problem formulation

Mathematical optimization modeling heavily relies on domain experts and suffers from low automation. Method: This work systematically investigates how large language models (LLMs) can empower automated mathematical modeling, focusing on data synthesis, instruction fine-tuning, reasoning framework design, benchmark construction, and evaluation methodology. To address pervasive labeling errors (>40%) in mainstream benchmarks (e.g., OptiMath, MOBench), we conduct the first large-scale manual verification and cleaning, yielding the high-quality OptiClean dataset. Contribution/Results: Based on OptiClean, we establish the first fair, reproducible automated modeling leaderboard; release an open-source repository integrating datasets, code, literature, and an online evaluation platform; and provide a standardized evaluation framework, reliable benchmark, and scalable technical paradigm for LLM-driven modeling automation—significantly advancing the field’s standardization and rigor.

Bilevel programming lacks a well-defined solution concept when multiple lower-level optimal solutions exist; existing optimistic/pessimistic formulations rely on strong assumptions—such as strict convexity or value attainability—that limit applicability. Method: Breaking free from continuity and value-attainability constraints, we systematically investigate the logical relationships and equivalence conditions among optimistic, pessimistic, and set-valued solution concepts within a set-valued optimization framework. Using tools from set-valued analysis, nonsmooth optimization, and variational geometry, we construct a unified comparative framework. Contribution/Results: We rigorously characterize the inclusiveness and limitations of these three solution paradigms. A key finding is that the set-valued formulation does not inherently outperform classical optimistic/pessimistic models in general settings; its theoretical advantages require additional structural assumptions. This work establishes rigorous criteria for selecting appropriate solution concepts in bilevel modeling, offering both theoretical foundations and practical guidance.

This work addresses the autoformulation problem—automatically translating natural-language problem descriptions into solvable mathematical optimization models. We propose the first LLM-driven Monte Carlo Tree Search (MCTS) framework for this task, enabling dynamic hypothesis generation and formal correctness evaluation. Our method integrates hierarchical optimization modeling representations, LLM-based semantic understanding, and MCTS-based search strategies. A key innovation is an equivalence-aware pruning mechanism that reduces search overhead by over 40%. Empirically, our approach achieves state-of-the-art performance on LP/MIP benchmarks, outperforming all existing baselines. LLM-assisted verification accelerates correctness assessment significantly. Moreover, this work formally defines the autoformulation task for the first time, establishing a scalable, automated paradigm to lower the barrier to optimization modeling and empower domain experts.

To address the accuracy bottleneck in automatic natural language-to-mixed-integer linear programming (NL-to-MILP) modeling—stemming from scarce high-quality annotated data and insufficient integration of domain expertise—this paper proposes an optimization-knowledge-enhanced large language model (LLM) framework. Our method comprises three core components: (1) a fine-grained, category-specific error analysis–driven data cleaning strategy; (2) a MILP-semantic-structured, class-aware multi-turn reasoning prompting framework; and (3) an iterative validation and refinement mechanism incorporating solver feedback. Extensive experiments across multiple foundational LLMs demonstrate an average 14.2-percentage-point improvement in modeling accuracy. Notably, robustness is significantly enhanced on critical subtasks—including complex constraint formulation and integer variable identification. The proposed approach establishes a new, interpretable, and solver-verified paradigm for AI-driven operations research modeling.

Existing approaches for identifying structured constraints—such as one-hot and special-ordered set (SOS) constraints—in mathematical optimization modeling suffer from low efficiency and poor robustness, especially when handling complex, nested algebraic expressions. Method: This paper proposes a symbolic-level constraint identification method based on e-graphs, pioneering the integration of the egg e-graph framework into industrial-grade optimization modeling systems. We design an algebraic congruence–driven heuristic rewriting system and develop egg_recursive, an open-source library supporting recursive abstract syntax tree (AST) representations to simplify maintenance of complex S-expressions. Contribution/Results: The method is implemented and deployed in JijModeling, significantly improving constraint identification accuracy and generalization across diverse modeling patterns. Benchmark evaluations demonstrate a 3.2× speedup in preprocessing time. The approach has been successfully applied to real-world quantum and hybrid optimization tasks, validating its engineering practicality, scalability, and production readiness.

This work addresses the problem of solving quantified constraints over the reals, involving existentially quantified parameters (user-specified) and universally quantified parameters (representing unknown or infinitely many scenario configurations). To overcome limitations in modeling expressiveness, systematic taxonomy, and cross-domain adaptability of existing approaches, we propose—firstly—a principled application classification scheme and literature indexing framework tailored to real-valued quantified constraints. Methodologically, we integrate Satisfiability Modulo Theories (SMT) over real arithmetic, quantifier elimination, interval analysis, and symbolic computation to enhance solver robustness and scalability. The contributions include an open, domain-spanning literature repository covering mathematics, control theory, formal verification, and optimization; standardized problem templates; and a publicly available benchmark suite. These advances significantly facilitate the engineering deployment of quantified reasoning tools within formal methods.

This work addresses the lack of systematic methodologies in model optimization, which often relies on heuristic choices and struggles to accommodate diverse deployment constraints. It formalizes model compression and acceleration as a constraint-aware multi-objective engineering decision problem, establishing a unified and actionable framework grounded in five key dimensions: data availability, latency, memory footprint, accuracy tolerance, and retraining budget. By integrating techniques such as quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference optimization, the study proposes tailored optimization pipelines for four representative industrial scenarios, delivering a reproducible and quantifiable guide for technology selection.

This work proposes a multi-agent collaborative framework that automatically translates natural language descriptions of operations research problems into solvable mathematical models and executable code. To address common modeling challenges—such as semantic misinterpretation, structural flaws, and mathematical inconsistencies—the approach employs specialized agents to extract decision variables and constraints, integrating structured information extraction, iterative self-correction, and a fourfold feedback validation mechanism to achieve end-to-end modeling. Its modular architecture enhances transparency and auditability throughout the modeling process. Evaluated on four standard benchmarks encompassing linear programming (LP), mixed-integer linear programming (MILP), and nonlinear programming, the method achieves state-of-the-art performance on three and demonstrates highly competitive results on the fourth.

Current large language models lack mechanisms to verify the structural soundness and solution validity of automatically generated mathematical optimization models, which limits their modeling accuracy. This work proposes Opt-Verifier, a novel framework that introduces a dual-loop verification mechanism by jointly assessing generated models along two dimensions: structural consistency and solution validity. By enforcing rigorous cross-checks between model formulation and feasible solutions, Opt-Verifier significantly enhances the logical coherence and mathematical correctness of the generated models. Empirical evaluations on standard benchmarks demonstrate that this approach improves modeling accuracy by over 20%, establishing a new paradigm for reliable automated optimization modeling.

This work addresses the challenge of large-scale automated translation of informal mathematical textbooks into machine-verifiable formal content. We propose AutoformBot, a multi-agent system comprising thousands of large language model agents equipped with Lean 4 verification tools, which leverages dependency-aware task scheduling and collaborative version control to achieve fully automated formalization of 26 graduate-level textbooks spanning analysis, algebra, topology, and related fields. The resulting Atlas formal mathematics library comprises over 45,000 theorem statements and 500,000 lines of Lean 4 code, demonstrating for the first time the technical and economic feasibility of large-scale automatic formalization of advanced mathematics. The complete framework and dataset are released as open-source resources.

Existing benchmarks struggle to evaluate the ability of large language models to perform end-to-end optimization tasks in real-world business settings. This work proposes the first comprehensive end-to-end evaluation benchmark that spans business requirement interpretation, mathematical modeling, algorithm selection, code implementation, and report generation. It introduces three key innovations: business-semantic anti-template traps, cross-module consistency checks, and a dual-layer ORAC validity verification framework, covering core optimization paradigms such as integer programming, robust optimization, stochastic programming, and non-convex optimization. Experiments reveal systematic deficiencies in current models—including omitted constraints and inconsistencies between formulated models and generated code—that remain undetected under conventional single-metric evaluations, thereby demonstrating the necessity and effectiveness of this benchmark for assessing complex, multi-stage optimization workflows.