Think in Strategies, Act with Tools: Traceable Agentic Optimization for Combinatorial Problems

Optimization by PROmpting (OPRO) directly leverages Large Language Models (LLMs) to generate candidate solutions through natural-language prompting. However, OPRO's optimization process is difficult to track, which prevents LLMs from capturing useful information accumulated over previous iterations, thereby limiting solution quality. To address this limitation, we propose a Tool-Augmented Strategic Agent (TASA) which summarizes and exploits trajectory to improve solution quality. Specifically, TASA plans the strategy for each step based on the optimization trajectory, which decomposes the optimization process into traceable strategy selections. Moreover, we leverage LLM to construct problem-specific tools and introduce a strategy-guided adaptive tool planner, which efficiently utilizes the information of trajectory to update solutions. We establish local convergence under persistent exploration and evaluate the complete framework under a shared candidate-evaluation budget. The results support its solution quality and the traceability of strategy-guided search.