# Diagnosing Infeasible Optimization Problems Using Large Language Models

arXiv: https://arxiv.org/abs/2308.12923 · HTML: https://mlsanity.com/paper/2308.12923/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [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)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [TalkToModel: Explaining Machine Learning Models with Interactive Natural Language Conversations](https://mlsanity.com/paper/2207.04154/) (2022)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [Mediators: Conversational Agents Explaining NLP Model Behavior](https://mlsanity.com/paper/2206.06029/) (2022)

## Built on by (most cited first, 27 of 27)

- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and Opportunities](https://mlsanity.com/paper/2405.10825/) (2024)
- [OptiMUS: Optimization Modeling Using MIP Solvers and large language models](https://mlsanity.com/paper/2310.06116/) (2023)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [Large Language Models for Combinatorial Optimization: A Systematic Review](https://mlsanity.com/paper/2507.03637/) (2025)
- [Autonomous Industrial Control using an Agentic Framework with Large Language Models](https://mlsanity.com/paper/2411.05904/) (2024)
- [Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms](https://mlsanity.com/paper/2410.20848/) (2024)
- [From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto](https://mlsanity.com/paper/2402.16269/) (2024)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://mlsanity.com/paper/2502.14760/) (2025)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [LLM-OptiRA: LLM-Driven Optimization of Resource Allocation for Non-Convex Problems in Wireless Communications](https://mlsanity.com/paper/2505.02091/) (2025)
- [MoE2: Optimizing Collaborative Inference for Edge Large Language Models](https://mlsanity.com/paper/2501.09410/) (2025)
- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [DualSchool: How Reliable are LLMs for Optimization Education?](https://mlsanity.com/paper/2505.21775/) (2025)
- [Symbiotic Agents: A Novel Paradigm for Trustworthy AGI-driven Networks](https://mlsanity.com/paper/2507.17695/) (2025)
- [Large Language Model-Based Automatic Formulation for Stochastic Optimization Models](https://mlsanity.com/paper/2508.17200/) (2025)
- [FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving](https://mlsanity.com/paper/2608.25220/) (2026)
- [Optimization Problem Solving Can Transition to Evolutionary Agentic Workflows](https://mlsanity.com/paper/2505.04354/) (2025)
- [Infeasibility Aware Large Language Models for Combinatorial Optimization](https://mlsanity.com/paper/2604.01455/) (2026)
- [SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery](https://mlsanity.com/paper/2609.13945/) (2026)
- [A property-registry contract for retrieve-or-refuse thermal-mechanical lattice search](https://mlsanity.com/paper/2609.14741/) (2026)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)
- [TACIT: Optimization Models that Learn from Their Mistakes](https://mlsanity.com/paper/2609.38434/) (2026)

## Abstract (arXiv)

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering and manufacturing, transportation, and health care. Optimization models are mathematical abstractions of the problem of making the best decision while satisfying a set of requirements or constraints. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, also known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.