TLDR: This research paper surveys the integration of Large Language Models (LLMs) into Operations Research (OR), categorizing methods into automatic modeling, auxiliary optimization, and direct solving. It highlights LLMs’ potential to translate natural language into mathematical models, enhance existing optimization algorithms, and directly solve complex problems. The paper also discusses current evaluation benchmarks, real-world applications in supply chain, urban planning, food science, job shop scheduling, and communication, and outlines key challenges and future research directions for developing intelligent optimization systems.
Operations Research (OR) has long been a cornerstone for making decisions in complex systems, with widespread applications in areas like transportation, supply chain management, and production scheduling. However, traditional OR methods, which often rely on expert knowledge and manual adjustments, struggle with the increasing scale, dynamism, and complexity of modern problems.
The emergence of Large Language Models (LLMs) presents a significant opportunity to transform how we approach these challenges. LLMs, known for their ability to understand language, generate structured content, and control reasoning, can bridge the gap between natural language problem descriptions and formal optimization solutions. They can translate natural language into mathematical models or executable code, generate intelligent shortcuts (heuristics), evolve algorithms, and even directly solve optimization tasks.
This research paper provides a comprehensive overview of how LLMs are being integrated into Operations Research, categorizing the methods into three primary areas:
Automatic Modeling
One major direction is automatic modeling, where LLMs take natural language descriptions of problems and convert them into formal mathematical models or executable code. This process typically involves several steps: first, understanding the problem to identify objectives and constraints; second, extracting key elements like variables and functions; third, generating a standard mathematical model; fourth, transforming this model into code that an optimization solver can run; and finally, verifying the solution and providing feedback for corrections. Researchers are exploring various ways to achieve this, including using carefully crafted prompts, combining prompts with model fine-tuning, and guiding LLMs with external knowledge bases.
LLM-assisted Optimization
Another key area is LLM-assisted optimization, where LLMs work alongside existing optimization algorithms to improve their effectiveness and adaptability. Here, LLMs can help in several ways: by evolving heuristic structures and optimizing strategies, collaborating in multi-objective optimization tasks, and transferring capabilities across different optimization paradigms. This means LLMs can assist in designing better search operators, guiding the optimization process, and even integrating with classical algorithms, reinforcement learning, or neuro-symbolic systems to enhance problem-solving capabilities.
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LLM-dominated Optimization Solving
The most advanced direction involves LLMs directly solving optimization problems without relying on traditional mathematical models or heuristic algorithms. These methods use natural language or even multimodal prompts (combining text and images) to guide LLMs in generating solutions. This “zero-modeling” approach offers flexibility and ease of transfer, moving from direct solution generation to more sophisticated techniques that incorporate reasoning, historical data, and self-correction. Multimodal approaches, for instance, can use visual information to improve spatial understanding for tasks like path planning.
To ensure the reliability and effectiveness of these LLM-driven OR methods, researchers are developing specialized benchmarks. These benchmarks go beyond just evaluating modeling accuracy, focusing on the LLMs’ reasoning and decision-making abilities in complex optimization scenarios, including graph-structured reasoning and path planning.
The integration of LLMs is already showing promise in various real-world applications. In supply chain optimization, LLMs enhance interpretability by translating user requirements into optimization expressions. For urban planning, they help interpret natural language requirements and historical data to generate objective functions for city management. In food science, LLMs assist in sustainable food management by combining knowledge with human preferences for combinatorial optimization. They are also being applied to challenging problems like Job Shop Scheduling and in communication and networking for tasks such as server allocation and critical node identification.
While the progress is significant, several challenges remain. These include ensuring stable mapping between semantics and structured models, unifying fragmented research efforts, improving generalization and interpretability, developing more comprehensive evaluation tools, and addressing the high computational costs associated with large-scale LLM deployment. Future research will focus on robust representations, closed-loop mechanisms, standardized workflows, symbolic reasoning, and lightweight deployment strategies.
This survey highlights that LLM-enabled Operations Research is moving towards a systematic development phase. By fostering methodological innovation, enhancing interpretability, and establishing comprehensive evaluation systems, LLMs are poised to drive the creation of next-generation intelligent optimization systems. For more in-depth information, you can refer to the full research paper here.
