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

2025-10-19

AI Summary

Existing optimization solvers suffer from poor generalization—relying heavily on prompt engineering—or high training costs—requiring supervised fine-tuning. This paper introduces SolverLLM, a training-free, large language model (LLM)-guided search framework for general-purpose optimization. Methodologically, it integrates three key components: (1) a test-time dynamic expansion mechanism that transforms natural-language problems into formal mathematical models and executable code; (2) an enhanced Monte Carlo Tree Search (MCTS) incorporating dynamic action expansion, prompt backpropagation, and uncertainty backpropagation to improve search efficiency and decision robustness; and (3) a feedback-driven prompt optimization and reward reliability assessment module. Evaluated on six heterogeneous benchmark datasets, SolverLLM consistently outperforms both prompt-engineering-based and supervised-learning baselines, demonstrating strong cross-task generalization and zero training overhead.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Solvers and Tools
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• SolverLLM solves diverse optimization problems without training
• It generates mathematical formulations and solver-ready code
• It enhances search via modified Monte Carlo Tree Search

Innovation

• Training-free framework using test-time scaling
• Generates mathematical formulations into solver code
• Modified MCTS with dynamic expansion and backpropagation