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Large Language Model-Driven Surrogate-Assisted Evolutionary Algorithm for Expensive Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Two large language models, one scoring solutions and one choosing algorithm components, can configure a surrogate-assisted evolutionary algorithm online, and the resulting method outperforms several existing SAEAs on most benchmark…

desk verdict The collaboration-of-experts idea is worth discussing, but the paper's own Table 3 does not show that LLM-driven selection beats random, alternating, or Q-learning selection. read the letter →

arxiv 2507.02892 v1 pith:UH4RB5C3 submitted 2025-06-20 cs.NE cs.AI

Lindong Xie , Genghui Li , Zhenkun Wang , Edward Chung , Maoguo Gong This is my paper · ORCID
classification cs.NEcs.AI
keywords largelanguagemodelsurrogate-assistedevolutionaryalgorithmexpensiveoptimizationconfigurationonlineinfillsamplingcriterioncollaboration-of-expertsbenchmark
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the hand-designed part of surrogate-assisted evolutionary optimization—choosing which surrogate model and which infill sampling criterion to use at each step—can be delegated to two collaborating large language models. It proposes LLM-SAEA, in which a scoring expert LLM rates each newly evaluated solution from 0 to 1, and a decision expert LLM uses those ratings plus selection frequencies to recommend actions, with a softmax-and-roulette fallback when it is unsure. On 10- and 30-dimensional benchmark problems, the method reports lower average function error than several existing SAEAs on most test cases, and ablation studies support the contribution of both LLMs. If the claim holds, expensive black-box optimization would no longer require a human expert to pre-select a model-criterion pair or to engineer a reward function for online selection.

What carries the argument

The load-bearing mechanism is the collaboration-of-experts loop, in which two LLM roles are connected by an online action-value statistic. An 'action' is a named pair (surrogate model, infill sampling criterion) chosen from eight fixed combinations. The decision expert (LLM-DE) receives the current budget, iteration, and each action's average score $s_a(t)$ and selection frequency $f_a(t)$, then returns a recommended action set with self-generated confidence labels ('certain' or 'uncertain'); uncertain actions are replaced by a softmax over average scores followed by roulette-wheel selection. The scoring expert (LLM-SE) converts the rank and objective value of each newly evaluated solution into a score $r_a \in [0,1]$, and the action's average is updated by $s_a(t+1) = \frac{f_a(t)s_a(t) + r_a}{f_a(t) + 1}$ and $f_a(t+1) = \frac{f_a(t)+1}{t+1}$. This loop makes the LLMs the online configurator, replacing hand-coded heuristic rules, reward engineering, or bandit update laws.

What would settle it

Record the LLM-SE score and the actual improvement in best-so-far objective for every selected action in the released code on F1–F15 (10D), and compute their rank correlation; a near-zero correlation would indicate that the reward signal feeding the update equation is not what drives performance, and a rerun with the true improvement as the score would then settle the matter.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that LLM-SAEA—a surrogate-assisted evolutionary algorithm whose online configuration is driven by two LLMs—achieves lower function error than eight existing SAEAs on the majority of 20 benchmark problems at both dimensions, while keeping the best average Friedman ranking. The algorithm maintains a fixed set of eight actions, each pairing a surrogate model (GP, RBF, PRS, or KNN) with an infill criterion (LCB, EI, prescreening, local search, L1-exploitation, or L1-exploration). At each iteration, the decision-expert LLM reads each action's average score and selection frequency and proposes an action set; each proposed action is executed to generate one new expensive evaluation, and the scoring-expert LLM assigns the resulting solution a score in $[0,1]$, which is folded into the action's running average by the update equations. For actions the decision expert labels 'uncertain', selection falls back to softmax probabilities and roulette-wheel choice. The paper also reports that the advantage over the reinforcement-learning-based ESA and the multi-armed-bandit-based AutoSAEA is not statistically significant in the Friedman test, while the advantage over static-configuration baselines is.

Load-bearing premise

The whole method depends on the scoring LLM's 0-to-1 ratings being a stable and truthful measure of how much an action helped; if those ratings are noisy or biased, the decision LLM's choices degrade toward random selection.

Editorial extensions

If this is right

  • For expensive problems, the added LLM calls are a small per-iteration overhead compared with the cost of one function evaluation, so the automation comes at low practical cost.
  • The ablation comparisons against single-action, sequential, random, and alternating variants imply that the performance gain comes from the LLM configuration loop, not from any one surrogate–infill pairing.
  • Because the configuration is updated online, the method can shift between exploration and exploitation as the evaluation budget runs down, something static SAEAs cannot do.
  • The Friedman test does not show a statistically significant advantage over ESA and AutoSAEA, so the paper's superiority claim is clearest against the static-configuration baselines.
  • The release of source code makes the prompts, the action set, and the update equations directly repeatable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same two-expert loop could be applied to other online algorithm-selection problems with a finite portfolio and an observable per-step outcome, such as choosing acquisition functions in Bayesian optimization or mutation operators in evolutionary strategies.
  • Replacing the scoring expert with the true improvement in best-so-far objective would test whether the LLM's ratings or the decision prompt is the load-bearing component; the paper does not run that experiment.
  • The framework is not tied to the fixed eight actions; an LLM could propose new surrogate/infill pairs, converting the method from a configurator into an open-ended algorithm designer.
  • The experiments use a single hosted LLM, so sensitivity to model choice and response randomness is untested; temperature and model changes are the natural next variables to explore.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes LLM-SAEA, a surrogate-assisted evolutionary algorithm that uses two LLM-based modules—a decision expert (LLM-DE) and a scoring expert (LLM-SE)—to configure online the surrogate model and infill criterion from a fixed action set of eight (model, criterion) combinations. LLM-DE outputs recommended actions with confidence labels; LLM-SE assigns a 0–1 score to the newly evaluated solution, and average action scores and selection frequencies are updated by Eqs. (7)–(8). The method is tested on five classic benchmarks plus the CEC2005 F1–F15 problems at dimensions 10 and 30, with 1000 function evaluations and 20 independent runs, and compared against eight existing SAEAs and twelve ablated variants. The paper reports that LLM-SAEA significantly outperforms the static-configuration baselines on a majority of problems, while explicitly acknowledging that it is not significantly better than ESA or AutoSAEA in the Friedman test. The ablation studies compare LLM-SAEA with fixed-action variants, a sequential variant, random, alternating, and Q-learning action selection.

Significance. If the central claim were fully established, LLM-SAEA would be a useful contribution: it would show that LLM-based online configuration can replace hand-designed dynamic configuration mechanisms in SAEAs, with public code and a component-wise ablation framework. The paper has genuine strengths: the experimental design includes Wilcoxon rank-sum tests, Friedman tests with Hommel correction, multiple benchmark suites, and an openly available implementation. The comparisons against static-configuration SAEAs are mostly convincing, and the self-reflection and collaboration ablations (Tables 4 and 5) show positive evidence for those components. However, the paper's own Table 3 shows that LLM-SAEA is not statistically distinguishable from random, alternating, or Q-learning action selection, which directly undermines the load-bearing claim that the LLM's dynamic configuration is effective. The unvalidated and apparently uncontrolled LLM scoring mechanism adds further uncertainty. The contribution is therefore promising but not yet supported at the level claimed in the abstract and Section 4.3.1.

major comments (3)
  1. [Section 4.3.1, Table 3] The sentence "These results confirm the effectiveness of LLMs in the dynamic configuration of SAEAs" is not supported by the reported statistics. Against the dynamic-selection controls, LLM-SAEA wins on only 5 of 15 problems versus V-Random and V-Q and on 4 of 15 versus V-Alter, and the Friedman p-values are 0.37, 0.82, and 0.82, respectively. Since none of these comparisons reaches significance, the data are consistent with LLM-driven configuration being no better than random or simple online-selection rules. The claim should be softened, or the experiment strengthened, for example with more runs, more problem instances, or a direct measurement of selection quality.
  2. [Section 3.2.2, Algorithm 3, Fig. 2, Eqs. (7)-(8)] The LLM-SE reward signal is not validated. The 0–1 score produced by GPT-3.5-turbo is the only feedback used to update average action scores, and Eq. (7) propagates this score into every subsequent decision through Eq. (6) and Algorithm 2. The paper never reports the correlation between the LLM score and an actual quality measure, such as normalized improvement in objective value, nor does it report the LLM temperature, random seed, or repeated-call variance. Without such information, one cannot distinguish a meaningful credit-assignment signal from stochastic noise; noisy scores would make softmax/roulette selection approach uniform selection, which is exactly the pattern observed in Table 3. A validation study, or replacement of the LLM score with a deterministic surrogate reward plus controlled LLM inference, is needed before the dynamic-configuration claim can be accepted.
  3. [Algorithm 1, lines 13-14; Algorithm 2] The final executed action is chosen by random.choice(a*), not directly by the LLM's ranking. Because the LLM-DE prompt explicitly requires that each action be explored, a* can contain many or even all eight actions, so the uniform draw over a* can dilute whatever preference the LLM produces. This design may explain why LLM-SAEA is statistically indistinguishable from V-Random in Table 3. The authors should report the distribution of |a*| over the optimization process and either select actions according to their scores or probabilities rather than uniformly, or demonstrate that the LLM-DE output substantively constrains the random draw.
minor comments (5)
  1. [Fig. 2] The prompt heading "Soring Expert" is a typo for "Scoring Expert."
  2. [Fig. 4 vs. Section 3.1] The legend of Fig. 4 labels Action 1 as (GP, EI) and Action 2 as (GP, LCB), but Section 3.1 defines the action set with (GP, LCB) first and (GP, EI) second; the legend should match the formal definition of A.
  3. [Abstract and Section 4.1] The abstract says "another LLM" acts as the decision expert, but Section 4.1 states that GPT-3.5-turbo-0125 is used for both expert roles; the wording should say the same LLM with different prompts, or the experimental setup should use two different models.
  4. [Algorithm 1 and Algorithm 2] The pseudocode contains rendering artifacts, such as "while A* ≠ ∅" appearing as "while /u1D440... ≠ )uni2205(vardo" in Algorithm 1 and "Set A* ← ∅" appearing as "← )uni2205(var" in Algorithm 2; these should be cleaned before publication.
  5. [Section 3.3, Eq. (9)] The complexity expression uses an iteration-count symbol that is not consistently named in the text, and it should account for the internal DE optimizer used by the local-search actions in Eq. (5), which consumes 100D+1000 surrogate-based evaluations per call rather than a single constant cost C_SAEA.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is an empirical LLM/SAEA configuration study validated against external baselines, with no prediction or derived result that reduces to its inputs.

full rationale

This is an empirical method paper rather than a derivation chain. The central claims are that LLM-SAEA outperforms state-of-the-art SAEAs on benchmarks and that its ablations support the effectiveness of LLM-driven dynamic configuration. These claims are evaluated against external algorithms (ESAO, IKAEA, TS-DDEO, SA-MPSO, SAMFEO, GL-SADE, ESA, AutoSAEA) and against internally defined variants; no parameter is fitted to the benchmark results and then presented as a prediction. The LLM prompts, scoring rule, and decision rule are fixed design choices, not quantities inferred from the test data. The self-citation to AutoSAEA [27], from the same research group, supplies the combinatorial action set and background on surrogate models and infill criteria; it is not used to justify a uniqueness claim or to forbid alternatives, so it is not load-bearing circularity. The LLM-SE/LLM-DE loop is an online feedback mechanism in which scores are updated from observed outcomes and then read by the decision expert; this is a control structure, not a definitional equivalence between input and output. The paper itself discloses limitations: Section 4.2 states that LLM-SAEA is not statistically significantly better than ESA or AutoSAEA in the Friedman test, and Table 3 reports non-significant Friedman p-values (0.37, 0.82, 0.82) against V-Random, V-Alter, and V-Q. That tension between the text's wording and the reported statistics concerns evidentiary overstatement, not circularity, and is better addressed as a correctness or statistical-claims issue. No equation, fitted parameter, or cited result is shown to reduce to the paper's own target claim.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities, forces, or conserved quantities are introduced. The LLM-SE and LLM-DE are software modules, not scientific entities. The free parameters are standard hyperparameters plus an unspecified LLM sampling parameter.

free parameters (2)
  • population size N = 100 (recommended range 80-120)
    The paper's only tunable hyperparameter, chosen to match baseline algorithms. Sensitivity analysis (Table 6) shows N=60 degrades performance; the authors recommend [80,120].
  • LLM sampling temperature
    Not reported. Sampling temperature and other API parameters control the stochasticity of LLM-SE and LLM-DE outputs and affect reproducibility of the 20-run statistics.
assumptions (4)
  • domain assumption The benchmark suite (five standard functions plus CEC2005 F1-F15 at D=10 and D=30) is representative of expensive optimization problems.
    The central empirical claim is evaluated on these problems; the paper does not test real-world expensive simulators.
  • domain assumption A budget of 1000 function evaluations is fair to all algorithms.
    Standard budget in the cited SAEA literature (e.g., SA-MPSO, GL-SADE), but it may favor algorithms with fast early exploitation.
  • domain assumption GPT-3.5-turbo-0125 produces scores and action selections that are stable and informative enough to support the reported statistics.
    The entire method depends on LLM outputs; the paper does not measure variance across different LLM calls for the same input.
  • standard math Wilcoxon rank-sum and Friedman tests with Hommel correction are appropriate for comparing 9 algorithms across 20 runs.
    These are standard procedures in the SAEA literature, though the small number of runs limits power.

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Cite this review

Pith. "Pith review of Large Language Model-Driven Surrogate-Assisted Evolutionary Algorithm for Expensive Optimization." pith.science (2026). https://pith.science/paper/UH4RB5C3

@misc{pith2026250702892,
  author       = {Pith},
  title        = {Pith review of: Large Language Model-Driven Surrogate-Assisted Evolutionary Algorithm for Expensive Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UH4RB5C3}},
  note         = {Machine review of arXiv:2507.02892}
}
read the original abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are a key tool for addressing costly optimization tasks, with their efficiency being heavily dependent on the selection of surrogate models and infill sampling criteria. However, designing an effective dynamic selection strategy for SAEAs is labor-intensive and requires substantial domain knowledge. To address this challenge, this paper proposes LLM-SAEA, a novel approach that integrates large language models (LLMs) to configure both surrogate models and infill sampling criteria online. Specifically, LLM-SAEA develops a collaboration-of-experts framework, where one LLM serves as a scoring expert (LLM-SE), assigning scores to surrogate models and infill sampling criteria based on their optimization performance, while another LLM acts as a decision expert (LLM-DE), selecting the appropriate configurations by analyzing their scores along with the current optimization state. Experimental results demonstrate that LLM-SAEA outperforms several state-of-the-art algorithms across standard test cases. The source code is publicly available at https://github.com/ForrestXie9/LLM-SAEA.

Figures

Figures reproduced from arXiv: 2507.02892 by the authors.

Figure 1
Figure 1. Illustration of the collaboration-of-experts frame￾work. In each iteration, an LLM decision expert analyzes the contextual information of the action set to select actions. These selected actions are then randomly executed in the optimization environment until the current optimal solution is updated. An LLM scoring expert scores the executed actions and updates their contextual information. Once the stopping criterio… view at source ↗
Figure 2
Figure 2. Prompts used in the decision expert and scoring expert. L. Xie et al.: Submitted to Elsevier Page 12 of 10 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. The convergence curve of the mean function error value for each algorithm on 10D problems. L. Xie et al.: Submitted to Elsevier Page 13 of 10 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The frequency of each action being selected throughout the optimization process of LLM-SAEA on the F1-F9 (D=10) problems. L. Xie et al.: Submitted to Elsevier Page 14 of 10 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Janus: An Algorithm-Evaluator Co-Evolution Framework for LLM-Driven Discovery under Expensive Evaluation Budgets

    cs.AI 2026-08 conditional novelty 7.0 of 10

    Janus co-evolves LLM-generated proxy evaluators with target programs, reaching the same or better final performance with about 59% fewer real evaluations across five design benchmarks.

  2. A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving

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    A literature survey that classifies LLM-based optimization research into modeling and solving, with solving divided into LLMs as optimizers, low-level components, and high-level managers.

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    Output only the score with two decimal places in the format <start>value<end>

    Excluding point x, the best, average, and worst objective values in set P are {the best objective value}, {the average objective value} , and {the worst objective value} , respectively. Output only the score with two decimal places in the format <start>value<end>. Do not give ...

    2000

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.