Natural Language to Optimization Modeling

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The field studies how to turn written or multimodal requirements into decision variables, objectives, constraints, and executable models for operations research solvers. Approaches include structured intermediate representations and domain-specific languages, retrieval-augmented generation, multi-agent refinement, and post-training with solver execution or verification feedback. Benchmarks such as NL4OPT, MAMO, and IndustryOR test formulation accuracy and executability, while newer evaluations probe harder domains, industrial workflows, and computational efficiency. A central challenge is that code can run or match an objective value yet still misrepresent the intended constraints, especially when requirements are ambiguous or data must be grounded correctly.

Latest papers

76 papers14 papers in the last four weeks, up 40% on the four weeks before. 0.1% of all new papers.

Strategy-Aware Optimization Modeling with Reasoning LLMs
May 4, 2026Ruiqing Zhao, Fengzhi Li, Yuan Zuo +5RL for Code Generation LLM-Based Program Synthesis
School of Computer Science and Engineering, Beihang University, Beijing, China · JIUTIAN Research, Beijing, China · MIIT Key Laboratory of Data and Decision Intelligence, Beihang University, Beijing, China
EngiAgent: Fully Connected Coordination of LLM Agents for Solving Open-ended Engineering Problems with Feasible Solutions
May 4, 2026Xiyuan Zhou, Ruixi Zou, Xinlei Wang +4Multi-Agent LLM Systems Software Engineering Agents
Nanyang Technological University · The Chinese University of Hong Kong, Shenzhen · INSAIT, Sofia University “St. Kliment Ohridski” +2
From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling
Apr 28, 2026Jianghao Lin, Zi Ling, Chenyu Zhou +4Multi-Agent Debate Multi-Agent LLMs
Antai College of Economics and Management, Shanghai Jiao Tong University · University of Chicago Booth School of Business · School of Economics and Management, Tsinghua University +1
OptiVerse: A Comprehensive Benchmark towards Optimization Problem Solving
Apr 23, 2026Xinyu Zhang, Boxuan Zhang, Yuchen Wan +5LLM Evaluation Benchmark Design
School of Computer Science and Technology, Xi’an Jiaotong University · 2Ministry of Education Key Laboratory of Intelligent Networks and Network Security, China · 4Lenovo Research +1
AutoOR: Scalably Post-training LLMs to Autoformalize Operations Research Problems
Apr 18, 2026Sumeet Ramesh Motwani, Chuan Du, Aleksander Petrov +4LLM Post-Training RL Fine-Tuning
1X · University of Oxford
Text2Model: Modeling Copilots for Text-to-Model Translation
Apr 14, 2026Serdar Kadioglu, Karthik Uppuluri, Akash SingirikondaNatural Language to Optimization Modeling Large Language Model-Guided Optimization
AI Center of Excellence, Fidelity Investments · Department of Computer Science, Brown University
Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers
Apr 9, 2026Roko Peran, Luka Hobor, Mihael Kovac +1Large Language Model-Guided Optimization Natural Language to Optimization Modeling
Student at University of Zagreb Faculty of Electrical Engineering and Computing, Zagreb, Croatia · University of Zagreb Faculty of Electrical Engineering and Computing, Zagreb, Croatia
NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling
Apr 2, 2026Zhijing Hu, Yufan Deng, Haoyang Liu +1Natural Language to Optimization Modeling Large Language Model-Guided Optimization
College of System Engineering, National University of Defense Technology · University of Science and Technology of China
Execution-Verified Reinforcement Learning for Optimization Modeling
Apr 1, 2026Runda Guan, Xiangqing Shen, Jiajun Zhang +3Natural Language to Optimization Modeling Learning to Optimize
School of Computer Science and Engineering, Nanjing University of Science and Technology · School of Intelligence Science and Technology, Nanjing University · Institute of Automation, Chinese Academy of Sciences
AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control
Mar 27, 2026Shaoliang Yang, Jun Wang, Yunsheng WangTopology Optimization Natural Language to Optimization Modeling
Santa Clara University, Santa Clara, CA
BeamAgent: LLM-Aided MIMO Beamforming with Decoupled Intent Parsing and Alternating Optimization for Joint Site Selection and Precoding
Mar 19, 2026Xiucheng Wang, Yue Zhang, Nan ChengWireless Resource Allocation Large Language Model-Guided Optimization
State Key Laboratory of ISN and School of Telecommunications Engineering, Xidian University, Xi’an 710071, China
Type-Aware Retrieval-Augmented Generation with Dependency Closure for Solver-Executable Industrial Optimization Modeling
Mar 3, 2026Y. Zhong, R. Huang, M. Wang +4Natural Language to Optimization Modeling Retrieval-Augmented Generation
School of Petroleum, China University of Petroleum (Beijing) at Karamay, Karamay, 834000, China
ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization
Feb 17, 2026Junbo Jacob Lian, Yujun Sun, Huiling Chen +3LLM-Based Program Synthesis LLM Reliability
Institute of Operations Research and Analytics, National University of Singapore · McCormick School of Engineering, Northwestern University · Wenzhou Buyi Pharmacy Chain Co., Ltd. +2
A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving
Sep 10, 2025Yisong Zhang, Ran Cheng, Guoxing Yi +1Evolutionary Optimization Large Language Model-Guided Optimization
Optimizing Prompt Sequences using Monte Carlo Tree Search for LLM-Based Optimization
Aug 8, 2025Fei Xu Yu, Gina Adam, Nathaniel D. Bastian +1Natural Language to Optimization Modeling Large Language Model-Guided Optimization
The George Washington University · United States Military Academy
OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale
Jul 29, 2024Ali AhmadiTeshnizi, Wenzhi Gao, Herman Brunborg +3Mixed-Integer Linear Programming Large Language Model-Guided Optimization
a School of Management Science and Engineering, Stanford University, Stanford, California 94305 · b Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305

May 4, 2026J/K move · Enter open · S save

Strategy-Aware Optimization Modeling with Reasoning LLMs

Ruiqing Zhao, Fengzhi Li, Yuan Zuo, Rui Liu+4

School of Computer Science and Engineering, Beihang University, Beijing, China · JIUTIAN Research, Beijing, China · MIIT Key Laboratory of Data and Decision Intelligence, Beihang University, Beijing, China

RL for Code Generation LLM-Based Program Synthesis Constrained Optimization Natural Language to Optimization Modeling

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Large language models (LLMs) can generate syntactically valid optimization programs, yet often struggle to reliably choose an effective modeling strategy, leading to incorrect formulations and inefficient solver behavior. We propose SAGE, a strategy-aware framework that makes Modeling Strategy explicit in both data construction and post-training. SAGE builds a solver-verified multi-strategy dataset and trains a student model with supervised fine-tuning followed by Segment-Weighted GRPO using a composite reward over format compliance, correctness, and solver efficiency. Across eight benchmarks spanning synthetic and real-world settings, SAGE improves average pass@1 from 72.7 to 80.3 over the strongest open-source baseline. With multiple generations, SAGE discovers more distinct correct formulations and improves component-level diversity at pass@16 by 19-29%. At the largest scale, SAGE produces more compact constraint systems with 14.2% fewer constraints than the baseline, consistent with solver-efficient modeling. Overall, these results show that making Modeling Strategy explicit improves automated optimization modeling. Code is available at https://github.com/rachhhhing/SAGE.