The use of Large Language Models (LLMs) in data cleaning tasks has demonstrated impressive capabilities. However, the high inference costs associated with LLMs pose significant challenges, particularly when managing large-scale datasets within constrained budgets. While many studies focus on direct methods to reduce inference costs, we propose a novel framework to alleviate the high inference costs of LLMs by transforming the task into a multi-objective optimization problem. This framework begins by decomposing the complex data cleaning task into smaller, well-defined sub-tasks. For each sub-task, the most appropriate method is selected from a range of options, such as rule-based tools, code generation methods, smaller pre-trained language models, or LLMs, depending on the trade-off between cost and effectiveness. This allows for a systematic balance between cost and quality, enabling the completion of high-quality data cleaning tasks within budget constraints. Experimental results validate the effectiveness of this approach. The framework significantly reduces inference costs while maintaining high-quality data processing. This framework offers a practical pathway to optimizing LLM-based data cleaning methods, balancing computational efficiency and data processing quality. Future work could explore the dynamic adaptations for evolving sub-tasks or deeper integrations with explainable AI and human-in-the-loop approaches to enhance trust and interpretability in data cleaning pipelines.