aiqbench analysis
This research advances the intersection of large language models and mathematical optimization by training LLMs to generate computationally challenging Mixed Integer Linear Programming (MILP) instances using solver feedback. By leveraging asymmetric self-play between an LLM challenger and a solver verifier, the method creates high-difficulty benchmarks without relying on pre-existing seed problems or manual parameter tuning. This approach significantly improves instance hardness metrics, offering a scalable way to stress-test optimization algorithms and expand public benchmarking datasets.
Teaching LLMs to Generate Challenging MILP Instances via Solver Feedback
arXiv:2609.37356v1 Announce Type: new Abstract: Generating optimization instances that are both feasible and computationally challenging is crucial for benchmarking solvers and training learning-based optimization algorithms. Existing non-LLM generators rely on seed instances or parameter tuning, resulting in high test-time computational cost, while existing LLM generators lack explicit hardness measures. Recent reinforcement learning methods with verifier feedback evaluate only binary correctness, which is misaligned with generating challenging problems. We note that an optimization solver reports the cost of solving at several stages of its pipeline, and leverage this to design a reward that scores both the solvability and the hardness of generated problems, measured by branch-and-bound nodes and post-cut relaxation gaps. Our key idea is a challenger-solver asymmetric self-play approach, where an LLM challenger generates progressively harder instances and the solver verifies feasibility and hardness, so no seed or training MILP instances are required. We fine-tune Gemma-4-12B and Qwen3.5-4B with GRPO and a size curriculum into OptiScribe-12B and OptiScribe-4B, which generate feasible yet challenging MILP problems from natural language instructions. On capacitated facility location and max-cut, OptiScribe-12B raises median SCIP search nodes by 1.7-5x and post-cut gaps by 1.1-1.7x over its base model and improves the feasibility rate on facility location by 9-19 points, while OptiScribe-4B raises median nodes by up to 15.6x. The problems cover a wider difficulty range than public benchmarks of the same size, follow instructions on density and difficulty, and can tune solver settings for families that public libraries lack. These results indicate that optimization-specific rewards, used in self-play mode, can teach LLMs to generate high-difficulty optimization benchmarks. We will release our code and models publicly on acceptance.
Abstract:Generating optimization instances that are both feasible and computationally challenging is crucial for benchmarking solvers and training learning-based optimization algorithms. Existing non-LLM generators rely on seed instances or parameter tuning, resulting in high test-time computational cost, while existing LLM generators lack explicit hardness measures. Recent reinforcement learning methods with verifier feedback evaluate only binary correctness, which is misaligned with generating challenging problems. We note that an optimization solver reports the cost of solving at several stages of its pipeline, and leverage this to design a reward that scores both the solvability and the hardness of generated problems, measured by branch-and-bound nodes and post-cut relaxation gaps. Our key idea is a challenger-solver asymmetric self-play approach, where an LLM challenger generates progressively harder instances and the solver verifies feasibility and hardness, so no seed or training MILP instances are required. We fine-tune Gemma-4-12B and Qwen3.5-4B with GRPO and a size curriculum into OptiScribe-12B and OptiScribe-4B, which generate feasible yet challenging MILP problems from natural language instructions. On capacitated facility location and max-cut, OptiScribe-12B raises median SCIP search nodes by 1.7-5x and post-cut gaps by 1.1-1.7x over its base model and improves the feasibility rate on facility location by 9-19 points, while OptiScribe-4B raises median nodes by up to 15.6x. The problems cover a wider difficulty range than public benchmarks of the same size, follow instructions on density and difficulty, and can tune solver settings for families that public libraries lack. These results indicate that optimization-specific rewards, used in self-play mode, can teach LLMs to generate high-difficulty optimization benchmarks. We will release our code and models publicly on acceptance.
Artificial Intelligence (cs.AI); Optimization and Control (math.OC)
arXiv:2609.37356 [cs.AI]
(or arXiv:2609.37356v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.37356 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 364 words
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