Mathematical optimization is a foundational pillar of modern AI, underpinning decision-making in supply chains, energy systems, finance, and scheduling. Despite its importance, building and deploying optimization models remains a challenging, expert-driven process that requires significant domain knowledge and technical expertise.
This tutorial surveys the emerging interface between LLMs and optimization along two synergistic themes. First, we examine how LLMs can act as copilotsacross the optimization pipeline — assisting with problem formulation, model construction, solver configuration, and validation. Second, we explore the growing role of LLMs in algorithmic discovery, generating, refining, and discovering new optimization algorithms and heuristics.
The tutorial bridges machine learning and optimization, covering foundational concepts, surveying state-of-the-art methods and systems, and highlighting key challenges such as correctness, robustness, and handling ambiguous problem specifications.
Objectives and audience
The tutorial bridges AI researchers new to optimization, OR researchers curious about how LLMs can assist modeling and algorithm design, and practitioners building AI-enabled decision-support systems.
- Understand the core optimization pipeline and where LLMs can intervene.
- Survey the state of the art in LLM-based auto-formulation, from prompting to fine-tuning to agentic systems.
- Reason about correctness and equivalence for LLM-generated optimization models.
- Recognize how LLMs can assist solver configuration without large training datasets.
- Map the taxonomy of LLM-driven algorithmic discovery and its open research directions.
Graduate students and researchers with little or no formal background in optimization.
Optimization and operations research researchers curious about how LLMs can assist modeling and algorithm design.
Builders of AI-enabled decision-support systems in logistics, planning, scheduling, and resource allocation.
- Basic mathematical maturity (variables, constraints, functions).
- General exposure to modern AI / machine learning.
- No prior expertise in integer programming, solver engineering, or LLM training required.
Detailed schedule
Total duration 3 hours 30 minutes with a 30-minute coffee break. Start times are placeholders relative to a 09:00 session start — click any row to expand.
Introduction
A broad overview of mathematical optimization, centered on mixed integer linear programming (MILP) as a core AI and OR technique.
- The optimization pipeline: understand → formulate → tune → validate.
- Where current bottlenecks lie, and where LLMs can help.
- Framing the two halves of the tutorial: copilot + discovery.
Optimization Model Formulation
Translating informal problem descriptions into precise optimization models — a central bottleneck for domain experts without formal training in optimization.
- Agentic frameworks: OptiMUS, LEAN-LLM-OPT, Chain-of-Experts, MCTS-based approaches.
- Fine-tuned models specialized for optimization: ORLM, LLM-OPT.
- Benchmark datasets: textbook-style, synthetic, and real-world collections such as IndustryOR.
Optimization Model Evaluation
How do we know a generated formulation actually solves the right problem? Recent frameworks for assessing correctness and equivalence.
- Graph-isomorphism-based approaches (Xing et al., 2024).
- Execution-based accuracy metrics (AhmadiTeshnizi et al., 2024).
- EquivaMap: formal equivalence checking (Zhai et al., 2025).
Coffee Break
Optimization Model Solving
Modern solvers (Gurobi, CPLEX) expose many configuration parameters whose tuning is time-consuming even for experts. Can LLMs help?
- LLMs leveraging documentation, code, and prior research for cold-start configuration.
- Contrast with traditional data-driven configuration methods.
- Strengths, limitations, and open challenges in deployment.
Algorithmic Discovery with LLMs
LLMs as a new paradigm for automating algorithm design — lowering the barrier to entry and exploring design spaces hard to navigate manually.
- A taxonomy: LLM as optimizer · extractor · predictor · designer.
- Methods: EoH, ReEvo, Llamea, HSEvo, MEoH, MLES.
- Applications across combinatorial optimization, black-box optimization, ML, and scientific discovery.
- Open challenges: domain LLMs, benchmarking, human–AI collaboration.
Presenters
Four researchers working at the boundary of machine learning, operations research, and human–computer interaction.
Connor Lawless
Stanford University
Postdoc, Stanford, Connor Lawless is a Human-Centered AI postdoctoral researcher at Stanford, with a PhD in Operations Research and Information Engineering from Cornell. His work blends machine learning, computational optimization, and human–computer interaction to create human-centered artificial intelligence.
Fei Liu
University of Zurich · ETH Zurich
Postdoc, UZHÐ Zurich, Researcher focused on automated algorithm design, evolutionary algorithms, neural combinatorial optimization, and multiobjective optimization. Lead author on [LLM4AD](https://github.com/Optima-CityU/LLM4AD).
Hanzhang Qin
National University of Singapore
Assistant Professor at NUS. Operations researcher working on optimization, revenue management, and the application of large language models to large-scale optimization workflows.
Ellen Vitercik
Stanford University
Assistant Professor at Stanford with a joint appointment between the Management Science & Engineering and Computer Science departments. Her research—which has been recognized with a Schmidt Sciences AI2050 Early Career Fellowship and an NSF CAREER award, among other honors—spans machine learning and discrete optimization.
Key references
A curated subset of the growing literature at the LLM × optimization interface. Filter by theme.
OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models
Autoformulation of Mathematical Optimization Models Using LLMs
Chain-of-Experts: When LLMs Meet Complex Operations Research Problems
ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling
LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch
Large-Scale Optimization Model Auto-Formulation: Harnessing LLM Flexibility via Structured Workflow
Towards Human-Aligned Evaluation for Linear Programming Word Problems
EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations
LLMs for Cold-Start Cutting Plane Separator Configuration
Large Language Models as Optimizers
Large Language Model-Enhanced Algorithm Selection: Towards Comprehensive Algorithm Representation
LLM-TPF: Multiscale Temporal Periodicity-Semantic Fusion LLMs for Time Series Forecasting
Evolution of Heuristics (EoH): Towards Efficient Automatic Algorithm Design Using LLMs
ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution
Llamea: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics
HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs
Multi-Objective Evolution of Heuristics Using Large Language Models
Multimodal LLM-Assisted Evolutionary Search for Programmatic Control Policies
A Systematic Survey on Large Language Models for Algorithm Design
Integer Programming
Previous editions
A preliminary version was delivered at AAAI 2026. Content has been expanded through invited talks and updated research for IJCAI 2026.
CEC 2025 · IJCCI 2025 · IEEE Web Seminar
Invited talks on automated algorithm design with LLMs; materials online.
↗ materialsIJCAI 2026 Tutorial
Expanded version with algorithmic discovery track.
Ethics and oversight
LLM-generated optimization artifacts are proposals, not authoritative solutions.
Incorrect or hallucinated formulations can lead to unsafe or harmful decisions in high-stakes applications — logistics, energy, finance, healthcare. LLMs may also inherit biases from training data and from problem descriptions, which can propagate into objectives, constraints, and recommendations.
The tutorial discusses these risks directly. We emphasize evaluation, validation, transparency, reproducibility, and human oversight, and highlight responsible-use considerations for deploying these methods in real-world decision systems.