Improving Constraint Models with LLM Agents

• URL: http://arxiv.org/abs/2608.08127v1
• Date: Sat, 08 Aug 2026 13:22:30 GMT
• Title: Improving Constraint Models with LLM Agents
• Abstract summary: We introduce an agentic framework that reformulates a constraint model from an open-ended space and establishes correctness empirically rather than by construction.<n>A Large Language Model (LLM) agent, given a model and three training instances, proposes alternative formulations, validates each by injecting its solution back into the original model.<n>Across nine optimization problems, the generated models outperform the originals on 21 of 27 test instances, and on some problems solve more than two orders of magnitude faster.
• Score: 23.96475985648844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The runtime of Constraint Programming (CP) solvers is highly sensitive to modeling choices, such as symmetry breaking, implied constraints, global constraints, constraint reformulation, and variable representation. Improving these constraint models has traditionally required human expertise, and existing automated reformulation systems are restricted to a predefined library of hand-crafted transformation rules. We introduce an agentic framework that instead reformulates a constraint model from an open-ended space and establishes correctness empirically rather than by construction: a Large Language Model (LLM) agent, given a model and three training instances, proposes alternative formulations, validates each by injecting its solution back into the original model, and diagnoses and repairs failures, returning the best variant it finds in a median of about fifteen minutes. The models are expressed in the CPMpy modeling library, and each proposed model is evaluated on three larger test instances. Across nine combinatorial optimization problems, the generated models outperform the originals on 21 of 27 test instances, and on some problems solve more than two orders of magnitude faster. A comparison against non-agentic baselines that reuse the same validation and selection tools indicates that the gains stem from the agent's iterative diagnosis and repair, not merely from sampling several candidates. These results demonstrate that autonomous agentic methods can support the improvement of constraint models.

Related papers

• LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency [5.774119507201688]
  Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve.<n>We use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model.<n>Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context.<n>We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection.
  arXiv  Detail & Related papers  (2026-07-30T14:21:55Z)
• Model-Driven Discipline for Multi-Agent LLMs: Requirement-to-Verification Generation of Traceable System Models [62.62160094849002]
  RADIANT is an engineering methodology that combines MDE with Multi-Agent Large Language Models.<n>It automatically generates heterogeneous models across engineering phases.<n>It provides exact, automated change-impact analysis.
  arXiv  Detail & Related papers  (2026-07-18T08:50:55Z)
• Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification [53.763212981479455]
  We propose a novel framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives.<n> Experiments on popular benchmarks demonstrate that our approach achieves over 20% improvement in accuracy.
  arXiv  Detail & Related papers  (2026-05-28T08:09:52Z)
• MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research [15.28095645151852]
  MIRROR is a fine-tuning-free, end-to-end multi-agent framework for operations research.<n>It translates natural language optimization problems into mathematical models and solver code.<n>Experiments show that MIRROR outperforms existing methods on standard Operations Research benchmarks.
  arXiv  Detail & Related papers  (2026-02-03T09:46:56Z)
• Composition and Alignment of Diffusion Models using Constrained Learning [79.36736636241564]
  Diffusion models have become prevalent in generative modeling due to their ability to sample from complex distributions.<n>Two commonly used methods are: (i) alignment, which involves fine-tuning a diffusion model to align it with a reward; and (ii) composition, which combines several pre-trained diffusion models, each emphasizing a desirable attribute in the generated outputs.<n>We propose a constrained optimization framework that unifies alignment and composition of diffusion models by enforcing that the aligned model satisfies reward constraints and/or remains close to (potentially multiple) pre-trained models.
  arXiv  Detail & Related papers  (2025-08-26T15:06:30Z)
• CP-Bench: Evaluating Large Language Models for Constraint Modelling [6.250460397062786]
  Constraint programming (CP) is widely used to solve problems, but its core process, namely constraint modelling, requires significant expertise and is considered to be a bottleneck for wider adoption.<n>Recent studies have explored using Large Language Models (LLMs) to transform problem descriptions into executable constraint models.<n>Existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios.<n>This work addresses this gap by introducing CP-Bench, a novel benchmark that includes a diverse set of well-known problems sourced from the CP community, structured
  arXiv  Detail & Related papers  (2025-06-06T12:56:02Z)
• EMR-Merging: Tuning-Free High-Performance Model Merging [55.03509900949149]
  We show that Elect, Mask & Rescale-Merging (EMR-Merging) shows outstanding performance compared to existing merging methods. EMR-Merging is tuning-free, thus requiring no data availability or any additional training while showing impressive performance.
  arXiv  Detail & Related papers  (2024-05-23T05:25:45Z)
• Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures [14.551812310439004]
  We introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass.
  arXiv  Detail & Related papers  (2024-03-07T19:02:13Z)
• When to Update Your Model: Constrained Model-based Reinforcement Learning [50.74369835934703]
  We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL) Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
  arXiv  Detail & Related papers  (2022-10-15T17:57:43Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.