SolverLLM: Leveraging Test-Time Scaling for Optimization Problem via LLM-Guided Search

Large Language Models (LLMs) offer promising capabilities for tackling complex reasoning tasks, including optimization problems. However, existing methods either rely on prompt engineering, which leads to poor generalization across problem types, or require costly supervised training. We introduce SolverLLM, a training-free framework that leverages test-time scaling to solve diverse optimization problems. Rather than solving directly, SolverLLM generates mathematical formulations and translates them into solver-ready code, guided by a novel Monte Carlo Tree Search (MCTS) strategy. To enhance the search process, we modify classical MCTS with (1) dynamic expansion for adaptive formulation generation, (2) prompt backpropagation to guide exploration via outcome-driven feedback, and (3) uncertainty backpropagation to incorporate reward reliability into decision-making. Experiments on six standard benchmark datasets demonstrate that SolverLLM outperforms both prompt-based and learning-based baselines, achieving strong generalization without additional training.