Can Large Language Models Reason and Optimize Under Constraints?

Fabien Bernier; Salah Ghamizi; Pantelis Dogoulis; Maxime Cordy

cs.AIMar 24, 2026

Can Large Language Models Reason and Optimize Under Constraints?

Authors: Fabien Bernier, Salah Ghamizi, Pantelis Dogoulis, Maxime Cordy

Organizations: SnT – University of Luxembourg, Luxembourg · Luxembourg Institute of Health (LIH), Luxembourg

Abstract

Large Language Models (LLMs) have demonstrated great capabilities across diverse natural language tasks; yet their ability to solve abstraction and optimization problems with constraints remains scarcely explored. In this paper, we investigate whether LLMs can reason and optimize under the physical and operational constraints of Optimal Power Flow (OPF) problem. We introduce a challenging evaluation setup that requires a set of fundamental skills such as reasoning, structured input handling, arithmetic, and constrained optimization. Our evaluation reveals that SoTA LLMs fail in most of the tasks, and that reasoning LLMs still fail in the most complex settings. Our findings highlight critical gaps in LLMs' ability to handle structured reasoning under constraints, and this work provides a rigorous testing environment for developing more capable LLM assistants that can tackle real-world power grid optimization problems.

Figures & tables

Figure 1: Overview of our study. LLMs are evaluated with simple in-context learning, and in the evaluation settings after supervised fine-tuning (for non-reasoning models) and group relative policy optimization (for reasoning models); all models outputs are evaluated with the same metrics: MSE, constraint satisfaction, and structure validity.

Figure 2: Performance of vanilla models (before fine-tuning) on cases 14, 30 and 118.

Figure 3: Performance of vanilla models (before fine-tuning) and of fine-tuned models on N and N-1 cases.

Model	Case	Scenario	Gen. limits	Voltage limits	PF
Deepseek-R1 Qwen3-8B	14	Vanilla $N$	100%	98.7%	7.5%
		GRPO $N$	100%	99.6%	6.25%
		GRPO $N-1$	100%	98.6%	3.19%
	30	Vanilla $N$	100%	98.9%	11.7%
		GRPO $N$	100%	99.5%	12.5%
		GRPO $N-1$	99.8%	97%	9.71%

Table 1: % of satisfied constraints by model, case, and scenario.

Figure 4: Performance of reasoning models, before GRPO (vanilla) and after GRPO, on N and N-1 scenarios.

Case	Model	in-context			zero-shot
		Valid (%)	CS (%) $\uparrow$	MSE $\downarrow$	Valid (%)	CS (%) $\uparrow$	MSE $\downarrow$
case14	llama3.1-8b	95.0	57.8	3.91e-03	99.7	63.8	5.26e-03
	qwen3-8b	99.3	58.4	3.52e-03	32.8	59.5	2.94e-02
	qwen2.5-32b	93.5	58.2	2.48e-03	78.8	64.7	5.40e-03
case30	llama3.1-8b	47.1	55.1	4.22e-03	82.5	61.9	2.60e-02
	qwen3-8b	97.5	56.5	1.43e-03	35.6	55.1	2.46e-02

Table 2: Performance of fine-tuned models, in-context learning vs. zero-shot inference.

Case	Model	basic			enhanced
		Valid (%)	CS (%) $\uparrow$	MSE $\downarrow$	Valid (%)	CS (%) $\uparrow$	MSE $\downarrow$
case14	llama3.1-8b	100.0	58.0	4.80e-03	100.0	58.0	4.92e-03
	qwen3-8b	99.8	58.8	3.61e-03	99.6	59.0	3.61e-03
case30	llama3.1-8b	100.0	54.6	1.65e-03	99.9	55.4	1.57e-03
	qwen3-8b	91.2	54.7	1.56e-03	98.5	60.4	1.66e-03

Table 3: Performance of inference with the basic system prompt defined above, and inference with an LLM-enhanced system prompt.

Model	Case	Scenario	Gen. limits	Voltage limits	PF
QwQ 32B	14	Vanilla $N$	100%	100%	0.415%
QwQ 32B	30	Vanilla $N$	100%	100%	0.199%
Qwen2.5-32B	14	Vanilla $N$	100%	100%	1.19%
		SFT $N$	100%	100%	1.41%
		SFT $N-1$	100%	100%	0.426%
	30	Vanilla $N$	100%	100%	0.134%

Table 4: % of satisfied constraints by model, case, and scenario

Figure 5: Prompt used for the OPF task assessment.

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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.

Abstract

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