Optimization modeling plays a critical role in supporting optimal decision-making across various domains. Previous works have demonstrated that large language models (LLMs) tailored for optimization modeling have significantly automated and simplified this process. However, these models typically employ a straightforward input-output paradigm and struggle with challenging instances. In contrast, recent advances in general-purpose reasoning LLMs (RLLMs), such as DeepSeek-R1, have shown impressive capabilities in complex domains like mathematics and coding. In this paper, we introduce DeepOR, the first RLLM specifically designed for optimization modeling. Instead of directly outputting solutions, DeepOR explicitly performs multiple intermediate reasoning steps. To adapt a base LLM into an RLLM, we begin by synthesizing long chain-of-thought (CoT) data guided by a flowchart, which is automatically generated using a self-exploration algorithm. Once the training data are prepared, we employ supervised fine-tuning on the base LLM to endow it with reasoning capabilities tailored for optimization modeling. To fully leverage the model's reasoning potential, we further apply reinforcement learning with reward-shaping derived from solver feedback. Experimental results on benchmarks confirm that DeepOR consistently and significantly outperforms existing state-of-the-art approaches.

With the advent of Large Language Models (LLMs), generating rule-based data for real-world applications has become more accessible. Due to the inherent ambiguity of natural language and the complexity of rule sets, especially in long contexts, LLMs often struggle to follow all specified rules, frequently omitting at least one. To enhance the reasoning and understanding of LLMs on long and complex contexts, we propose a novel prompting strategy Multi-Lingual Prompt, namely MLPrompt, which automatically translates the error-prone rule that an LLM struggles to follow into another language, thus drawing greater attention to it. Experimental results on public datasets across various tasks have shown MLPrompt can outperform state-of-the-art prompting methods such as Chain of Thought, Tree of Thought, and Self-Consistency. Additionally, we introduce a framework integrating MLPrompt with an auto-checking mechanism for structured data generation, with a specific case study in text-to-MIP instances. Further, we extend the proposed framework for text-to-SQL to demonstrate its generation ability towards structured data synthesis.

Operations Research (OR) is vital for decision-making in many industries. While recent OR methods have seen significant improvements in automation and efficiency through integrating Large Language Models (LLMs), they still struggle to produce meaningful explanations. This lack of clarity raises concerns about transparency and trustworthiness in OR applications. To address these challenges, we propose a comprehensive framework, Explainable Operations Research (EOR), emphasizing actionable and understandable explanations accompanying optimization. The core of EOR is the concept of Decision Information, which emerges from what-if analysis and focuses on evaluating the impact of complex constraints (or parameters) changes on decision-making. Specifically, we utilize bipartite graphs to quantify the changes in the OR model and adopt LLMs to improve the explanation capabilities. Additionally, we introduce the first industrial benchmark to rigorously evaluate the effectiveness of explanations and analyses in OR, establishing a new standard for transparency and clarity in the field.

By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals. With the advent of large language models (LLMs), new opportunities have emerged to automate the procedure of mathematical modeling. This survey presents a comprehensive and timely review of recent advancements that cover the entire technical stack, including data synthesis and fine-tuning for the base model, inference frameworks, benchmark datasets, and performance evaluation. In addition, we conducted an in-depth analysis on the quality of benchmark datasets, which was found to have a surprisingly high error rate. We cleaned the datasets and constructed a new leaderboard with fair performance evaluation in terms of base LLM model and datasets. We also build an online portal that integrates resources of cleaned datasets, code and paper repository to benefit the community. Finally, we identify limitations in current methodologies and outline future research opportunities.

Selecting an appropriate reasoning method for a given query remains a key challenge in language model generation. Existing approaches typically generate multiple candidate responses and use an aggregation strategy to select the output answer, often assuming that more candidate answers yield higher accuracy. We revisit this assumption through a rigorous theoretical analysis, deriving accuracy bounds for standard aggregation methods under fixed generation distributions and candidate sizes. Building on these insights, we introduce EPIC, an Ensemble Planning with Contrastive learning framework to learn a shared representation space that captures both model reasoning abilities and query-method compatibility. EPIC incorporates our probability bounds as a regularizer in a utility-driven optimization that balances accuracy and computational cost. Experiments on diverse mathematical reasoning tasks show that EPIC consistently selects optimal reasoning methods, improving accuracy while reducing computational overhead. Our code can be found at https://github.com/nguyenngocbaocmt02/EPIC.

Math Word Problem (MWP) is a crucial NLP task aimed at providing solutions for given mathematical descriptions. A notable sub-category of MWP is the Linear Programming Word Problem (LPWP), which holds significant relevance in real-world decision-making and operations research. While the recent rise of generative large language models (LLMs) has brought more advanced solutions to LPWPs, existing evaluation methodologies for this task still diverge from human judgment and face challenges in recognizing mathematically equivalent answers. In this paper, we introduce a novel evaluation metric rooted in graph edit distance, featuring benefits such as permutation invariance and more accurate program equivalence identification. Human evaluations empirically validate the superior efficacy of our proposed metric when particularly assessing LLM-based solutions for LPWP.

Large language models (LLMs) have emerged as powerful techniques for various NLP tasks, such as mathematical reasoning and plan generation. In this paper, we study automatic modeling and programming for complex operation research (OR) problems, so as to alleviate the heavy dependence on domain experts and benefit a spectrum of industry sectors. We present the first LLM-based solution, namely Chain-of-Experts (CoE), a novel multi-agent cooperative framework to enhance reasoning capabilities. Specifically, each agent is assigned a specific role and endowed with domain knowledge related to OR. We also introduce a conductor to orchestrate these agents via forward thought construction and backward reflection mechanism. Furthermore, we release a benchmark dataset (ComplexOR) of complex OR problems to facilitate OR research and community development. Experimental results show that CoE significantly outperforms the state-of-the-art LLM-based approaches both on LPWP and ComplexOR.

Verbal and visual-spatial information processing are two critical subsystems that activate different brain regions and often collaborate together for cognitive reasoning. Despite the rapid advancement of LLM-based reasoning, the mainstream frameworks, such as Chain-of-Thought (CoT) and its variants, primarily focus on the verbal dimension, resulting in limitations in tackling reasoning problems with visual and spatial clues. To bridge the gap, we propose a novel dual-modality reasoning framework called Vision-Augmented Prompting (VAP). Upon receiving a textual problem description, VAP automatically synthesizes an image from the visual and spatial clues by utilizing external drawing tools. Subsequently, VAP formulates a chain of thought in both modalities and iteratively refines the synthesized image. Finally, a conclusive reasoning scheme based on self-alignment is proposed for final result generation. Extensive experiments are conducted across four versatile tasks, including solving geometry problems, Sudoku, time series prediction, and travelling salesman problem. The results validated the superiority of VAP over existing LLMs-based reasoning frameworks.