Advances in reasoning, coding, and tool use enable LLM agents to solve operations research (OR) problems through iterative problem modeling, program construction, and verification. Yet passing self-authored verification does not ensure that the solutions satisfy task constraints and meet optimization quality. This gap can arise from correlated specification errors, where the generated program and its checks share omissions or misinterpretations of task requirements, alongside incomplete verification coverage and ineffective optimization strategies. We propose VERAS, a verification-guided adaptive search harness for reliable OR that uses verification evidence to prioritize feasibility repair, constraint-coverage review, and solution-quality improvement. VERAS combines task-specific solution checkers with a separate verification agent to examine candidate solutions against the task requirements. It uses verification feedback to guide feasibility repair, additional constraint checking, and objective improvement, while candidate acceptance criteria screen revisions for deterioration in output validity or constraint satisfaction. On ORAgentBench, VERAS achieves a 42.99% pass rate, exceeding the reported 35.51% of Codex using the same LLM. Across two industrial-scale OR problems, VERAS reduces inter-datacenter peak bandwidth by 10.34% relative to native Codex and lowers annualized distribution network planning costs by 6.28% compared with expert-designed solutions. Code and evidence are available at https://github.com/holimario/VERAS.
Figures & tables
Figure 1: Correlated specification errors in OR agent. The optimization objective (yellow), the task constraints (green). The solver program and its self-authored verification both omit cross-room equipment occupancy, allowing an infeasible schedule to pass internal checks but failing in independent evaluation.
Figure 2: Overview of the Veras framework. A coding agent constructs and executes OR programs, while task-grounded verification guides conditional refinement, and verification-filtered updates retain accepted candidates.
Table 1: Main results on ORAgentBench (107 tasks). Overall feasibility and quality are task-count-weighted across the easy, medium, and hard splits. Rows are grouped by harness and ordered by Overall pass rate within each group (ties are broken by Overall quality). Bold and underline denote the best and second-best results in each column, respectively.
Figure 3: Ablation study on six Hard tasks. (a) Feasibility and pass outcomes across variates. (b) Mean normalized solution quality. VERAS reports the frozen original evaluation results.
Method
Peak (Gbps) ↓
Migration (PB) ↓
Operational mapping
19,495.167
0.000
Historical-majority heuristic
18,276.071
0.333
Native Codex
1,238.625
25.473
VERAS
1,110.603
25.901
Table 2: Inter-datacenter placement results. Lower peak bandwidth and migration are better.
Method
Total ↓
Investment ↓
Operation ↓
Hourly MISOCP
42.065
18.984
23.081
Varying-timestep MISOCP
42.923
19.012
23.911
Native Codex
45.690
18.490
27.200
VERAS
39.424
16.154
23.269
Table 3: Annualized costs for 54-bus active distribution network planning and fault restoration (million USD/year). Lower is better.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Role
Input and output
Producer
Task packet, prior-stage artifacts, and refinement feedback; executable program and decisions
Observer
Task inputs and exported artifact; structural checks, constraint residuals, and declared coverage
Challenger
Task packet, candidate artifact, and observer evidence; read-only search for counterexamples
Evaluator
Submitted artifact and evaluation instance; feasibility and quality scores
Appendix
Table 4: Inputs and outputs of the solving and evaluation roles. Evaluation scores a submitted artifact; it is not a replacement for the controller’s online checks.
Parameter
Value
Model / reasoning effort
GPT-5.4 / high
Concurrent task workers
2
Task-stage wall-clock ceiling
2,700 s
Timeout scale
1.00
Reserved recovery fraction
0.30
Challenger fraction of remaining budget
0.22
Appendix
Table 5: VERAS configuration for the 107-task ORAgentBench evaluation.
Parameter
Inter-datacenter placement
54-bus network planning
Model / reasoning effort
GPT-5.6 Sol / xhigh
GPT-5.6 Sol / xhigh
Agent wall-time limit
19,800 s
15,360 s
Timeout scale
3.0
2.0
Recovery reserve / challenger cap
0.40 / 180 s
0.40 / 480 s
Candidate execution contract
120-s output generator
900-s solver; at most four threads
Selected source replay
45.842 s
829.552 s (750-s solver limit)
Appendix
Table 6: Configurations of the selected VERAS application runs. Source replay includes setup and artifact generation; its elapsed time is not the solver-only time.
Figure 4: VERAS schedules for eVTOL vertiport recovery. Blue intervals denote passenger flights and gold intervals denote charging. Flight labels are request identifiers with the leading “R” omitted. The accepted request set is shared across scenarios; operational schedules vary with the weather scenario.
Figure 5: August 10 replay of archived VERAS and the later native Codex run: (a) maximum directional bandwidth peak; (b) migration volume; and (c) resource utilization. All four utilization ratios are below the capacity limit.
Figure 6: Selected VERAS grid solution: (a) installed integer units by technology and bus; and (b) scenario-1 active power, with the fault interval (hours 7–8) shaded. Positive net storage power denotes discharge. Load shedding is reconstructed from the saved decisions.
Large language models are increasingly deployed as autonomous agents for multi-step tasks in executable environments, yet their ability to perform realistic operations research (OR) work remains unclear. Existing OR evaluations often decouple modeling from solving, rely on pre-formalized or text-only instances, and rarely test the full workflow from operational artifacts to validated decisions. In this work, we introduce ORAgentBench, an execution-grounded benchmark for evaluating autonomous agents on challenging end-to-end operations research tasks. It contains 107 human-reviewed tasks across diverse operational scenarios, each packaged in an isolated environment with a natural-language brief, multi-file data, configuration artifacts, and a required submission schema. Agents must write and run solution code, and their submissions are evaluated by hidden validators for schema validity, hard-constraint feasibility, and normalized objective quality. Experiments with fourteen frontier agent-model configurations show that current agents remain far from reliable OR practice. The best agent passes only 35.51% of all tasks and 20.59% of hard tasks, and many feasible submissions still fall below the required quality threshold. Failure analysis further shows that errors are dominated by strategic weaknesses, including missed operational rules, brittle formulations, weak feasible-solution construction, and insufficient solution improvement. OR-specific procedural skills increase hard-task feasibility, but do not reliably improve solution quality or pass rate. These results suggest that progress in OR agents requires moving beyond plausible optimization code toward dependable, high-quality operational decision-making.
Jiajun Li, Mingshu Cai, Yixuan Li +5
School of Computer Science and Engineering, Southeast University · Waseda University · Nanyang Technological University +1
Can large language model (LLM) agents deliver expert-level operations research (OR) solutions directly from original client materials, without prior expert reformulation? Existing OR benchmarks typically begin with self-contained descriptions or predefined optimization tasks, underrepresenting the translation of original business materials into professionally validated solutions. We introduce OR-License, an end-to-end benchmark of 31 instances across 10 industrial scenarios from paid OR engagements totaling USD 3.68 million. It preserves original requirements, input data, deliverable formats, and information boundaries after de-identification. To study information acquisition, we introduce ORSim, a controlled client simulator that discloses business facts without supplying OR expertise. Hidden evaluation checks feasibility and compares objective quality against original expert solutions accepted by clients before benchmark construction. Deployment-Adjusted Quality (DAQ) averages expert-relative quality across instances, assigning zero to infeasible deliveries. Across 11 frontier LLMs using coding-agent harnesses, several exceed the expert reference in conditional objective quality, but none matches its DAQ; the strongest primary Claude Code configuration achieves 88.39% strict feasibility and a DAQ of 0.87 against the expert reference of 1. Client information acquisition extends beyond clarification into solution development and validation, with some later stages showing higher confirmed issue-resolution proportions. Trajectory analysis identifies formulation and implementation failures, while task-equalized research-chain completion rates range from 24% to 45% across models on evaluable tasks. These findings motivate sustained information-gap resolution, faithful problem formulation, and evidence-linked self-improvement for reliable long-horizon agents.
Operations Research (OR) provides a rigorous framework for high-stakes decision-making, but effective OR modeling requires substantial domain knowledge, mathematical abstraction, and solver expertise. Recent LLM-based systems automate parts of this pipeline, yet remain limited by low accuracy on complex problems, opaque outputs, and narrow solver support. We propose COOPA (COoperative OPerations Agent), a modular LLM-agent architecture for interpretable and scalable OR decision support. It combines three components: iterative confidence-based modeling, which generates multiple candidate formulations, self-evaluates them across modeling dimensions, and selects one using a max-min confidence criterion; element-level provenance and confidence explanations, which link variables, parameters, constraints, and objectives to quoted source text and provide an audit trail for human verification; and multi-solver routing to specialized optimizer agents for different OR problem classes. Across three OR benchmarks, eight LLM backbones, and four baselines under identical conditions, COOPA achieves the best macro-average accuracy on six of eight backbones and improves over the strongest baseline by up to 6.7 percentage points. A within-system ablation isolates the contribution of iterative confidence-based modeling, while additional analyses and case studies illustrate the value of source traceability and multi-solver dispatch.
Chuanhao Li, Xiaoan Xu, Dirk Bergemann +3
1Tsinghua University · 2Duke University · 3Yale University