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.

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers mainly focus on end-to-end solution learning, which suffers from the scalability issue due to the high dimensionality of the solution space. Instead of directly learning the optimal solution, this paper aims to learn a reduced and equivalent model of the original MILP as an intermediate step. The reduced model often corresponds to interpretable operations and is much simpler, enabling us to solve large-scale MILP problems much faster than existing commercial solvers. However, current approaches rely only on the optimal reduced model, overlooking the significant preference information of all reduced models. To address this issue, this paper proposes a preference-based model reduction learning method, which considers the relative performance (i.e., objective cost and constraint feasibility) of all reduced models on each MILP instance as preferences. We also introduce an attention mechanism to capture and represent preference information, which helps improve the performance of model reduction learning tasks. Moreover, we propose a SetCover based pruning method to control the number of reduced models (i.e., labels), thereby simplifying the learning process. Evaluation on real-world MILP problems shows that 1) compared to the state-of-the-art model reduction ML methods, our method obtains nearly 20% improvement on solution accuracy, and 2) compared to the commercial solver Gurobi, two to four orders of magnitude speedups are achieved.

Teng Wang, Wing Yin Yu, Zhenqi He, Zehua Liu, HaileiGong HaileiGong, Han Wu, Xiongwei Han, Wei Shi, Ruifeng She, Fangzhou Zhu, Tao Zhong. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

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.

Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. Solving realistic optimization (OPT) problems in application scenarios requires advanced and applied mathematics ability. However, current OPT benchmarks that merely solve linear programming are far from complex realistic situations. In this work, we propose **OptiBench**, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs. **OptiBench** contains rich optimization problems, including linear and nonlinear programming with or without tabular data, which can comprehensively evaluate LLMs' solving ability. In our benchmark, LLMs are required to call a code solver to provide precise numerical answers. Furthermore, to alleviate the data scarcity for optimization problems, and to bridge the gap between open-source LLMs on a small scale (e.g., Llama-3-8b) and closed-source LLMs (e.g., GPT-4), we further propose a data synthesis method namely ***ReSocratic***. Unlike general data synthesis methods that proceed from questions to answers, \ReSocratic first incrementally synthesizes formatted optimization demonstration with mathematical formulations step by step and then back-translates the generated demonstrations into questions. Based on this, we synthesize the ***ReSocratic-29k*** dataset. We further conduct supervised fine-tuning with ***ReSocratic-29k*** on multiple open-source models. Experimental results show that ***ReSocratic-29k*** significantly improves the performance of open-source models.

Large language models (LLMs) exhibit varying strengths and weaknesses across different tasks, prompting recent studies to explore the benefits of ensembling models to leverage their complementary advantages. However, existing LLM ensembling methods often overlook model compatibility and struggle with inefficient alignment of probabilities across the entire vocabulary. In this study, we empirically investigate the factors influencing ensemble performance, identifying model performance, vocabulary size, and response style as key determinants, revealing that compatibility among models is essential for effective ensembling. This analysis leads to the development of a simple yet effective model selection strategy that identifies compatible models. Additionally, we introduce the \textsc{Uni}on \textsc{T}op-$k$ \textsc{E}nsembling (\textsc{UniTE}), a novel approach that efficiently combines models by focusing on the union of the top-k tokens from each model, thereby avoiding the need for full vocabulary alignment and reducing computational overhead. Extensive evaluations across multiple benchmarks demonstrate that \textsc{UniTE} significantly enhances performance compared to existing methods, offering a more efficient framework for LLM ensembling.

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.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10% improvements on the challenging benchmarks.

Recent research has increasingly focused on reconciling the reasoning capabilities of System 2 with the efficiency of System 1. While existing training-based and prompt-based approaches face significant challenges in terms of efficiency and stability, model merging emerges as a promising strategy to integrate the diverse capabilities of different Large Language Models (LLMs) into a unified model. However, conventional model merging methods often assume uniform importance across layers, overlooking the functional heterogeneity inherent in neural components. To address this limitation, we propose \textbf{A}ctivation-Guided \textbf{C}onsensus \textbf{M}erging (\textbf{ACM}), a plug-and-play merging framework that determines layer-specific merging coefficients based on mutual information between activations of pre-trained and fine-tuned models. ACM effectively preserves task-specific capabilities without requiring gradient computations or additional training. Extensive experiments on Long-to-Short (L2S) and general merging tasks demonstrate that ACM consistently outperforms all baseline methods. For instance, in the case of Qwen-7B models, TIES-Merging equipped with ACM achieves a \textbf{55.3\%} reduction in response length while simultaneously improving reasoning accuracy by \textbf{1.3} points. We submit the code with the paper for reproducibility, and it will be publicly available.

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.

Recent advances in natural language processing, primarily propelled by Large Language Models (LLMs), have showcased their remarkable capabilities grounded in in-context learning. A promising avenue for guiding LLMs in intricate reasoning tasks involves the utilization of intermediate reasoning steps within the Chain-of-Thought (CoT) paradigm. Nevertheless, the central challenge lies in the effective selection of exemplars for facilitating in-context learning. In this study, we introduce a framework that leverages Dual Queries and Low-rank approximation Re-ranking (DQ-LoRe) to automatically select exemplars for in-context learning. Dual Queries first query LLM to obtain LLM-generated knowledge such as CoT, then query the retriever to obtain the final exemplars via both question and the knowledge. Moreover, for the second query, LoRe employs dimensionality reduction techniques to refine exemplar selection, ensuring close alignment with the input question's knowledge. Through extensive experiments, we demonstrate that DQ-LoRe significantly outperforms prior state-of-the-art methods in the automatic selection of exemplars for GPT-4, enhancing performance from 92.5\% to 94.2\%. Our comprehensive analysis further reveals that DQ-LoRe consistently outperforms retrieval-based approaches in terms of both performance and adaptability, especially in scenarios characterized by distribution shifts. DQ-LoRe pushes the boundaries of in-context learning and opens up new avenues for addressing complex reasoning challenges.

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.

An algebraic modeling system (AMS) is a type of mathematical software for optimization problems, which allows users to define symbolic mathematical models in a specific language, instantiate them with given source of data, and solve them with the aid of external solver engines. With the bursting scale of business models and increasing need for timeliness, traditional AMSs are not sufficient to meet the following industry needs: 1) million-variable models need to be instantiated from raw data very efficiently; 2) Strictly feasible solution of million-variable models need to be delivered in a rapid manner to make up-to-date decisions against highly dynamic environments. Grassland is a rapid AMS that provides an end-to-end solution to tackle these emerged new challenges. It integrates a parallelized instantiation scheme for large-scale linear constraints, and a sequential decomposition method that accelerates model solving exponentially with an acceptable loss of optimality. Extensive benchmarks on both classical models and real enterprise scenario demonstrate 6-10x speedup of Grassland over state-of-the-art solutions on model instantiation. Our proposed system has been deployed in the large-scale real production planning scenario of Huawei. With the aid of our decomposition method, Grassland successfully accelerated Huawei's million-variable production planning simulation pipeline from hours to 3-5 minutes, supporting near-real-time production plan decision making against highly dynamic supply-demand environment.