# Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming

arXiv: https://arxiv.org/abs/2410.12112 · HTML: https://mlsanity.com/paper/2410.12112/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 58 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Builds on (most cited first, 27 of 27)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Inner Monologue: Embodied Reasoning through Planning with Language Models](https://mlsanity.com/paper/2207.05608/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [Translating Natural Language to Planning Goals with Large-Language Models](https://mlsanity.com/paper/2302.05128/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [AutoTAMP: Autoregressive Task and Motion Planning with LLMs as Translators and Checkers](https://mlsanity.com/paper/2306.06531/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [ISR-LLM: Iterative Self-Refined Large Language Model for Long-Horizon Sequential Task Planning](https://mlsanity.com/paper/2308.13724/) (2023)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Formal-LLM: Integrating Formal Language and Natural Language for Controllable LLM-based Agents](https://mlsanity.com/paper/2402.00798/) (2024)
- [Robust Planning with LLM-Modulo Framework: Case Study in Travel Planning](https://mlsanity.com/paper/2405.20625/) (2024)
- [Automating the Generation of Prompts for LLM-based Action Choice in PDDL Planning](https://mlsanity.com/paper/2311.09830/) (2023)

## Built on by (most cited first, 30 of 35)

- [PlanGenLLMs: A Modern Survey of LLM Planning Capabilities](https://mlsanity.com/paper/2502.11221/) (2025)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [LLMs as Planning Formalizers: A Survey for Leveraging Large Language Models to Construct Automated Planning Models](https://mlsanity.com/paper/2503.18971/) (2025)
- [A Survey on Large Language Models for Automated Planning](https://mlsanity.com/paper/2502.12435/) (2025)
- [Evaluating the Goal-Directedness of Large Language Models](https://mlsanity.com/paper/2504.11844/) (2025)
- [Teaching LLMs to Plan: Logical Chain-of-Thought Instruction Tuning for Symbolic Planning](https://mlsanity.com/paper/2509.13351/) (2025)
- [CodeSteer: Symbolic-Augmented Language Models via Code/Text Guidance](https://mlsanity.com/paper/2502.04350/) (2025)
- [Talk to Your Slides: High-Efficiency Slide Editing via Language-Driven Structured Data Manipulation](https://mlsanity.com/paper/2505.11604/) (2025)
- [PLANET: A Collection of Benchmarks for Evaluating LLMs' Planning Capabilities](https://mlsanity.com/paper/2504.14773/) (2025)
- [Simulation to Rules: A Dual-VLM Framework for Formal Visual Planning](https://mlsanity.com/paper/2510.03182/) (2025)
- [The Road to Generalizable Neuro-Symbolic Learning Should be Paved with Foundation Models](https://mlsanity.com/paper/2505.24874/) (2025)
- [TAPE: Tool-Guided Adaptive Planning and Constrained Execution in Language Model Agents](https://mlsanity.com/paper/2602.19633/) (2026)
- [Unifying Inference-Time Planning Language Generation](https://mlsanity.com/paper/2505.14763/) (2025)
- [Language Model as Planner and Formalizer under Constraints](https://mlsanity.com/paper/2510.05486/) (2025)
- [Neuro-Symbolic Compliance: Integrating LLMs and SMT Solvers for Automated Financial Legal Analysis](https://mlsanity.com/paper/2601.06181/) (2026)
- [Large Language Models as Common-Sense Heuristics](https://mlsanity.com/paper/2501.18816/) (2025)
- [Improving the Data-efficiency of Reinforcement Learning by Warm-starting with LLM](https://mlsanity.com/paper/2505.10861/) (2025)
- [PEA: Enhancing LLM Performance on Computational-Reasoning Tasks](https://mlsanity.com/paper/2502.10938/) (2025)
- [Evaluating Human Trust in LLM-Based Planners: A Preliminary Study](https://mlsanity.com/paper/2502.20284/) (2025)
- [Iterative Formalization and Planning in Partially Observable Environments](https://mlsanity.com/paper/2505.13126/) (2025)
- [A Reality Check of Language Models as Formalizers on Constraint Satisfaction Problems](https://mlsanity.com/paper/2505.13252/) (2025)
- ["Don't Do That!": Guiding Embodied Systems through Large Language Model-based Constraint Generation](https://mlsanity.com/paper/2506.04500/) (2025)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)
- [Constraints-of-Thought: A Framework for Constrained Reasoning in Language-Model-Guided Search](https://mlsanity.com/paper/2510.08992/) (2025)
- [Agentic LLM Planning via Step-Wise PDDL Simulation: An Empirical Characterisation](https://mlsanity.com/paper/2603.06064/) (2026)
- [MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku](https://mlsanity.com/paper/2607.12711/) (2026)
- [Replan, Repair, or Edit? A Unified Empirical Evaluation of Travel Agents for Itinerary Revision under Resource Disruptions](https://mlsanity.com/paper/2609.19654/) (2026)
- [Foundation Models for Logistics: Toward Certifiable, Conversational Planning Interfaces](https://mlsanity.com/paper/2507.11352/) (2025)
- [Verbalized Algorithms: Classical Algorithms are All You Need (Mostly)](https://mlsanity.com/paper/2509.08150/) (2025)
- [Who Does What? Archetypes of Roles Assigned to LLMs During Human-AI Decision-Making](https://mlsanity.com/paper/2602.11924/) (2026)

## Abstract (arXiv)

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons. Project page: https://sites.google.com/view/llmfp.