Automatically solving optimization problems from natural language descriptions with both efficiency and reliability is highly desirable but remains challenging. Language model hallucinations and the limited availability of labeled datasets often result in misaligned formulations, code errors, and feasibility failures We propose UMCTS, an Uncertainty-aware Monte Carlo Tree Search framework that combines the language understanding capability of large language models with the reliability of well-established solvers. UMCTS structures the solution process into four stages: global instruction, assumptions, mathematical formulation, and solver code generation. It employs Monte Carlo Tree Search with semantic-equivalence pruning, prior-guided exploration, and solver-based feasibility checks. An LLM judge provides numerical reward signals, qualitative error information, and uncertainty estimates. These signals are backpropagated to guide the search and flag unreliable outputs. Across six public benchmarks, UMCTS achieves state-of-the-art solution accuracy, improves efficiency by reducing token usage.

Large language models (LLMs) integrated into multi-step agent systems enable complex decision-making processes across various applications. However, their outputs often lack reliability, making uncertainty estimation crucial. Existing uncertainty estimation methods primarily focus on final-step outputs, which fail to account for cumulative uncertainty over the multi-step decision-making process and the dynamic interactions between agents and their environments. To address these limitations, we propose SAUP (Situation Awareness Uncertainty Propagation), a novel framework that propagates uncertainty through each step of an LLM-based agent’s reasoning process. SAUP incorporates situational awareness by assigning situational weights to each step’s uncertainty during the propagation. Our method, compatible with various one-step uncertainty estimation techniques, provides a comprehensive and accurate uncertainty measure. Extensive experiments on benchmark datasets demonstrate that SAUP significantly outperforms existing state-of-the-art methods, achieving up to 20% improvement in AUROC.