用智能代理自动优化提示词，兼顾探索与利用。

High-quality prompts are crucial for Large Language Models (LLMs) to achieve exceptional performance. However, manually crafting effective prompts is labor-intensive and demands significant domain expertise, limiting its scalability. Existing automatic prompt optimization methods either extensively explore new prompt candidates, incurring high computational costs due to inefficient searches within a large solution space, or overly exploit feedback on existing prompts, risking suboptimal optimization because of the complex prompt landscape. To address these challenges, we introduce GreenTEA, an agentic LLM workflow for automatic prompt optimization that balances candidate exploration and knowledge exploitation. It leverages a collaborative team of agents to iteratively refine prompts based on feedback from error samples. An analyzing agent identifies common error patterns resulting from the current prompt via topic modeling, and a generation agent revises the prompt to directly address these key deficiencies. This refinement process is guided by a genetic algorithm framework, which simulates natural selection by evolving candidate prompts through operations such as crossover and mutation to progressively optimize model performance. Extensive numerical experiments conducted on public benchmark datasets suggest the superior performance of GreenTEA against human-engineered prompts and existing state-of-the-arts for automatic prompt optimization, covering logical and quantitative reasoning, commonsense, and ethical decision-making.