# DualSchool: How Reliable are LLMs for Optimization Education?

arXiv: https://arxiv.org/abs/2505.21775 · HTML: https://mlsanity.com/paper/2505.21775/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 16 of 16)

- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [MathTutorBench: A Benchmark for Measuring Open-ended Pedagogical Capabilities of LLM Tutors](https://mlsanity.com/paper/2502.18940/) (2025)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2308.12923/) (2023)
- [Holy Grail 2.0: From Natural Language to Constraint Models](https://mlsanity.com/paper/2308.01589/) (2023)
- ["I Want It That Way": Enabling Interactive Decision Support Using Large Language Models and Constraint Programming](https://mlsanity.com/paper/2312.06908/) (2023)
- [RLSF: Fine-tuning LLMs via Symbolic Feedback](https://mlsanity.com/paper/2405.16661/) (2024)
- [Decision Information Meets Large Language Models: The Future of Explainable Operations Research](https://mlsanity.com/paper/2502.09994/) (2025)
- [Synthesis of Mathematical programs from Natural Language Specifications](https://mlsanity.com/paper/2304.03287/) (2023)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)

## Built on by (most cited first, 4 of 4)

- [LISTEN to Your Preferences: An LLM Framework for Multi-Objective Selection](https://mlsanity.com/paper/2510.25799/) (2025)
- [Democratizing Large-Scale Re-Optimization with LLM-Guided Model Patches](https://mlsanity.com/paper/2605.18692/) (2026)
- [Text2Model: Modeling Copilots for Text-to-Model Translation](https://mlsanity.com/paper/2604.12955/) (2026)
- [Learn2Zinc: Fine-tuning Small Language Models for Text-to-Model Translation in MiniZinc](https://mlsanity.com/paper/2607.20456/) (2026)

## Abstract (arXiv)

Consider the following task taught in introductory optimization courses which addresses challenges articulated by the community at the intersection of (generative) AI and OR: generate the dual of a linear program. LLMs, being trained at web-scale, have the conversion process and many instances of Primal to Dual Conversion (P2DC) at their disposal. Students may thus reasonably expect that LLMs would perform well on the P2DC task. To assess this expectation, this paper introduces DualSchool, a comprehensive framework for generating and verifying P2DC instances. The verification procedure of DualSchool uses the Canonical Graph Edit Distance, going well beyond existing evaluation methods for optimization models, which exhibit many false positives and negatives when applied to P2DC. Experiments performed by DualSchool reveal interesting findings. Although LLMs can recite the conversion procedure accurately, state-of-the-art open LLMs fail to consistently produce correct duals. This finding holds even for the smallest two-variable instances and for derivative tasks, such as correctness, verification, and error classification. The paper also discusses the implications for educators, students, and the development of large reasoning systems.