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arxiv: 2605.02933 · v1 · submitted 2026-04-30 · 💻 cs.NE

Recognition: unknown

Relation Reasoning with LLMs in Expensive Optimization

Ye Lu , Bingdong Li , Aimin Zhou , Hao Hao
Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:36 UTC · model grok-4.3

classification 💻 cs.NE
keywords expensive optimizationsurrogate-assisted evolutionary algorithmslarge language modelspairwise relation reasoningreinforcement learningblack-box optimizationevolutionary algorithmszero-shot surrogate
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The pith

A large language model fine-tuned to reason about solution relations can guide evolutionary optimization of expensive problems without retraining.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Expensive optimization problems restrict how many times the true objective function can be evaluated because each evaluation costs a great deal. Surrogate-assisted evolutionary algorithms therefore use predictive models to choose promising candidates, yet conventional surrogates typically require retraining at every generation as the population shifts. This paper shows that a large language model, trained via reinforcement learning on evolutionary trajectories to judge pairwise relations between solutions, can serve as a stable surrogate. An anchor-based prompting method keeps the input size linear rather than quadratic in population size, while a voting step converts the model's relation outputs into selection scores. Experiments on standard single- and multi-objective benchmarks report higher optimization performance than prior surrogate methods and general large language models, together with support for quantization and zero-shot use.

Core claim

The paper establishes that relation-based surrogate modeling, cast as an in-context pairwise reasoning task inside a large language model, enables effective guidance within evolutionary algorithms for expensive black-box problems. Training the model on trajectories with GRPO, combined with anchor-based iterative context construction and voting-based aggregation of predicted relations into scores, produces improved relation prediction and state-of-the-art optimization results on single- and multi-objective benchmarks while allowing a zero-shot surrogate paradigm without per-generation retraining.

What carries the argument

The anchor-based iterative context construction strategy that reduces prompt complexity from quadratic to linear in population size, together with a voting-based aggregation scheme that converts predicted relations into scores for offspring selection.

Load-bearing premise

That the LLM's predictions of relations between candidate solutions, learned from evolutionary trajectories, will generalize reliably to new problems and supply accurate guidance for selection without any retraining during the search.

What would settle it

A test on held-out optimization benchmarks in which the R2SAEA algorithm produces final solution quality no better than strong SAEA baselines after the same evaluation budget, or in which the model's pairwise relation accuracy falls sharply on populations not seen during training.

Figures

Figures reproduced from arXiv: 2605.02933 by Aimin Zhou, Bingdong Li, Hao Hao, Ye Lu.

Figure 1
Figure 1. Figure 1: Overview of the R2SAEA framework. It comprises three components: an SAEA module, an LLM-driven relation model, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Prompt template for relation reasoning. A naive construction would enumerate all pairwise relations within Dctx ∪ Dquery. Let |Dctx| = n and |Dquery| = q. This yields O [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Median runtime performance of LSEA and R2SAEA [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Offline evaluation of ReLLM-C1 and general LLMs [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Offline evaluation of ReLLM-C2 and general LLMs [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Element Acc (accele) on the offline test set under different decision dimensions (D) and subsample sizes (N) [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Binary Acc (accbin) on the offline test set under different decision dimensions (D) and subsample sizes (n). E. The Impact of Normalization Strategies Normalization is required in our RL fine-tuning and infer￾ence pipeline, since decision variables originate from different benchmark functions and different evolutionary stages, and therefore may have heterogeneous value ranges. We denote the context set as … view at source ↗
Figure 9
Figure 9. Figure 9: Completion tokens per second (CTs) by Model Size [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Total tokens per second (TTs) by Model Size and [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes R2SAEA, a surrogate-assisted evolutionary algorithm (SAEA) for expensive optimization problems (EOPs) that replaces conventional surrogates with a relation-reasoning LLM. The LLM (Qwen2.5) is fine-tuned via GRPO on evolutionary trajectories to predict pairwise relations between candidate solutions. An anchor-based iterative context construction reduces prompt length from quadratic to linear in population size, and a voting aggregation converts relation predictions into scalar scores for offspring selection. The method is positioned as enabling a zero-shot surrogate paradigm without per-generation retraining. Experiments on single- and multi-objective benchmarks are reported to show improved relation prediction and state-of-the-art optimization performance relative to strong SAEA baselines and general LLMs; quantization for edge deployment is also demonstrated.

Significance. If the generalization claims hold, the work would be significant for the SAEA community by showing that relation-based LLM reasoning can serve as a reusable, low-overhead surrogate that avoids repeated retraining. The open release of code and models is a clear strength that supports reproducibility and follow-on research. The approach also opens a new direction for leveraging LLM reasoning capabilities in black-box optimization rather than direct value prediction.

major comments (2)
  1. [§4 (Training Pipeline)] §4 (Training Pipeline): The paper does not characterize the distribution of evolutionary trajectories used for GRPO fine-tuning (problem classes, dimensions, objective landscape features, or diversity metrics). This is load-bearing for the zero-shot generalization claim, because without such characterization it is impossible to determine whether reported gains on the test benchmarks reflect true out-of-distribution robustness or partial overlap with the training distribution.
  2. [§5 (Experimental Results)] §5 (Experimental Results): The optimization performance claims (SOTA over SAEA baselines) are presented without reported statistical tests, number of independent runs, or variance measures. In addition, the precise configuration of the “strong SAEA baselines” is not detailed enough to allow direct replication or assessment of whether the comparison is fair on evaluation budget and hyperparameter tuning.
minor comments (2)
  1. [Abstract] The abstract states “improved relation prediction” without naming the metric or reporting numerical gains; adding a brief quantitative statement would strengthen the summary.
  2. [§5] Figure captions and axis labels in the experimental plots should explicitly state the number of function evaluations used and whether shaded regions represent standard deviation or standard error.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help strengthen the presentation of our work on R2SAEA. We address each major comment below and will incorporate revisions to improve clarity and rigor.

read point-by-point responses

  1. Referee: [§4 (Training Pipeline)] The paper does not characterize the distribution of evolutionary trajectories used for GRPO fine-tuning (problem classes, dimensions, objective landscape features, or diversity metrics). This is load-bearing for the zero-shot generalization claim, because without such characterization it is impossible to determine whether reported gains on the test benchmarks reflect true out-of-distribution robustness or partial overlap with the training distribution.

    Authors: We agree that a detailed characterization of the training trajectories is important for supporting the zero-shot generalization claims. In the revised manuscript, we will add a new subsection in §4 describing the distribution of evolutionary trajectories collected for GRPO fine-tuning. This will include the specific problem classes (e.g., CEC 2017/2020 single- and multi-objective benchmarks), dimension ranges (10D to 50D), objective landscape features (unimodal/multimodal, separable/non-separable), and diversity metrics such as average population variance and convergence statistics across the collected trajectories. revision: yes

  2. Referee: [§5 (Experimental Results)] The optimization performance claims (SOTA over SAEA baselines) are presented without reported statistical tests, number of independent runs, or variance measures. In addition, the precise configuration of the “strong SAEA baselines” is not detailed enough to allow direct replication or assessment of whether the comparison is fair on evaluation budget and hyperparameter tuning.

    Authors: We acknowledge that the current experimental reporting lacks sufficient statistical detail and baseline transparency. In the revised §5, we will explicitly state the number of independent runs (20 per benchmark instance), report mean performance with standard deviations, and include statistical significance tests (Wilcoxon rank-sum test with p-values) comparing R2SAEA against each baseline. We will also expand the baseline descriptions with a dedicated table listing exact configurations, including population sizes, surrogate hyperparameters, evaluation budgets per generation, and any tuning procedures used, to enable direct replication and confirm fairness of the comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on independent benchmark evaluation after training on trajectories

full rationale

The paper trains the LLM surrogate via GRPO on evolutionary trajectories, then deploys the resulting model for relation prediction and offspring selection on separate single- and multi-objective benchmarks. The anchor-based context construction and voting aggregation are procedural engineering steps that convert LLM outputs into selection scores without defining the performance metric in terms of the training data itself. No equations, self-citations, or uniqueness theorems are invoked that reduce the reported SOTA gains to a fitted quantity or prior result by construction. Generalization to new EOPs is presented as an empirical outcome of the experiments rather than a definitional necessity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Since only the abstract is available, the full set of assumptions cannot be audited. The central claim rests on the LLM learning generalizable pairwise relations from optimization trajectories and on the anchor-based and voting mechanisms preserving useful information.

free parameters (1)
  • GRPO and fine-tuning hyperparameters
    The reinforcement learning pipeline and model fine-tuning necessarily involve multiple hyperparameters whose values are chosen or fitted during training.
axioms (2)
  • domain assumption LLM pairwise relation predictions can be aggregated via voting into reliable scalar scores that improve evolutionary selection
    This conversion step is required for the surrogate to guide offspring selection.
  • domain assumption Anchor-based iterative context construction retains sufficient relational information while reducing prompt complexity
    The linear-complexity strategy is presented as preserving accuracy.

pith-pipeline@v0.9.0 · 5505 in / 1566 out tokens · 48214 ms · 2026-05-09T20:36:35.303222+00:00 · methodology

discussion (0)

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Reference graph

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