ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization
arXiv:2602.22465v1 Announce Type: new 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 bottlene
arXiv:2602.22465v1 Announce Type: new 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% constraint satisfaction, 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 83.3% in the production mix 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.
Executive Summary
This article introduces ConstraintBench, a benchmark designed to evaluate Large Language Models (LLMs) on their ability to directly produce correct solutions to fully specified constrained optimization problems without access to a solver. The study evaluates six frontier models on 200 tasks across 10 operations research domains and finds that feasibility is the primary bottleneck, with the best model achieving only 65.0% constraint satisfaction. However, feasible solutions average 89 to 96% of the Gurobi-optimal objective. The study highlights large variation in difficulty across domains and identifies systematic failure modes, including duration constraint misunderstanding and entity hallucination. The authors' findings suggest that LLMs still have a long way to go in terms of constrained optimization, but the development of ConstraintBench provides a valuable tool for advancing this research.
Key Points
- ▸ ConstraintBench is a benchmark designed to evaluate LLMs on direct constrained optimization
- ▸ Feasibility is the primary bottleneck for LLMs in constrained optimization
- ▸ Large variation in difficulty exists across different operations research domains
Merits
Strength in Design
ConstraintBench is a well-designed benchmark that specifically targets the ability of LLMs to directly produce correct solutions to constrained optimization problems.
Comprehensive Evaluation
The study evaluates six frontier models on 200 tasks across 10 operations research domains, providing a comprehensive understanding of the capabilities and limitations of LLMs in constrained optimization.
Demerits
Limited Generalizability
The study is limited to a specific set of operations research domains and may not generalize to other areas of application.
Need for Further Research
The study highlights the need for further research in constrained optimization, particularly in addressing the identified systematic failure modes.
Expert Commentary
The development of ConstraintBench is a significant step forward in evaluating the performance of LLMs in constrained optimization. However, the study's findings also highlight the need for further research in addressing the systematic failure modes identified in the study. Specifically, the study highlights the need for research in developing more robust LLMs that can accurately understand duration constraints and avoid entity hallucination. Additionally, the study's findings have implications for the development of more effective optimization algorithms that can take into account the limitations of LLMs in constrained optimization. Overall, the study provides a valuable contribution to the field of constrained optimization and highlights the importance of continued research in this area.
Recommendations
- ✓ Develop more robust LLMs that can accurately understand duration constraints and avoid entity hallucination
- ✓ Investigate the development of more effective optimization algorithms that can take into account the limitations of LLMs in constrained optimization
