用大模型搜索求解优化问题，无需训练即可跨类型通用
SolverLLM: Leveraging Test-Time Scaling for Optimization Problem via LLM-Guided Search
- 用蒙特卡洛树搜索生成数学公式并转为可执行代码
- 在6个基准数据集上超越提示和学习类方法，无需额外训练
- 适合需要快速适配新优化任务的研究者或工程师
大型语言模型（LLM）在解决复杂推理任务方面展现出巨大潜力，包括优化问题。然而，现有方法要么依赖提示工程，导致跨问题类型泛化能力差；要么需要昂贵的监督训练。我们提出SolverLLM，一种无需训练的框架，通过测试时扩展来求解多样化的优化问题。SolverLLM不直接求解，而是生成数学表达式，并将其转化为求解器可用的代码，由一种新型蒙特卡洛树搜索（MCTS）策略引导。为提升搜索效率，我们改进经典MCTS：(1) 动态扩展以自适应生成公式，(2) 提示反向传播，通过结果驱动反馈引导探索，(3) 不确定性反向传播，将奖励可靠性纳入决策。在六个标准基准数据集上的实验表明，SolverLLM在不需额外训练的情况下，优于基于提示和基于学习的基线方法，展现出强大的泛化能力。
原文摘要 · Abstract (English)
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.
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