designed to select the optimal prompt engineering strategy based on dataset and model characteristics. To ensure an objective and quantitative evaluation of MLLM responses, we employed a range of evaluation metrics, including BLEU, ROUGE, METEOR, S-BERT, MoverScore, and CIDEr. Additionally, a weighted aggregate evaluation score was introduced to facilitate a holistic comparison of model performance.  
Experimental results demonstrate that the optimal PES varies depending on the dataset and the model used. General image captioning datasets benefited most from ICL, ToT, and RAG, suggesting that multimodal models require enhanced contextual reasoning, structured thought processing, and external knowledge retrieval for effective caption generation. Mathematical reasoning tasks (mathematical category) were best addressed by ICL, SSR, and ToT, highlighting the importance of incremental, structured reasoning in mathematical problem-solving. Scientific reasoning tasks (science category) showed the highest gains with RAG and SSR, reinforcing the need for external knowledge augmentation and systematic logical inference in scientific domains.  
In the absence of prompt engineering, Owen-2 emerged as the most effective model across various benchmarks. However, when Greedy PES was applied, Phi-3.5 also achieved competitive performance, despite being the smallest model in terms of parameter count. This finding underscores the potential of PES to significantly enhance the efficiency of smaller-scale models, making Phi-3.5 a highly efficient and accurate model when coupled with optimized prompt strategies.  
These results empirically validate the hypothesis that PE can significantly enhance model performance and compensate for inherent model limitations. Moving forward, future research should extend the validation of Greedy PES to a broader range of multimodal applications and explore additional techniques to mitigate hallucination effects within MLLMs. Furthermore, domain-specific optimizations (e.g., medical, legal applications) should be investigated to refine PES methodologies for specialized fields where precision and reliability are paramount.  
Conceptualization, S.L.; methodology, S.L. and M.S.; software, M.S.; validation, S.L. and M.S.; formal analysis, S.L.; investigation, S.L.; resources, S.L.; data curation, M.S.; writing--original draft preparation, S.L.; writing--review and editing, S.L.; visualization, S.L. and M.S.; supervision, S.L.; project administration, S.L.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Soonchunhyang University Research Fund.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
We acknowledge the support by the Soonchunhyang University Research Fund.  
The authors declare no conflicts of interest.