mlsanityData to 14 Oct 2026

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

arXiv 2510.16916 ↗First posted 19 Oct 2025cs.LGcited by 10

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

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.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 17 of its 29 references that are in the map. First posted on arXiv 19 Oct 2025.

Builds on

17 of 29 references.

Closest ancestors · 3

Same direction, newest first

  1. 2025A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?31 Mar
  2. 2025Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?17 Feb
  3. 2022Language Models (Mostly) Know What They Know11 Jul

Other references · 14

  1. 2023GPT-4 Technical Reportcited by 18,396
  2. 2024GPT-4o System Cardcited by 4,588
  3. 2023Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debatecited by 1,011
  4. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  5. 2023Large Language Models as Optimizerscited by 864
  6. 2023Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generationcited by 819
  7. 2023Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoningcited by 391
  8. 2023Planning with Large Language Models for Code Generationcited by 182
  9. 2024ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modelingcited by 124
  10. 2024LLMOPT: Learning to Define and Solve General Optimization Problems from Scratchcited by 102
  11. 2024Autoformulation of Mathematical Optimization Models Using LLMscited by 48
  12. 2024LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generationcited by 45
2 more
  1. 2023OptiMUS: Optimization Modeling Using MIP Solvers and large language modelscited by 39
  2. 2024The Fusion of Large Language Models and Formal Methods for Trustworthy AI Agents: A Roadmapcited by 20

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 10.

10 papers.

  1. 2026LLM-Enhanced Energy Contrastive Learning for Out-of-Distribution Detection in Text-Attributed Graphscited by 1
  2. 2026AutoOR: Scalably Post-training LLMs to Autoformulate Operations Research Problemscited by 1
  3. 2026Automated Reformulation of Robust Optimization via Memory-Augmented Large Language Modelscited by 1
  4. 2026Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimizationcited by 1
  5. 2026StarOR: Synergizing Tree Search and Test-Time Reinforcement Learning for Optimization Modelingcited by 1
  6. 2026Coupled Hierarchical Search over Topology and Execution for Agentic Workflow Synthesiscited by 1
  7. 2026Entropy Centroids as Intrinsic Rewards for Test-Time Scalingcited by 0
  8. 2026Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontierscited by 0
  9. 2026Learning to Optimize through Solver-Grounded Self-Playcited by 0
  10. 2026SemOPT: Fixing Semantic Errors in LLM-based Optimization Modeling via Reward-Guided Searchcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling
  2. 2025Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution
  3. 2026Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces
  4. 2026LLMs as Adaptive Meta-Solvers: Strategy-Diverse RL for Industrial-Scale Optimization
  5. 2025Large Language Models as End-to-end Combinatorial Optimization Solvers
  6. 2025LLMize: A Framework for Large Language Model-Based Numerical Optimization
  7. 2025OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems
  8. 2025Unifying Tree Search Algorithm and Reward Design for LLM Reasoning: A Survey