# Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers

arXiv: https://arxiv.org/abs/2606.15577 · HTML: https://mlsanity.com/paper/2606.15577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 52 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Large Language Models as Tool Makers](https://mlsanity.com/paper/2305.17126/) (2023)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [AdaPlanner: Adaptive Planning from Feedback with Language Models](https://mlsanity.com/paper/2305.16653/) (2023)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation](https://mlsanity.com/paper/2403.01131/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Understanding the Dark Side of LLMs' Intrinsic Self-Correction](https://mlsanity.com/paper/2412.14959/) (2024)
- [Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming](https://mlsanity.com/paper/2410.12112/) (2024)
- [Large Language Models can Implement Policy Iteration](https://mlsanity.com/paper/2210.03821/) (2022)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [Large Language Model for Multi-objective Evolutionary Optimization](https://mlsanity.com/paper/2310.12541/) (2023)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly involved in complex mathematical optimization, even if the pragmatic user who triggers them is unaware of it. After all, many real-world problems reduce to the search for better or the best solutions. The field of LLM-as-optimizer has three paradigms: direct optimization, tool-augmented optimization, and tool-creating optimization. Direct optimization uses iterative prompting and heuristic generation to navigate solution spaces. Tool-augmented optimization translates natural language problems into formal specifications and orchestrates external solvers. Tool-creating optimization goes further, using LLMs to discover reusable algorithms or heuristics that can be deployed at zero marginal LLM cost. We describe current performance frontiers based on the benchmarks from the literature. We identify the critical reasoning gap in current architectures and argue for trade-offs between the future potential of direct optimization and the auditability of tool-augmented optimization. Even future, more powerful models might opt for tool-making to improve operational efficiency for repetitive families of problems.