ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization

• URL: http://arxiv.org/abs/2602.22465v2
• Date: Fri, 27 Feb 2026 16:43:01 GMT
• Title: ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization
• Abstract summary: We introduce ConstraintBench, a benchmark for evaluating large language models on direct constrained optimization.<n>We evaluate six frontier models on 200 tasks and find that feasibility, not optimality, is the primary bottleneck.<n>No model exceeds 30.5% on joint feasibility and optimality within 0.1% of the solver reference.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models are increasingly applied to operational decision-making where the underlying structure is constrained optimization. Existing benchmarks evaluate whether LLMs can formulate optimization problems as solver code, but leave open a complementary question. Can LLMs directly produce correct solutions to fully specified constrained optimization problems without access to a solver? We introduce ConstraintBench, a benchmark for evaluating LLMs on direct constrained optimization across 10 operations research domains, with all ground-truth solutions verified by the Gurobi solver. Each task presents a natural-language scenario with entities, constraints, and an optimization objective; the model must return a structured solution that a deterministic verifier checks against every constraint and the solver-proven optimum. We evaluate six frontier models on 200 tasks and find that feasibility, not optimality, is the primary bottleneck. The best model achieves only 65.0% feasibility, yet feasible solutions average 89 to 96% of the Gurobi-optimal objective. No model exceeds 30.5% on joint feasibility and optimality within 0.1% of the solver reference. Per-domain analysis shows large variation in difficulty, with average feasibility spanning from 85.0% in the facility location domain to 0.8% in the crew assignment domain. Further, systematic failure modes include duration constraint misunderstanding, entity hallucination, and a feasibility-optimality decoupling in facility location and vehicle routing where models achieve high feasibility but 0% optimality. ConstraintBench and all evaluation infrastructure will be publicly released.

Related papers

• AlgoWorlds: Benchmarking Tool Use for Global Optimization in Algorithmic Worlds [58.529749203758634]
  Tool-use benchmarks generally evaluate whether an agent completes a workflow using appropriate tools and valid arguments.<n>We introduce AlgoWorlds, a benchmark that transforms formally specified optimization problems into partially observed decision environments.<n>AlgoWorlds contains 240 environments covering ten optimization families and four workload levels.
  arXiv  Detail & Related papers  (2026-08-29T18:37:41Z)
• FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization [61.43300970020897]
  Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation.<n>Existing benchmarks are limited to small or simplified examples far below real-world scale and complexity.<n>We introduce FrontierOR, among the first benchmarks to evaluate LLM-based efficient algorithm design for realistic large-scale optimization problems.
  arXiv  Detail & Related papers  (2026-05-24T20:10:42Z)
• Execution-Verified Reinforcement Learning for Optimization Modeling [49.171122807323634]
  Execution-verified learning framework treats a mathematical programming solver as a deterministic, interactive verifier.<n>Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that EVOM matches or outperforms process-supervised SFT.
  arXiv  Detail & Related papers  (2026-04-01T03:39:11Z)
• ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference [60.958331943869126]
  ODAR-Expert is an adaptive routing framework that optimize the accuracy-efficiency trade-off via principled resource allocation.<n>We show strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam.
  arXiv  Detail & Related papers  (2026-02-27T05:22:01Z)
• Hard Constraints Meet Soft Generation: Guaranteed Feasibility for LLM-based Combinatorial Optimization [14.17648636921649]
  We introduce FALCON, a framework that ensures 100% feasibility through three key innovations.<n>FALCON achieves perfect feasibility while matching or exceeding the solution quality of state-of-the-art neural and LLM-based solvers.
  arXiv  Detail & Related papers  (2026-02-01T08:09:06Z)
• Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation [0.0]
  We present a component-level evaluation framework for large language models (LLMs)<n>We evaluate GPT-5, LLaMA 3.1 Instruct, and DeepSeek Math across optimization problems of varying complexity.<n>Results show GPT-5 consistently outperforms other models, with chain-of-thought, self-consistency, and modular prompting proving most effective.
  arXiv  Detail & Related papers  (2025-10-19T17:47:59Z)
• OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling [3.8366697175402225]
  We introduce OptiHive, a framework that produces high-quality solvers for optimization problems from natural-correction descriptions without iterative self-language.<n>OptiHive uses a single batched LLM query to generate diverse components (solvers, problem instances, and validation tests) and filters out erroneous components to ensure fully interpretable outputs.<n>On tasks ranging from traditional optimization problems to challenging variants of the Multi-Depot Vehicle Routing Problem, OptiHive significantly outperforms baselines.
  arXiv  Detail & Related papers  (2025-08-04T15:11:51Z)
• Feasibility-Driven Trust Region Bayesian Optimization [0.048748194765816946]
  FuRBO iteratively defines a trust region from which the next candidate solution is selected.<n>We empirically demonstrate the effectiveness of FuRBO through extensive testing on the full BBOB-constrained benchmark suite.
  arXiv  Detail & Related papers  (2025-06-17T15:16:22Z)
• MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliability [11.997050225896679]
  We propose a unified optimization framework that directly solves the primal constrained optimization problem to identify optimal subgroups.<n>Our key innovation is a reformulation of the constrained primal problem as an unconstrained differentiable min-max objective, solved via a gradient descent-ascent algorithm.<n>The framework is model-agnostic, compatible with a wide range of CATE estimators, and propensity to additional constraints like cost limits or fairness criteria.
  arXiv  Detail & Related papers  (2025-04-29T16:25:23Z)
• Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization [78.82586283794886]
  $chi2$-Preference Optimization ($chi$PO) is an efficient offline alignment algorithm provably robust to overoptimization.<n>$chi$PO implements the principle of pessimism in the face of uncertainty via regularization.<n>$chi$PO's simplicity and strong guarantees make it the first practical and general-purpose offline alignment algorithm provably robust to overoptimization.
  arXiv  Detail & Related papers  (2024-07-18T11:08:40Z)
• OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling [62.19438812624467]
  Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning.<n>We propose OptiBench, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs.
  arXiv  Detail & Related papers  (2024-07-13T13:27:57Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Extracting Optimal Solution Manifolds using Constrained Neural Optimization [6.800113407368289]
  Constrained Optimization solution algorithms are restricted to point based solutions. We present an approach for extracting optimal sets as approximate, where unmodified non-informed constraints are defined.
  arXiv  Detail & Related papers  (2020-09-13T15:37:44Z)
• Optimizing Wireless Systems Using Unsupervised and Reinforced-Unsupervised Deep Learning [96.01176486957226]
  Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems.
  arXiv  Detail & Related papers  (2020-01-03T11:01:52Z)

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.