Junbo Jacob Lian, Huiling Chen, Hanzhang Qin +1cs.AI
Experience-learning agents for optimization modeling improve by storing verified skills, but existing learners admit knowledge by checking against known answers, which real ticket streams do not provide. The natural label-free alternatives are unreliable: on a 300-problem label-blind stream, admitting every executable model poisons roughly one admission in four, while single-instance agreement accepts models that match at one value but differ elsewhere. We propose AdmitOR, an admission gate built on calibrated external behavioral evidence. Candidates from three model families, prompting strategies, and solver stacks are run on instances resampled from an extracted parameter domain; agreement across the resulting value-function traces is summarized by a cross-family clique, and a calibrated threshold returns accept, abstain, or escalate. The preregistered false-discovery criterion holds on calibration data but not on the wild stream. We report this negative result in full and trace most failures to benchmark texts that do not faithfully encode their labeled instances. Comparing four admission judges on one collection of logs inside a state-of-the-art skill learner, AdmitOR raises admission precision to 0.927, against 0.871 for majority vote and 0.726 for execution success, yielding 3.1x and 8.0x fewer poisoned admissions. Its library is the smallest and attains the highest macro accuracy across five public benchmarks, 58.4 against 54.8 for majority vote and 53.9 for the ground-truth-labeled library. The 3.5-point gain over majority vote is supported by a paired bootstrap and survives correction for a host-side anomaly. To our knowledge, AdmitOR is the first label-free admission mechanism designed around an explicitly calibrated false-discovery target. The transfer failure identifies a necessary condition for extending it to wild streams.
Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations. While recent works have leveraged LLMs to automate optimization modeling, current frameworks predominantly rely on a rigid mixed-integer linear programming (MILP) paradigm. In this paper, we argue that not all problems are best modeled as MILP, as forcing complex domains into linear constraints can induce prohibitive modeling complexity and severely restrict solver flexibility. To address this, we propose OptiDSL, a framework that shifts the focus from rigid MILP formulations to domain-specific language (DSL) representations. By utilizing LLMs to map natural language onto standardized, domain-accepted structures, OptiDSL decouples problem formulation from execution. This paradigm enables seamless integration with a diverse library of specialized solvers, ranging from traditional heuristics to modern learning-based methods. Experimental results on the comprehensive benchmark of 44 COP types show that OptiDSL significantly surpasses MILP-based pipelines, yielding a 51.66% gain in formulation accuracy and a 91.71% decrease in modeling time. Notably, it also outperforms MILP-based pipelines on the existing benchmark, achieving a 23.09% higher formulation accuracy. Our code is available at https://anonymous.4open.science/r/OptiDSL.
Large language models (LLMs) can translate natural-language optimization problems into solver-ready formulations, but direct code generation is brittle: schema, indexing, and semantic errors can cause compilation failures, infeasible models, or incorrect objectives, while iterative repair, search, and multi-agent workflows increase inference cost. We present IR2Solve, an intermediate-representation-first autoformulation pipeline that uses a single semantic LLM call to produce a schema-constrained ModelIR, followed by two deterministic stages: verification and IR-to-solver compilation. ModelIR explicitly represents sets, parameters, variables, objectives, and constraints using restricted Python-like expression strings. A concrete scalar-constraint convention represents finite per-index constraint families as individual entries, reducing free-index and implicit-quantification errors while simplifying downstream verification and compilation. Across six cleaned optimization benchmarks, IR2Solve achieves strong objective correctness and remains competitive with recent optimization-modeling systems. A controlled ablation on 153 IndustryOR and ComplexLP instances shows sequential gains from the structured IR interface, the scalar-constraint instruction, and deterministic verification. On a matched ten-instance cost panel, IR2Solve uses one semantic call per instance, whereas Chain-of-Experts and SAC-Opt use 8 and 39 calls per instance and consume 3.3 and 22.9 times the token volume of IR2Solve, respectively. These results show that structured intermediate representations, combined with deterministic post-generation processing, provide a practical accuracy-cost trade-off for LLM-based optimization autoformulation.
Adriana Laurindo Monteiro, Nayse Fagundes, Gabriel Mattos Langeloh +4cs.AI cs.MA
We propose OptiAgent, a multi-agent framework that, given a natural language description of an Operations Research problem, is able to output a solver-ready mathematical formulation as well as executable code. Our architecture prioritizes the mathematical modeling step, where dedicated agents extract structures, such as decision variables and constraints, enabling iterative self-correction. We introduce a novel multi-loop validation architecture with four specialized feedback mechanisms, each targeting a distinct failure mode such as misinterpretation, structural defects, mathematical inconsistencies, validation failures, and code errors. Alongside accuracy, our modular design improves the process of solving optimization problems by improving transparency, as each agent exposes its reasoning and feedback, making the full modeling process auditable. Our framework achieves state-of-the-art performance on 3 out of 4 benchmarks across LP, MILP, and Nonlinear Programming tasks, while remaining highly competitive on the remaining dataset.
Automating optimization modeling from natural language with large language models (LLMs) faces two key challenges. First, training corpora lack structural diversity. Second, data generation pipelines remain static and decoupled from model learning. To address these challenges, we propose EvoOptiGraph, a novel framework where data and model co-evolve, driven by model weaknesses. EvoOptiGraph represents each mixed-integer linear program (MILP) as an attributed bipartite graph and applies validity-preserving evolutionary operators to generate structurally diverse instances. The evolved graphs are converted into solver code and natural language via deterministic compilation and verified back-translation. Training proceeds in two stages: supervised fine-tuning (SFT) on an initial dataset, followed by reinforcement learning with verifiable rewards (RLVR), where graph-derived weakness signals guide the generation of new instances targeting the model's failures. This forms a closed loop that continuously updates the training distribution. Empirical results on six public datasets show that EvoOptiGraph significantly outperforms larger generalist models, agentic methods, and specialized baselines in accuracy, executability, and generalization. These results demonstrate that targeted data-model coevolution is an effective strategy for improving LLMs on optimization modeling tasks.
Both optimization modeling and constraint modeling are non-trivial problems requiring deep domain expertise and proficiency in modeling formalism languages. Despite their importance across logistics, healthcare, and supply chain management, current large language models regularly produce structurally inconsistent or incomplete optimization formulations, particularly in combinatorial settings. This paper evaluates whether a Retrieval-Augmented Generation pipeline built on a curated synthetic dataset can meaningfully improve LLM optimization modeling performance. A total of 500 optimization problems were synthesized using seed descriptions from the Text2Zinc dataset and professional personas created using an LLM, specified in JSON and associated with validated Python solver scripts. These problems were encoded in a Chroma vector database. For each inference problem, semantically similar problems were retrieved and used as contextual guidance for a LangChain LLM agent. Three benchmark testbeds were used to evaluate the proposed pipeline under the Qwen 3 30B Instruct model. Accuracy rose from 40% to 72% on NL4OPT, 40% to 56% on MAMO Easy, and 32% to 56% on MAMO Complex. The use of semantically validated synthetic examples greatly improves both solution accuracy and structure. The combination of synthetic dataset generation with retrieval augmentation provides an effective alternative to fine-tuning, suggesting that domain-specific synthetic corpora paired with retrieval augmentation can serve as a practical pathway for deploying LLM-based optimization tools in real-world decision-support contexts without costly model retraining.
Optimization modeling is inherently hierarchical, requiring a precise sequence of symbolic commitments. Traditional learning-based automated optimization modeling methods improve modeling policies through large-scale annotated or curated training data, but are costly to adapt to new problem distributions. Meanwhile, one-shot generation remains brittle in hierarchical modeling, where early symbolic errors can propagate into invalid formulations. Test-time scaling offers a promising alternative by enabling structural exploration with additional instance-level computation; however, existing search-based methods typically rely on a fixed policy, causing repeated rollouts to inherit similar modeling biases and providing limited credit assignment for intermediate decisions. To address these limitations, we propose StarOR, a synergistic search-and-adaptation framework that couples MCTS with Test-Time Reinforcement Learning for optimization modeling. StarOR decomposes the modeling process into four stages and updates a transient LoRA adapter via GRPO at each non-terminal node. By using MCTS-generated siblings as local comparison sets, StarOR transforms search-time exploration into instance-specific policy refinement. Moreover, an unsupervised multi-faceted reward system provides fine-grained feedback for intermediate formulation decisions without ground-truth labels. Experiments across five optimization benchmarks show that StarOR achieves state-of-the-art performance even with a 4B backbone, outperforming existing methods and the frontier LLMs.
Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code. Yet for constraint-dense operations research (OR) problems, existing data-filtering and training pipelines largely rely on objective-equivalence signals such as differential testing and answer agreement, which a program can pass while adding spurious constraints or silently omitting required ones, whenever those constraints are non-binding on the tested instance. We propose constraint injection, which uses feasible probes to expose spurious over-constraint and one-constraint-violating probes to reveal silent constraint omission. Combined with differential testing, it forms a dual verifier. We instantiate and evaluate it on vehicle routing problems (VRPs), a representative constraint-dense combinatorial optimization testbed with coupled operational constraints. We develop VRPCoder, an 8B end-to-end model that translates natural-language VRP scenarios into Gurobi scripts, together with an expert-verified VRP benchmark suite covering 21 variants. The verifier is reused as a rejection-sampling filter during data synthesis and as a per-rollout reward in group relative policy optimization (GRPO). Across four VRP benchmarks, VRPCoder-GRPO reaches 93\% average Pass@1, outperforms Gemini-3.1-Pro Preview on three benchmarks, exceeds Claude-Sonnet-4.5 by 28 average points, and surpasses prior OR-LLMs by 78 average points.
This paper presents ORPilot, an open-source agentic AI system that translates real-world business problems into solver-ready optimization models. Unlike academic LLM-for-OR tools that assume clean problem specifications with preformatted inline data, ORPilot is designed for production conditions: ambiguous descriptions, large-scale raw operational data, and the need for portability across solver backends. The system introduces four novel components: (1) a conversational interview agent to elicit complete problem specifications, (2) a data collection agent that retrieves data independently of prompts, (3) a parameter computation agent to bridge raw tabular data and model-ready parameters, and (4) a solver-agnostic Intermediate Representation (IR) for deterministic, zero-LLM-call recompilation to Gurobi, CPLEX, PuLP, Pyomo, or OR-Tools solvers. Additionally, self-correcting retry loops utilize solver tracebacks for targeted repairs. ORPilot represents the first attempt to target production-level business problems rather than textbook operations research (OR) cases. Evaluation on real-world problems demonstrates promising results. When tested against traditional academic benchmarks: IndustryOR, NL4OPT and NLP4LP, ORPilot outperformed state-of-the-art tools in accuracy on the IndustryOR benchmark and delivered comparable performance on NL4OPT and NLP4LP.
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.
Jianghao Lin, Zi Ling, Chenyu Zhou +4math.OC cs.AI cs.LG
Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose \emph{Agora-Opt}, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.