Relation Reasoning with LLMs in Expensive Optimization

Ye Lu; Bingdong Li; Aimin Zhou; Hao Hao

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arXiv · 2605.02933

Relation Reasoning with LLMs in Expensive Optimization

Ye Lu·Bingdong Li·Aimin Zhou·Hao Hao

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Abstract

Expensive optimization problems (EOPs) are black-box tasks with costly objective evaluations and no gradient access, making the evaluation budget the key bottleneck. Surrogate-assisted evolutionary algorithms (SAEAs) reduce evaluations via surrogate predictions, but conventional surrogates often require frequent retraining as populations evolve, incurring overhead. This paper proposes R2SAEA, a reinforcement-trained relation-based large language model (LLM) surrogate assisted evolutionary algorithm. We cast relation-based surrogate modeling as an in-context pairwise reasoning task. To enable efficient inference in evolutionary loops, we develop an anchor-based iterative context construction strategy that reduces prompt complexity from quadratic to linear in population size, and a voting-based aggregation scheme that converts predicted relations into scores for offspring selection. We further build an RL pipeline from evolutionary trajectories and fine-tune Qwen2.5 with GRPO. Experiments on single- and multi-objective benchmarks show improved relation prediction and state-of-the-art optimization performance over strong SAEA baselines and general LLMs. Quantization also enables efficient edge deployment, supporting a zero-shot surrogate paradigm without per-generation retraining. Code and models are available at https://github.com/Septend9/R2SAEA.

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Ye Lu, Bingdong Li, Aimin Zhou, Hao Hao. 2026-04-30. Relation Reasoning with LLMs in Expensive Optimization. https://arxiv.org/abs/2605.02933

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