AutoEP: LLMs-Driven Automation of Hyperparameter Evolution for Metaheuristic Algorithms
Authors: Zhenxing Xu
Yizhe Zhang
Weidong Bao
Hao Wang
Ming Chen
Haoran Ye
Wenzheng Jiang
Hui Yan
Ji Wang
Venue: ICLR 2026 Oral (2026)
Keywords: LLMs
Optimization
Metaheuristic algorithm
Automatic Algorithm Design
Primary area: optimization

Abstract: Dynamically configuring algorithm hyperparameters is a fundamental challenge in computational intelligence. While learning-based methods offer automation, they suffer from prohibitive sample complexity and poor generalization. We introduce AutoEP, a novel framework that bypasses training entirely by leveraging Large Language Models (LLMs) as zero-shot reasoning engines for algorithm control. AutoEP's core innovation lies in a tight synergy between two components: (1) an online Exploratory Landscape Analysis (ELA) module that provides real-time, quantitative feedback on the search dynamics, and (2) a multi-LLM reasoning chain that interprets this feedback to generate adaptive hyperparameter strategies. This approach grounds high-level reasoning in empirical data, mitigating hallucination. Evaluated on three distinct metaheuristics across diverse combinatorial optimization benchmarks, AutoEP consistently outperforms state-of-the-art tuners, including neural evolution and other LLM-based methods. Notably, our framework enables open-source models like Qwen3-30B to match the performance of GPT-4, demonstrating a powerful and accessible new paradigm for automated hyperparameter design.Our code is available at https://anonymous.4open.science/r/AutoEP-3E11.

Published as a conference paper at ICLR 2026
AUTOEP: LLMS- AUTOMATION OF HYPERPA- RAMETER EVOLUTION FOR METAHEURISTIC ALGO- RITHMS
Zhenxing Xu" Yizhe Z Weidong Bao'- Hao Wang', Ming Chen",
Haoran Ye,, Wenzheng Jiang', Hui Yan', Ji Wang'
National Key Laboratory of Big Data and Decision, National University of Defense Technology
DDepartment of Automation, Tsinghua University
SSchool of Intelligence Science and Technology, Peking University *Information Support Force Engineering University
txuzhenxing zyz, wdbao, whao 99, j angwenzheng, yanhui 13, wangji @nudt annut.edu... edd. cn amself0162 com, hrye@stu. pku. edu, en
ABSTRACT
Dynamically configuring algorithm hyperparameters fundamental challenge computational intelligence. While learning- based methods offer automation, they suffer from prohibitive sample complexity and poor generalization. We introduce AutoEP, novel framework that bypasses training entirely by leveraging Large Language Models (LLMs) as zero-shot reasoning engines for algorithm control. AutoEP's core innovation lies in a tight synergy between two components: (1) an online Exploratory Landscape Analysis (ELA) module that provides real-time, quantitative feedback on the search dynamics, and (2) multi-LLM reasoning chain that interprets this feedback to generate adaptive hyperparameter strategies. This approach grounds high-level reasoning in empirical data, mitigating hallu- cination. Evaluated on three distinct metaheuristics across diverse combinatorial optimization benchmarks, AutoEP consistently outperforms ofate-of-the-arr tuners, including neural evolution and other LLM-based methods. Notably, our framework enables open-source models like Qwen3-30t to match the performance of GPT-4, demonstrating powerful and accessible new paradigm for automated hyperparam- eter design. Our code available at http:://gghub.coom//ihhhhhiiiiie 12tt:///ZZhaann/A/oAtaa 12/Auto
INTRODUCTION
The performance of complex algorithms, from numerical optimizers to machine learning models, is critically governed by their internal hyperparameters. Dynamically adapting these parameters to suit the problem instance at hand represents a long-standing challenge in automated algorithm design Wu et al. [2024] 2025). Metaheuristic algorithms, a cornerstone of solving complex combinatorial problems, serve canonical example. Their effectiveneess hinges a delicate balance between exploration (diversifying the search) and exploitation (intensifying the search in promising regions), trade-off directly controlled by their hyperparameter configurations Eiben et al.) (2002). Mastering this balance crucial for achieving state-of-the-an performance but remains a formidable open problem.
Traditional approaches to dynamic hyperparameter adaptation fall into two categories. Manual, rule-
based strategies Eiben al. (2002): y Thierens (2005): Ansótegui al. (2009); Doshi & Bansal (2020); :
Leon & Xiong 2015);; Li et al. (2025); Shao et al. (2025) embed human expertise into hard hard-coded
logic. but are brittle. labor-intensive. and fail generalize across different problems or algorithms.
To overcome this, data-driven methods, particularly deep reinforcement learning (DRL) Tessari &
Iacca (2022); : Ma al. (2024); | [Luu et al.] (2023); TTatsis & Parsopoulos (2020); Yin et al.] (2021).
have attempted to learn adaptive policies from scratch. However, this paradigm faces fundamental
"Equal contribution. "ooresponniig author.

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Published as a conference paper at ICLR 2026
limitations: (1) prohibitive sample complexity, requiring millions of algorithm executions to train a single policy, and (2) poor generalization, where policies often overfit to the training distribution of problems and fail on unseen instances algorithm variants Guo al. (2024). This reveals critical gap: the need for a framework that can adapt algorithm behavior without requiring expensive, instance-specific training.
The recent advent of Large Language Models (LLMs) offers a paradigm shift. Unlike traditional learning models that learn policies from scratch, LLMs distill vast amounts of knowledge from pre-training on extensive corpora of text and code. This process endows them with powerful emergent reasoning capabilities and rich prior understanding of abstract concepts like "convergence, "diversity," " and "optimization" Liu et al. (2024); YE et al. (2024); Liu et al.] (2025); Hu et al. (2025). We hypothesize that this pre-trained knowledge can harnessed to reason about optimal hyperparameter adjustments in zero-shot manner, bypassing the costly training phase that plagues DRL-based approaches. This transforms the problem from one of learning a control policy to one of prompting reasoning engine.
In this paper, we introduce AutoEP, a novel framework that operationalizes this vision. AutoEP synergizes the quantitative analysis of Exploratory Landscape Analysis (ELA) with the qualitative rea- soning of LLMs, creating a new paradigm for zero-shot hyperparameter configuration. It overcomes the limitations of both manual design and data-intensive learning models. Our key contributions are:
We propose a novel, training-fri free framework where LLMs act "pluggable" reasoning core to dynamically control algorithm hyperparameters. This general-pune purpose approach is applicable to any metaheuristic algorithm without modification or costly retraining (see Figure [ for an overview).
(1) A Zero-Shot Paradigm for Algorithm Control:
To mitigate hallucinations and ensure data-driven decisions, ground the L.M''s inference in empirical evidence from the real-time search trajectory. We achieve this by continuously supplying the LLM with quantitative metrics, such as ELA features and historical decision data. These metries, including fitness distribution, solution diversity, and search difficulty estimates, provide the LLM with a concrete awareness of the current optimization state. This process anchors the model's abstract reasoning in the observable dynamics of the search.
(2) Grounding LLM Inference with Search Trajectory Analysis:
(3) Complex Reasoning via Collaborative Open-Source LLMs: We demonstrate that a collabo- rative pipeline of smaller, locally-deploeed open-source I.LMs (e.g., Qwen-72B, DeepSeek-677) can effectively decompose and solve complex control tasks. Our empirical results show that this approach achieves performance comparable to that of large-scale proprietary models, such GPT-4, while exhibiting significantly lower inference latency for the hyperparameter tuning task. This design substantially enhances the accessibility, reproducibility, and overall efficiency of sophisticated AI reasoning systems.
(4) Saate-of-the-Are Performance Across Diverse Benchmarks: Through extensive experiments on three distinct metaheuristics (GA, PSO, ACO Holland 1992); Dorigo et al. (2007); Kennedy & Eberhart (1995)) and four combinatorial optimization problems, show that AutoEP consistently and significantly outperforms both traditional hyperparameter tuning methods and recent L.-M-based approaches.
2 RELATED WORK
Rule-Based and Heuristic Control. Early attempts to au- tomate hyperparameter tuning relied on hard-coded, rule- based heuristics. These methods embed expert knowl- edge into predefined rules that adjust parameters based on simple metrics like iteration count or population di- versity Thierens (2005). For instance, strategies might deterministically increase mutation rates to escape lo- cal optima or adapt selection pressure over time Joshi & Bansal (2020). While an improvement over static set- tings, these approaches are fundamentally brittle. The underlying heuristics problem-dependent and require
Problem repat
Mezaheunkette
alpertive
problens
hyperperennter
Exploration
Target
Dynamic hyperpermente spthecaatioe
ExploMttiin
Popudation
output
End a
Fleol Result
Figure I: Process of hyperparameter tun- ing in metaheuristic algorithms using AutoEP.
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extensive manual calibration. They lack the ability to adapt to unforeseen dynamics in the search process, making them unable to generalize across different problem classes or algorithms.
Meta-Black--oe -Bx Optimization (Meta-BBO). To address the inherent rigidity of manual heuristics, the field has shifted toward Meta-BBOR Ma et al. (2023); : Tatsis & Parsopoulos (2020); Guo et al. Ma al. b): Li et al. This paradigm integrates data-driven and reinforcement learning (RL) approaches to automate algorithm configuration and design. Unlike traditional optimization that searches within decision space, Meta-BBO explores the algorithm space discover optimal optimizers, typically leveraging historical data to learn adaptive strategies. While early frameworks like GLEET Ma al. (2024) and NeuroCrossover Liu al. (2023) successfully employed Deep RL for operator selection, they were constrained by high sample complexity. Recent advancements have expanded this domain; for instance, Neural EL.A Ma et al. (2025) incorporates landscape features via neural exploratory landscape analysis, while DesignX Guo et al. (2025) proposes dual-agent RI framework to jointly learn algorithm structure and hyperparameters. Despite these advances, current Meta-BBO methodologies remain heavily reliant computationally expensive meta-training, This highlights a critical gap: the need for a zero-shot framework that retains the adaptivity of Meta-BBO while cireumventing prohibitive training costs.
LLMs for Algorithm Design: From Offline Generation to Online Control. Leveraging pre- trained code knowledge. LLMs have advanced algorithm design significantly Ma et al. (a). Offline
frameworks (e.g.. EoH Liu et al. (2024), ReEvo YE et al. (2024) successfully automate the generation of operators and configurations. However, optimization is inherently dynamic (urrina al. (2025). necessitating online adaptation. Recent attempts like M et al. (2024) employ LLMs as evolutionary operators for direct solution generation. Despite their novelty, such methods struggle with floating-point representation and context window constraints in high-dimensional search spaces.
This highlights a critical research gap. We argue that the optimal role for an LLM is not to mimic the solver, but to act as high-level supervisor. Unlike prior works that replace search operators, we propose a framework for dynamic hyperparameter control. This design grounds the LLM's semantic reasoning in real-time search dynamics without being hindered by numerical precision issues. By doing so, we overcome the brittleness of rule-based heuristics and the sample inefficiency of RI., offering robust and scalable solution for online control.
3
AUTOEP
3.1
GROUNDING REASONING WITH QUANTITATIVE SEARCH DYNAMICS
To effectively control a metaheuristic algorithm, the decision-makern agent requires a real-time, quantitative understanding of the search process. As metaheuristics are black-box methods, we employ Exploratory Landscape Analysis (ELA) (ersmann et al. (2011); Ma et al. (2025) to extract features that characterize the algorithm's 's state. We selected concise yet comprehensive set of features designed to capture four key aspects of the search: (1) the statistical distribution of the current population's 's fitness, (2) the structural properties the local fitness landscape, (3) the diversity of solutions, and (4) the recent progress of the search.
3.1.1 FITNESS DISTRIBUTION FEATURES.
Skewness (S), Measures the asymmetry of the solution distribution within the current population. It calculated follows:
1 En (y: S 12
8)3
(V E. (vs 7)2
3
where yi represent the fitness value of the i-th individual in the population, and ÿ denote the mean fitness value of the population, where n is the population size. For minimization goal, value near 0 suggests a balanced population. Positive skew (S>0) implies a long tail of low-quality solutions, indicating the search should intensify exploitation around the few discovered elites. Negative skew (S=0) suggests the population is converging on high-quality solutions and may be at risk premature convergence, necessitating more exploration.
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Kurtosis (K). Quantifies the "tailedness" of the solution distribution within the current population. It calculated as follows:
== - (ys 1)
3,
V (U: 7)²
high kurtosis (K>0) indicates fitness values are tightly clustered with heavy tails, signaling low diversity and the need for exploration. Low kurtosis (A (K) implics a flat, dispersed distribution, suggesting exploitation is warranted to refine existing solutions.
3.1.2 FITNESS LANDSCAPE AND DIVERSITY FEATURES
Meta-Model: Coefficient of Determination (R²). Quantifies the goodness-off-e of simple model (e.g., quadratic) sample of solutions, thereby assessing the structural predictability of the fitness landscape. It is calculated as:
R2 11 1 33 f(z.)) (Vi [E=(V 8)
where yi the fitness of the i-th individual, I is the mean fitness, and (x;; the fitness predicted by the model. A high R = 1 indicates well-structured landscape (i.e., a funnel), signaling need to increase exploitation. Conversely, a low R² se O implies a rugged or multi-modal landscape. requiring increase in exploration avoid premature convergence.
Dispersion Ratio (Dratio). Measures the population's 's diversity by comparing the spatial distribution of the best solutions against that of the worst solutions. A low ratio indicates convergence into single promising region. It calculated as follows:
D(Qnea)
Dratio
D(Quara))
where Qbest and weestt represent the sets of the best and worst solutions in the population based fitness quantile (top and bottom 10%), respectively. The function D(Q) TQ Ex,,,, ZqQiici d(T,, Tz) calculates the average pairwise distance among all individuals within given set Q, using distance metric -(: suitable for the decision space (e.g., Hamming distance for binary problems). A value Dratio < 1 (e.g.. < 0.2) is a strong indicator of a single funnel structure, the best solutions tightly clustered. This signals the need increase exploita- tion to refine the search within this promising basin. Conversely, a value of D Dratio & suggests a multi-modal landscape, where elite solutions found in disparate regions. This necessitates an increase in exploration to avoid premature convergence to local optimum.
3.1.3 SEARCH PROGRESS FEATURE
Variability (V). The four indicators above describe the solution structure within the population and reflect the current state of the algorithm's optimization process. To capture the dynamics of the search more effectively, we design a rate-of-change indicator:
Um
m=g-m
to measure the evolutionary progress of the population, we introduce rate of change indicator, V. Let Ty be the mean fitness of the population at generation g. The indicator V quantifies the improvement in Uy relative to the mean fitness over the previous generations. For minimization problems, value V > signifies sufficient progress, prompting the algorithm to intensify exploitation through local search. Conversely, V < suggests that the population is stagnating, which triggers an increase in exploration to diversify the search.
These ELA features transform the black-box state of the metaheuristic into structured, machine- readable format. This representation serves as the empirical foundation for the LLM's reasoning process, enabling make informed, data-driven decisions about hyperparameter adjustments.
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3.2 A LLOSED-LLor ARCHITECTurE FOR L.M-DRIVEN CONTROL
Task Scenarios
Understanding tasks and metaheuristic algorithms
Algorithm name
i Hyperparrmmee
Input
Analyze data experience to determine the current state
Experience pool
Multiple LLMs
Iteration number
Stepl: Hyperporometer generation
9
Hyperparameter
fx Target value
Metaheuristic algorithm
Exploration
Exploitation
ELA features
Step2: Result output
Adjust the hyperparameters based the current state,
History Information
Process Architecture
Construction of CoR
Figure 2: The AutoEP Framework.
AutoEP operates as a closed-loop control system that dynamically steers a metaheuristic algorithm. As shown in Figure 2 the framework iteratively performs three main functions: State-Sensing, Reasoning, and Action.
1. State-Sensing and Context Formulation: At each decision point, the framework captures the current state of the metaheuristic algorithm. This involves calculating the ELA features described in Sec 3.1 This real-time data is then combined with historical information from an Experience Pool. The pool stores a memory of past states, actions (hyperparameter settings), and their outcomes (fitness improvements). This collective information is formatted into a structured prompt that provides the LLM with both the current situation and relevant historical context.
The formulated prompt is passed to our Chain of Reasoning (CoR) engine (detailed in Sec 3.3). This engine, composed of multiple collaborating LLMs, ana- lyzes the current state in light of past experiences to determine whether to prioritize exploration or exploitation and translates this strategy into a concrete set of hyperparameter values.
2. Reasoning via Multi-LLM Chain:
3. Action and Feedback: The new hyperparameter configuration generated by the CoR engine is fed back to the metaheuristic algorithm, which uses it for the subsequent phase of the search. The performance outcome this action is recorded and added to the Experience Pool, completing the feedback loop. This iterative process allows AutoEP to continuously adapt its strategy based observed performance, effectively performing in-context learning throughout the optimization run.
3.3 DECOMPOSING CONTROL. LOGIC WITH CHAIN OF REASONING
Controlling complex algorithm requires multi-faceted reasoning: understanding the task, diagnosing the current state, and deciding on a precise action. Entrusting this entire process to a single LLM with monolithic prompt can lead to high inference latency and unstable outputs Wang et al. 2023). To address this, we introduce the CoR, a multi-LLM framework that decomposes the control task into a pipeline of specialized, more manageable reasoning steps. This approach not only improves performance through specialization (Shen et al. (2023) but also enhances robustness through cross- validation. Our CoR pipeline consists of three distinct agents:
The Strategist LLM (One-time Setup): At the start of run, the Strategist receives the problem description and the chosen metaheuristic algorithm, such as a GA. It generates a static "control mapping" that defines the qualitative effect of each hyperparameter (such mutation rate and crossover probability) on the search process. For example, it might map the mutation rate to the concept of "boosting exploration". This map is generated once and serves foundational reference for the other agents.
The Analyst LLM (State Diagnosis): At each decision point, the Analyst LLM uses real-time ELA features and historical data from the Experience Pool to diagnose the current search state. It addresses the core question of whether to prioritize exploration exploitation. To do this, it synthesizes ELA
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signals to identify consensus (where multiple indicators, like low diversity and stagnation, both suggest exploration) or conflict (where indicators are contradictory, such as low diversity but rapid progress). Based on this diagnosis, it outputs clear strategic directive, for instance, ACTION: Increase Exploration.
The Actuator LLM (Decision and Tuning): The Actuator receives the strategic directive from the Analyst (Increase Exploration) and the static control map from the Strategist. Its task is to translate the qualitative directive into quantitative hyperparameter configuration. performs this in two stages:
Parameter Selection: Using the control map, it identifies which hyperparameters modify (e.g.. increase mutation rate, decrease crossover probability).
Magnitude Determination: It determines the degree of adjustment. This is achieved through in-context learning, where it examines examples from the Experience Pool to infer effective tuning magnitudes from similar past situations. For instance, it might learn that small, incremental changes are better during stable progress, while large, aggressive changes are needed to escape deep stagnation.
This decomposed CoR pipeline transforms a complex, unstructured control problem into a series of focused, interconnected reasoning tasks, enabling more reliable and efficient automated algorithm configuration, as shown Figure The detailed prompts for each agent are provided in Appendix
Question1
Answer2
Could you analyze impact of crossover and probabilities the exploration exploitation balance genetic algorithms?
Based on the analysis of experience pool data, the algorithm currently requires increased exploration.
Question
Answer]
the GA, crossover probability promotes exploitation by controlling gene exchange, while murtation probability enhonces exploration by introducing random disturbances to search new solution spaces.
Answerl Annwwr2-+6 Expeeriencce Pool>How should the
hyperparame hyperparameters of the GA algorithm be adjusted adjusted? Please analyze and think carefully without outputting anything else.
Question2
Answer3
Here is the current data in the Experience Pool Refer to the <data characteristics and determine if the algorithm should prioritize exploration exploitation. are needed.
When GA needs increase exploration, the mutation probability should be increased, while the crossover probability should be reduced. The adjusted parameters are specific data >.
other outputs
Figure Demonstration of CoR.
EXPERIMENT
4.1 EXPERIMENTAL SETTINGS
To comprehensively evaluate AutoEP's performance, we selected classic combinatorial optimization datasets, including TSP Matai et al. (2110), Dantia & Ramser (1959), and FSSP FSSP Emmons Vairaktarakis (2012), as well as more complex, realistic optimization task involving UAV-enabled loT data collection Zhan et al. (0117). We compared AutoEP against three categories of algorithms:
Hyperparameter tuning methods for metaheuristic algorithms. Joshi & Bansal 2020) is
recent manually designed method for hyperparameter tuning. GLEET Ma et al. (2024) represents the SOTA in reinforcement learning baaend based hyperparameter tuning, retrained the network strictly
following the original experimental settings for different algorithms and datasets. BEA Lan et al.
(2022) is leading method using bayesian optimization for hyperparameter tuning.
Neural combinatorial optimization. DACT Ma et al. (202T) and LEHD Luo et al. 2003 are advanced methods for solving combinatorial optimization problems.
L-Mss-enancedd metaheuristic methods. ReEvo and EoH are SOTA methods leveraging LLMs to
enhance metaheuristic operators.
Experimental settings for AutoEP and the comparison algorithms are detailed in Appendix [ For performance testing these datasets, both EoH and ReEvo used the GPT-3.5-turkee model, as

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Published as a conference paper at ICLR 2026
mentioned in their respective papers, while AutoEP utilized the Qwen3-30B LLMs. To ensure statistical robustness and mitigate the effects of random variation, all experiments were repeated 30 times. The results presented in this paper are the mean values from these runs.
4.2 RESULTS
4.2.1
VALIDATION ON TSP
Table Comparison with various baselines on TSP. Opt.gap represents the percentage gap between the average run result and the optimal solution for this dataset; smaller value is better. Time is the average runtime (unit: minute).
Method
01S1
Kal00
Km
RE000
F31ST5
d510000
Opt.gan(S)
Optgapr
Opt.gaplS).
Ope gop(
Ope 0pr.g10//01
DACT
7.5mm
71 1.55m)
LEND
0.08
0.3mm)
0.31
0.20ml
0.96
0.3cm)
1.38
0.4(m)
2.64
0.6(m
5.54
1.8mm)
GA+PT
0.33
0.7mm:
0.5mm)
3.84
1.7(m)
1.8mm
9.43
3.3mm)
19.25
5.3mm)
GNELLEET
0.07
1.3mm)
1.49
1.5mm)
3.23
2.4(m)
7.11
1.5m)
9.06
1.0m
15:23
6 6.8mm)
GA+BEA
0.14
0.8mm:
1.mm
3.76
1.50]]
7.28
1.8m)
9.00
1.5m
15.91
5.5m)
GA+ReEvv
0.27
0.7m:
3.39
1.5mm
7.58
3.0mm)
8.38
144m)
16.53
GA-AmtoEP
0.11
3.30m)
1.06
34im)
2.15
4.3mml
6:27
3.8m)
6.92
5.8m0
14,02
7,8ml
GA Jope
0.17
3.3m:
0.43
0.87
1.62
56.3ml
3:35
161 (1.Mm)
7:14
28 8mm)
GA 2o--2ope-LLEET OLEET
0.00
3.5mm
7.
0.09
30 30.9mm
0.35
57.8mm
0.91
(mm)
5,47
311 51m)
GA-2ope-HEA
0.01
4.5mm)
0.00
8.0ml
0.25
30 mmm
0.41
57.20m)
1.03
160 (65.0m)
5.86
311.20m)
GA-lope-Eall
0.00
1.4mm:
0.04
0.27
70mmm
0.63
36.50m)
2.91
5.83
310.00m
GA-2ape-Antod AutoEP
0.00
5.8mm)
10.10m)
0.01
31.90m)
0.09
58.9m)
0.68
170.20m)
3.58
M22.mm)
GA-2opt-FFol Fot--n--oool-AutaPP
0.00
5m
0.01
(0.2m)
0.01
12 mm
0.11
[mm)
0.08
166 8mm)
3,61
812.8m)
GA-2ape--R So
0.00
6.2mm)
0.01
(000m)
0.01
32
(mm)
0.10
33.8m
0.07
170. (0m)
3.50
For the TSP problem, we selected the TSPL. (1991) dataset and used GAHHolland! (1922)
and GA-2opt (aabaa & Chikhi (2013) as baseline algorithms. GA is widely used metaheuristic algorithm, while GA-2opt, which combines global and local search, is a robust heuristic for TSP. Detailed experimental results are presented in Table The first row displays the performance of neural combinatorial optimization methods on various TSP datasets. The second row compares hyperparameter tuning methods and LLMssenhanced metaheuristic operators using the GA algorithm. Among hyperparameter tuning methods, GLEET performed the best, while ReEvo showed promising results in enhancing metaheuristic operators. AutoEP, after optimizing GA's hyperparameters, achieved the best results across all problem sizes.The third row evaluates GA-2opt, which combines couulation-basee and local search strategies, resulting in strong performance. The test results indicate that the algorithm with dynamically controlled hyperparameters by AutoEP achieved SOTA results across all test datasets, surpassing current neural combinatorial optimization SOTA methods like LEHD and DACT. These comparative results demonstrate that AutoEP, as a aadlu-and-play framework for tuning metaheuristic algorithm hyperparameters, significantly enhances the performance of the original algorithms. To validate AutoEP's ability dynamically adjust hyperparameters when integrated as plugin with any metaheuristic algorithm, we applied it to ReEvo and EoH-enhanced GA-2opt algorithms, as shown in the fourth row. Our results demonstrate that AutoEP further improves the performance of these enhanced algorithms, with final results closely matching those of GA-2opt+ This confirms two key points:
(1) Online adaptation is crucial: Even well-designed initial heuristic benefits from dynamic, state- aware control during the run.
(2) AutoEP is a general-purposs enhancer: It acts as a plug-and-plas module that can improve any given metaheuristic, including those already enhanced by other methods.
Computational Overhead is Minimal. Our CoR architecture, which leverages efficient 30B-pap -oB-paraeeter models, highly practical. The average inference latency per decision is negligible (30 ms). Over an entire optimization run with hundreds of adjustments, the total added time is minimal (e.g., 2-5 minutes on longer runs), a small price for a significant improvement in solution quality.
4.2.2 VALIDATION ON CVRP, FSSP, AND UAV TRAJECTORY OPTIMIZATION
detailed analysis of the experimental results on the CVRP, FSSP, and UAV trajectory optimization datasets can be found in Appendix B
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4.3
ABLATION STUDIES: DECONSTRUCTING AUTOEP's PERFORMANCE
To isolate the contributions of AutoEP's key components, we conducted two ablation studies on the
TSP benchmark.
The Criticality of State-Sensing (ELA) and Reasoning (CoR). Table demonstrates that both the ELA module and the CoR engine are essential for effective performance.
Without ELA, the LLM lacks situational awareness. Though it can still see past actions and outcomes from the experience pool, its performance degrades significantly, as it reasoning without real-time understanding of the search dynamics.
Without CoR (using single LLM),, performance drops to the level of the baseline. This shows that simply feeding raw state features to standard LLM is insufficient; our structured, decomposed reasoning pipeline is crucial for translating state information into an effective strategy.
Without both, the framework operates blindly, leading to chaotic adjustments that perform worse than the untuned baseline.
Efficiency and Accessibility: CoR vs. Monolithic SOTA LLMs. We then investigated whether our multi-LLM CoR could be replaced by a single, powerful, proprictary model (c.g.. GPT-o1, Gemini 2.5 Pro). As shown in Table 3 our CoR, built with efficient 30B 30B-class open-source models, achieves performance on par with these massive SOTA models. However, it does so with an order of magnitude less computational time (e.g., 5.8 min vs. 50 min eil51). This is critical finding: reasoning framework provides a path to achieving SOTA performance without relying on expensive, slow, and proprietary APIs. It makes advanced, LLM--riven algorithm control practical, accessible, and locally deployable.
structured
Table 2: Component ablation study of AutoEP TSP.
Method
ei15
Rd100
Kraa Opt.gap(S))
n3300
rat575
dsj1000
Opt.gapp
Opt_gap("3)
Opt.app(%
Opl.ga((33
Opt.gap(S.))
GA-2opt
0.17
0.43
0.87
1.62
3.35
7.14
AA-Eogt+AntoEP (Withett ELA)
0.06
0.33
0.57
1.30
3.11
6.46
GA-2opt+AunfFP (Without CoR)
0.16
0.43
0.81
1.60
3.37
7.11
GA-2opt+AntoEP (Witheut ELA+CoR)
0.21
0.56
1.37
3,91
7,93
AAtoopt
0.00
0.01
0.01
0.09
0.08
3.58
Table 3: Comparison of CoR components with other reasoning LLMs.
Malse
Rdi00
Kmaa150
n1500
RES75
daj (100000
Ope.gapf
Opt 21p
Opt pape
MootE epoor CONGEE 011
12-7001
6171
[117m0
2000
AmaEP withust C'and:
35.mm
3im)
Amm
2.5 Pro)
0.00
51
56.902)
0.01
2m
0.06
002
AuDEE withost Cok DeepSeek X1I
0.000
$3.9m)
0.01
58.2120
0.11
31.3mm)
0.09
107.4/00
0.11
318.0m)
1.39
Alm)
A12.80m)
4.4 ROBUSTNESS TO FOUNDATIONAL MODEL CAPABILITIES
key concern with LLM-based systems their dependence on the underlying model's power. We tested this by running AutoEP, EoH, and ReEvo with various LLMs. As shown in Figure 4 the performance of EoH and ReEvo, which rely on the LLM's raw generative ability, degrades significantly when using smaller models. In contrast, AutoEP maintains its high performance with less powerful models. This demonstrates that AutoEP's strength comes from its structured framework (grounding via ELA, reasoning via CoR), not just the raw intelligence of the LLM. This architectural robustness makes AutoEP more reliable and practical for real-world deployment.
4.5 SENSITIVITY ADJUSTMENT FREQUENCY
We analyzed the trade-off between decision frequency and performance the UAV problem (Figure 5). While adjusting at every iteration yields the fastest convergence, less frequent adjustments (e.g., every 3-5 iterations) still provide substantial benefits while reducing computational overhead. This provides practical "knob" " for users: on problems with very long runtimes, one can reduce the adjustment frequency save time without sacrificing the majority of the performance gain.
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TSP1000
12.
0ppl (ptpttt))
Owne5-301
Deepterk-22n
GPI-35 Tarto GPT-4 Turbo
Owm23-06
DerpSook-128 GPESS Turbs Turto
UAV Trajectory Optimization
1750
1500
1250
500
Owoni-388
DaspSeek-22n GPE13 GPF-
Owa11-368
DeepSed-222 GFE33 Tarbo GPT-4
differec LLMS
Figure 4: Comparison of Experimental Results Across Different LLMss The baseline algorithm for adjustment GA-2opt.
A critical concern in using LLMs for online control is the management of context length. As noted in Sed3.2, the Experience Pool stores historical states and actions. To prevent prompt bloat and minimize context noise, AutoEP employs sliding window mechanism, retaining only the most recent T. iterations. We conducted an ablation study on the TSP- 100 dataset using GA-2opt to determine the optimal window size. We compared short (L = 5), medium (L = 20), long (L = 50), and infinite (Full History) window sizes.
As shown in Table 4 utilizing the full history significantly degrades both efficiency and solu- tion quality. The performance drop in the "Full History" setting confirms that irrelevant histor- ical data (e.g., early-stage exploration metrics) acts context noise during later optimization stages, causing the LLM to generate subopti- mal strategies. Conversely, a very small window (L = 5) is computationally efficient but lacks sufficient temporal context to identify complex trends like stagnation. The default setting of
Convergecee Curve of Differee Ponmatrr
1250
400 sndehi
400 ha
300
205
170
38
30
150
150
= 20 strikes the optimal balance, providing sufficient history for trend analysis while main- taining low inference latency and filtering out obsolete data.
Figure 5: Comparison of hyperparameter tuning frequencciesUAAV-300)
Table 4: Impact of experience pool size (L) on performance and inference latency (TSP-100).
Pool Size (L)
Opt. Gap (%)
Avg, Inference Latency (s)
Observation
I. 5
0.04
0.18
I Limited context; reactive behavior Balanced context and efficiency Increased latency; minor distractions High latency; hallucination from noise
20 (Default)
0.01
0.31
L = 50
0.03
0.85
Full History
0.17
2.50
4.6 INTERPRETABILITY ANALYSIS: VISUALIZING LLM-DRIVEN CONTROL DYNAMICS
To demonstrate the interpretability of AutoEP, we visualize the evolutionary trajectory of GA hyper- parameters (Mutation and Crossover probabilities) the TSP-400 instance (Figure 6) The resulting

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Published as a conference paper at ICLR 2026
curves reveal sophisticated, state-aware control strategy that distinctively contrasts with manual, monotonic schedules.
Response to ELA Features (Attention to State): The LLM's decisions explainable through the observed ELA metrics. Periods of rapid parameter fluctuation correspond to specific landscape characteristics. For example, when the Dispersion Ratio (Dratio) indicates single-funnel structure4, AutoEP prioritizes exploitation. Conversely, when Skewness signals a risk of premature convergence5, the system triggers 'rescue' behavior by sharply increasing the mutation rate.
Operationalizing
the Exploration-
Exploitation Trade-off: The visualization confirms that AutoEP understands the mechan- ics of GA. The crossover and mutation curves often mirror each other (inverse correlation). This validates that the CoR engine successfully translates abstract directives (e.g., 'intensify exploration? )) into logically consistent numerical actions (High Mutation / Low Crossover).
probability
mutation probability
0.7
0.6
Parameter vuluee
0.5
0.4
Emergence of Search Policies via In-Context Learning: Beyond direction, the magniuude of adjustments shows structured patterns. The LLM utilizes the Experience Pool to determine not just what to change, but how much. This results in distinct phases: aggressive large-step adjustments to escape stagnation, followed by fine-grate gra-ngr small-step tuning for local conver- gence, proving the effective utilization of histor- ical search context.
0.3
100
200
300
400
500
Number of
Figure 6: Visualization of hyperparameter evolu-
tion for GA on TSP-400.
DISCUSSION AND CONCLUSION
In this work, we introduced AutoEP, a framework that pioneers a new paradigm for automated algorithm configuration. By synergizing real-time search analytics (ELA) with the reasoning capabil- ities of LLMs, we have demonstrated a system that can dynamically control complex metaheuristic algorithms in zero-shot, training-fie ffree manner. Our extensive experiments show that this approach not only outperforms state-of-te the the-art hyperparameter tuners but also elevates classical heuristics to a performance level competitive with specialized neural optimization methods.
Broader Implications: A Shift from Learning to Reasoning. Our work represents a fundamental departure from the dominant "learning from scratch" paradigm, exemplified by reinforeement learning. Instead of investing massive computational resources to train control policy for every new problem or algorithm variant, AutoEP leverages the rich prior knowledge embedded within pre-trained LLMs. This transforms the problem of algorithm control from one of sample-intensive learning to one of efficient, in-context reasoning. At the core of AutoEP is a gense-reason--e loop, where ELA provides the senses, the CoR provides the reasoning, and hyperparameter adjustments are the actions. This loop offers generalizable blueprint for creating more adaptive and intelligent computational systems.
Practical Advantages for World Optimization. Beyond its novelty, AutoEP designed for practicality. Its plug-and-play framework makes it general-purpose tool for enhancing any metaheuristic algorithm. Crucially, as demonstrated by our ablation studies, AutoEP's structured reasoning framework reduces the dependency architectural strength allows it to achieve SOTA performance using smaller, open open-source models (e.g.. 30B-32B class). This is critical advantage for real-world applications like factory scheduling logistics, where local deployment is necessary to ensure data privacy, low latency, and operational reliability, and where deploying massive proprietary models often infeasible.
single, monolithie LLM's 's raw intelligence. This
ETHICAL STATEMENT AND REPRODUCIBILITY STATEMENT
Our paper has no conflicts of interest and complies with ethical standards. Our paper code is reproducible, and we have provided an anonymous link to the reproducible code.
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ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 62273352, 72501290, and 72401287. The authors would like thank the anonymous reviewers for their constructive feedback, which helped improve the quality of this paper.
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data collection in enabled wireless
A LLM USAGE
We only used LLMs to polish the paper writing.
B DETAILED EXPERIMENTAL RESULTS
B. VALIDATION ON CVRP
For the CVRP problem, we used the VRPLIB Semet & Taillard (1993) dataset and included both GA-2opt and (00-2oot[Sabbee & Chikhi (203) algorithms to evaluate AutoEP's performance across different metaheuristic algorithms. The test results are presented In the first column, DACT and LEHD continue to show strong performance. The second column compares various methods for improving PSO-2opt, where AutoEP achieves superior results. The third column evaluates enhancements GA-2opt, with AutoEP demonstrating the best performance. Additionally, GA-2opt combined with AutoEP achieves the smallest gap from the optimal solutions across all datasets.
Table 5: Comparison with various baselines on CVRP. Opt.gap represents the percentage gap between the average result and the optimal solution; smaller value is better. Time is the average runtime (unit: minute).
Method
N-20
N-50
N-100
N-XII
N-500
Op.paap%)..
Time
Opt ppp()]]
Time
Opl.gap(8.)
Time
Opt gup
Time
Opt (ap(3))
Time
7.53
0.2(m)
0.3(m)
0.4(m)
PSO-3opt
3.00m)
7.50a))
28.0(m)
55.0(m)
0(m)
P50-2optePT
0.19
3.3mm)
0.29
7,9(m)
1.13
28. km))
3.77
55.3mm)
5.81
165.40 4(m)
P5O-ZogreGLBEE
0.08
3.3(m)
0.14
9.20pl
0.97
302(m)
2.95
57.1mm
4.82
167.2tm
P5O-1qp--BAA
011
4.1(m)
0.26
8.7(m)
1.04
20 3(m)
3.99
56.2(m)
5.31
166. 7(m)
P5O-2opt-Fott
0.12
3.2mm)
0.33
7.7(m)
1.30
28. 3(m)
4,71
55.2(m)
7.47
165 2(m)
Reo-
0.09
3.7mm)
0.27
8.3mm)
1.27
25.5(m
3.92
55.8mm)
6.1
15m8
PSO-2optrAutoEF
10.7(m)
31.2(m)
168.5tm)
31.Xm)
2opt-P
3.5(m)
GA-2opi-GLEET
0.01
3.7(m)
0.07
8.2(m)
8(m)
1.44
59.7(m)
4.07
8(m)
BA-2ogt-BLA
0.07
4.6km)
0.11
9.1ipal
0.24
32 32.1000
1,83
60.1/mm
4.71
179, [um)
FAA-2ptt-FoHt
0.88
3.6(m)
0.15
8.2(m)
0.63
31.2/m)
2.17
59.2(m)
6.55
178. 2(m)
GA Zopt-ReEivo
0.03
4.0km)
0.08
8.61m)
0.14
31.6(m)
1.69
59.61m)
5.27
178, 6im)
GA- 2opto AutoEE
0.01
6.10m)
0.05
10.9mm)
0.13
33.90m
1,08
62.100
3.17
181.1(m)
2opt-Lolt+AAutheP
11.2mm)
34.20m)
62.3mm
4tm)
Rhb-2egt-RoFo--Auube
11.10m)
34.1(m)
181.
B.2
VALIDATION ON FSSP
For the FSSP problem, we used the Taillard Taillard (1993) dataset and GA-2 as the baseline algorithm. We also included advanced methods for FSSP: NEH Nawaz et al. (1983), NEHFF Vergaadez-VVaggs Framinan (2014), and PFSPNet_NER Pan et al. (2021). The test results are presented in Table 6 In the first column, PFSPNet NEH shows superior performance among the comparison algorithms. The second column demonstrates that AutoEP significantly enhances GA-2opt across all datasets, consistently achieving the best results.
B.3 VALIDATION ON UAV TRAJECTORY OPTIMIZATION
In remote or disaster-stricken areas where ground-based network connectivity is unavailable, using UAVs for data collection and transmission has become a significant research focus Yan et al. (2023). Testing AutoEP's performance in more complex optimization scenarios is therefore highly relevant. UAV trajectory optimization for data collection involves factors such as flight speed, energy consump- tion due to environmental resistance, data collection rate, and storage capacity. The optimization goal is to minimize data collection time. The ACO Dorigo et al. (2077) algorithm, widely used in trajectory optimization, was chosen the baseline for comparison.A detailed mathematical model is presented in Liu et al. 2002)) Experimental results, presented in Table 7 show the minimized data collection times for varying sensor node numbers. Compared to other methods that improve ACO, AutoEP demonstrated the greatest enhancement, improving ACO's performance by 17. 16% with 300 sensor nodes.
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Table 6: Comparison with various baselines on FSSP. Opt.gap represents the percentage gap between the average run result and the optimal solution; a smaller value is better. Time is the average runtime (unit: minute).
Method
n.0mlT
V50mm0
N100m20
N200mm30
N:00mm0
Opicppp(3)
Time
Opt (X]
Time
Opt.sppSS1
Time
Opt.age [5)
Time
Opl.gpp(S.
Time
NER NEHFF
4.05
(14km)
3,47
0.7(1))
3.38
5:21
3.N(u
4.39
4.7mm)
4.15
0.5(m)
3.62
0.8(m)
3.73
2.0mm)
5.82
4.0(m)
4.83
4 4.5mm))
PESPNct
4,01
3.48
0,9(ca)
3.56
2.2mm)
6,05
4.2mm)
5.36
5.00m)
8.3
5m)m
GA--opt-PT
3.000)
8.6(a)
60.4(s)
(78,5(m)
GA-2opI-GLEET
2.64
4.1(m)
2,95
10.5(m)
3.67
33.8(m)
3.28
62.3ml
3.52
180.2tm)
6A-Zopt-BLA
291
4.5(m)
3.35
9.3mml
3.95
32 22.00m)
3,53
61.2
3.81
179.5tm)
FiA-2opt-FFoft
1.1
3.7(m)
1.87
8.4(m))
4.49
31 8(m)
1.64
60.2(m)
4.22
178. km))
GA Zopt-ReEiv
2.85
4.0km)
3.16
8,9(ca)
3.88
32.2(m
3.31
60.7mm)
3.74
178. Stm)
GA GGN-2epteAutoFP
2.09
6.3mm)
2,80
10.8(m
3,16
34.6mm)
2,93
63.2m
2.83
181,5(m)
11.0mm)
(iA-2opt- AuttA
(0.9(m)
2,81
(8m)6())
Table 7: Comparison of UAV Trajectory Optimization Experiments. Traj.Lengte is the length of the drone's flight trajectory, where a lower value indicates a better performance. Time the average runtime (unit: minute).
Method
n20
NI00
N200
N:000
Truj Langth
Time
Traj Length)
Time
Trai Lengthi
Time
Truj Lengih)
Time
Traji Traj-Lmmhh
Time
ACO
[47.35
2.5mm
312.23
4.05m)
607 20
20.0(m)
1.87.05
58.5m)
1912.74
(01km)
ACO4PT
133.04
2.5(m)
73
4.4(m)
576.18
20.5(m)
1182.78
50.0km)
ACO+GLEET
1125.31
ACO+BEA
131,70
2.6mm)
297
5.2(m)
572.84
21.2(m)
1146.79
39.7(m)
1706.41
91 21m)
ACD+FaH
136.41
2.4m)]
302 54
4.3(m)
587.46 46
20.3(m)
1208 19
58.8(m)
1774.25
90 k(m)
AcDoReEvo
131.56
2.5(m)
297 46
4.7(m)
571 26
20.9(m)
1184.46
39.2(an)
1690.83
90.5cl)
ACteAE
122.08
4.2ml
291.58
6.5mm)
550.31
23.00m)
1079.83
41.7(m)
1574.90
93.5(m)
ACO+EnlE-AuIEEP
122.09
4.5cm)
23.4tm)
42.0kmm)
ACOHReENo+AulcEP
122.06
4.3mm)
291 58
6.7mm)
530.30
23.2(m)
1079.82
41,9km)
1574.92
93.6(m)
C PROMPT
C.I PROMPT FOR THE GA
Below is the complete set of prompts used for the GA algorithm in solving the TSP problem:
In genetic algorithms, hyperparameters such crossover probability and mutation probability play critical role. Could you analyze the impact of these hyperporameters on the algorithm's 's exploration-expllitaiio balance?
Figure 7: GA:Prompt for Strategist LLM.
C.2 PROMPT FOR THE PSO
Below is the complete set of prompts for the PSO algorithm in solving the CVRP problem:
In the PSO algorithm, key hyperparometers include inertia weight, social learning factor, and individual learning factor. Could you analyze how these hyperparometers affect exploration-exploitar balance algorithm?
Figure 10: PSO: Prompt for Strategist L.M.
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Published as a conference paper at ICLR 2026
The experience pool contains data from previous iterations: Iterations: 10, Cressover Probability: 0.7, Mutation Probability: Best Fitness Value: 1168.
Current algorithm state features: Kurtosis: 0.3, Skewness: 0.27, Diversity: 1, :0:0,13, Datio :0.78.
Feature descriptions:
the solution distribution is symmetric, indicating balance between exploration and exploitation. If the skewness is significantly greater than 0, most solutions are poor, suggesting the need more
the skewness value
search and exploitation. If skewness significantly less local optimum, necessitating
there risk of converging to
increase in exploration.
2. If the kurtosis is near 0, the fitness values are balanced between the mean and the tails, When the kurtosis concentrated, and diversity low, requiring Conversely, when the kurtosis is significantly less than O, the solution set is dispersed, suggesting need to search for local optima, thus increasing exploitation.
significantly greater than 0, the solutions
exploration.
3. If the diversity value is greater than 1, the population still evolving, and increasing local search could improve exploitation. If the diversity less than or equal to 1. the population stuck, and increasing exploration necessary.
4. A high R² = 1 indicates well-structured landscape (i.e., funnel), signaling need to increase exploitation. Conversely, low
implies a rugged or multi-modal landscape, requiring an increase in exploration avoid premature convergence.
5. A value of Dratio < (e.g., 0.2) strong indicator of single funnel structure, as the best solutions are tightly clustered. This signals the need to increase exploitation to refine the search within this promising basin. Conversely. value of Dratio suggests multi-modal landscape, where elite solutions found in disparate regions. This necessitates increase in exploration to avoid premature convergence local optimum.
Based feature descriptions and historical decision information, determine whether the algorithm requires further exploration or development. No additional output is required.
Figure 8: GA: Prompt for Analyst LLM.
The current hyperparameters of the genetic algorithm are:
Crossover Probability: A7,,Mtation Probability: 0.1. The range of the crossover probability is (0.55, 0.7], and the range of the mutation probability is [0.1. 0.45). In genetic algorithms, crossover probability promotes development by controlling gene exchange, while mutation probability enhances exploration by introducing random disruptions to search new solution spaces. Based on the algorithm state analysis, there is need to increase exploration. Please analyze how to adjust hyperparameters by referencing historical decision information. No additional output required; only the specific values of the hyperporameters need to provided.
Figure 9: GA: Prompt for Actuator LLM.
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Published as a conference paper at ICLR 2026
The experience pool contains data from previous iterations:
Iterations: 20, Inertia Weight: 0.3, Social Learning Factor: 2.2. Individual Learning Factor: 1.5,Best Fitness Value:
790. Current algorithm state features: Kurtosis: 0.22, Skewness: -0.35, Diversity: 1.3, R²:0.85, 00.1.
Feature descriptions:
1. If the skewness value is close to 0, the solution distribution is symmetric, indicating balance between exploration and exploitation. If the skewness is significantly greater than 0, most solutions are poor, suggesting the need for
local search and exploitation. If skewness significantly a local optimum, necessitating an increase in exploration.
than
risk of converging
fitness values are balanced between mean and tails. the kurtosis significantly greater than 0, the solutions are concentrated, and diversity is low, requiring an increase in exploration. Conversely, when the kurtosis significantly less than O, the solution set is dispersed, suggesting need to search for local optima, thus increasing exploitation.
2. kurtosis is near 0,
3. If the diversity value is greater than 1, the population still evolving, and increasing local search could improve exploitation. the diversity less necessary.
equa! to 1, the population stuck, increasing exploration
4. A high R² = 1 indicates well-structured landscape (i.e., a funnel). signaling need to increase exploitation. Conversely. low R² implies rugged multi-modal landscape, requiring increase exploration avoid premature convergence.
of Dratio (e.g., 0.2) strong indicator of single funnel structure, tightly clustered. This signals the need increase exploitation refine the search within promising basin.
solutions are
Conversely, value of Dratio suggests mufti-modal landscape, where elite solutions are found in disparate regions. This necessitates an increase in exploration to avoid premature convergence to a local optimum.
Based feature descriptions and historical decision information, determine whether the algorithm requires further exploration or development. No additional output is required.
Figure 11: PSO: Prompt for Analyst LLM.
The current hyperporameters for the PSO algorithm are:
Inertia Weight: 0.3, Social Learning Factor: 2.2, Individual Learning Factor: 1.5. The range of the inertia weight is [0.2, 1]. In the PS0 algorithm, increasing inertia weight enhances exploration but weakens exploitation, while decreasing inertia weight strengthens exploitation but reduces exploration. Increasing the individual learning factor boosts exploration. whereas increasing the social learning factor enhances exploitation. Given the algorithm's need increased exploitation. Please analyze information. No additional output is required; only the specific values of the hyperparameters need be provided.
adjust hyperparameters by referencing historical decision
Figure 12: PSO: Prompt for Actuator LLM.
C.3
PROMPT FOR THE ACO
Below is the complete set of prompts for the ACO algorithm solving the UAV Trajectory Opti- mization problem:
In the Ant Colony Optimization algorithm, key hyperparameters include the pheromone factor, heuristic factor, and pheromone evaporation rate. Could you analyze these hyperparameters affect exploration-expllittiin balance of the algorithm?
Figure 13: ACO: Prompt for Strategist LLM.
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Published as a conference paper at ICLR 2026
The experience pool contains from previous iterations:
Iterations: 90, Pheromone Factor: 1.8, Heuristic Factor: 1.3, Pheromone Evaporation Rate: O.2, Best Fitness Value:
437. Current algorithm state features: Kurtosis: 0,02, Skewness: 0,02, Diversity: 1.1, 40.0,4 Dratio:
Feature descriptions:
1. If the skewness value is close to 0, the solution distribution is symmetric, indicating balance between
exploration and exploitation. If the skewness is significantly greater than 0, most solutions are poor, suggesting the need for
local search and exploitation. If skewness is significantly less than there risk of converging a local optimum, necessitating an increase in exploration.
the kurtosis near 0, the fitness values balanced between mean and tails. the kurtosis significantly greater than 0, the solutions are concentrated, and diversity is low, requiring increase in exploration. Conversely, when the kurtosis is significantly less than O, the solution set is dispersed, suggesting a need to search for local optima, thus increasing explortation.
3. If the diversity value is greater than 1, the population still evolving, and increasing local search could improve exploitation. If the diversity less than equa! to 1, the population stuck, increasing exploration necessary.
4. A high R² 1 indicates well-structured landscape (l.e., a funnel), signaling need to increase exploitation. Conversely. low R² = 0 implies rugged multi-modal landscape, requiring increase exploration avoid premature convergence.
of Dratio < (e.g., 0.2) strong indicator of single funnel structure, as best solutions are tightly clustered. This signals the need increase exploitation to refine the search within this promising basin. Conversely, value of Dratio =:1 suggests mufti-modal landscape, where elite solutions are found in disparate regions. This necessitates an increase in exploration to avoid premature convergence to a local optimum.
5.
Based the description of the features, determine whether the algorithm needs more exploration exploitation. additional output is required.
Figure 14: ACO; Prompt for Analyst LLM
The current hyperparameters for the ACO algorithm are:
Pheromone Factor: 1,8, Heuristic Factor: 1.3, Pheromone Evaporation Rate: 0,2. The pheromone factor and heuristic factor ranges are [1, 4], and the pheromone evaporation rate range is [0.1. 0.9]. In the ACO algorithm, increases increasing the pheromone factor and heuristic factor enhances exploitation, while decreasing exploration. Increasing the pheromone evaporation rate promotes exploration. Based the current algorithm state analysis, the gool to maintain a balance. Please analyze how to adjust hyperporameters by referencing historical decision information. No additional output is required.
Figure 15: ACO: Prompt for Actuator LLM.
D DETAILS OF THE EXPERIMENTAL. SETUP
All LLMS used in this study were accessed via the publicly available APIs provided by their respective developers. The experiments were conducted system equipped with an Intel Core i9- 1390KK CPU and an NVIDIA A800#4 GPU. On average, adjusting hyperparameters using AutoEP took 0.3 seconds per run. For performance evaluation, the L.M employed by AutoEP was Qwen3-30B, while the L.MS used in other methods followed the configurations specified in the original papers. The configurations for the comparison algorithms were strictly adhered as outlined in the original studies. The parameter settings for the improved base algorithm are shown in Table S
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Published as a conference paper at ICLR 2026
Table Parameterization of each meta heuristic algorithm
Algorithm
Parameter
Value
Population size
500
Maximum number of iterations
500
GA
Initial crossover probability
0.6
Initial mutation probability
0.1
Population size
500
Maximum number of iterations
500
PSO
Initial individual learning factor
1.5
Initial social learning factor
1.5
Inertia weights
0.3
Population size
500
Maximum number of iterations
500
ACO
Initial pheromone factor
2
Initial heuristic factor
Initial pheromone volatility factor
0.3
19


Reviews:
[{"review_id": "zs23O0EF1k", "reviewer": "Reviewer_yVzs", "summary": "This work describes a novel idea for dynamic algorithm configuration in optimization. The authors are motivated by the limitation of human-crafted configuration rules and generalization bottoleneck of latest learning-assisted approaches. To address these technical issues, the authors propose leveraging LLMs (with vast knowledge) to kick a balance between the configuration effectiveness and generalization. Specifically, the overall framework comprises a ELA calculator and a multi-role LLM system. Given an optimizer and corresponding optimizee at hand (e.g., GA for solving TSP), the ELA calculator summarizes per step dynamic landscape information and feeds such information into the multi-role LLM system. Then the LLM system analyse such information and dictates proper algorithm configuration for the optimizer to control the exploration and exploitation strength. Through extensive experiments, the effectivess of the proposed framework is validated.", "questions": "See Weaknesses.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Novelty: While some previous works may also considered using LLM for algorithm configuration or selection such as LLaMoCo (implicit and static algorithm configuration through code generation, https://arxiv.org/pdf/2403.01131) and AS-LLM (training algorithm selection mapping through LLM, https://openreview.net/forum?id=l7aD9VMQUq), I have to acknowledge this paper as a novel perspective, with reasonable usage of LLMs to relieve human efforts required for tuning optimization algorithms. Such novelty roots from the reasoning ability of existing LLMs.\n\n2. Systematic Design: I think the most important and significant contribution of this paper is that it demonstrates that through ELA anaysis, the strength of LLM and the performance of an optimizer can be bridged in a dynamic algorithm configuration fashion.\n\n3. Significance: the experiments results are solid, and especiall compared with latest EoH and ReeVO (LLM-based AAD methods), the performance gain is good.", "weaknesses": "Besides the strength of this paper, I wanna list several concerns.\n\n1. Efficiency: I understand that using LLM to provide ideal performance is already a breakthrough for automated algorithm configuration. However, I suggest the authors carefully claim their approach's superiority. Here, an interesting question is since AutoEP has to use LLM for reasoning, why the running time is still comparable with GA itself?\n\n2. The experience pool compreises per step action-reward entries, while it may provides certain heuristic on how to choose parameter value, it is still unclear why such myopia information could help AutoEP bypass RL-based approach such as GLEET, since in RL-based approaches, the bellman updates ensure the policy to learn long-term decision. This deserves in-depth investigation.\n\n3. The underlying optimzers are restricted within simple optimizer such as GA, PSO.... This might makes readers curious about the true potential of AutoEP on more complex optimizer with complex configuration space.\n\n4. The related work could be polished and refined further. Can the authors use Meta-Black-Box Optimization to denote learning-assisted or data-driven or reinforcement learning-based approaches? since recently these methods have been summarized and termed by this terminology. Also consider reviewing latest works in  Meta-Black-Box Optimization (surveys and papers in 2025).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Okzvrzj6Ps", "reviewer": "Reviewer_LhpG", "summary": "This paper proposes a LLM-based algorithm configuration framework with reasoning chain. The decision of configurations is decomposed into a multi-step reasoning chain. Starting from a strategist LLM which analyses the impact of the hyperparameters of the given algorithm, LLM analyses the current optimization status from ELA features, determine to enhance exploration or exploitation, and modify the algorithm hyperparameters to achieve that. Experimental results show that the proposed method surpasses RL-based algorthm configuration baselines and LLM-based metaheuristic methods on TSP, CVRP and UAV trajectory optimization tasks.", "questions": "1. The feature description explicitly instructs the LLM to explore or exploit based on whether feature values are high or low. If we already possess this deterministic knowledge about when to increase exploration or exploitation, why not replace this component with a simpler, more efficient machine learning model, such as a decision tree?\n\n2. The feature descriptions and experience pool appear to consume a significant number of tokens. How is the average inference latency per decision maintained within 30 ms despite this potential computational overhead?\n\n3. In Figure 4, AutoEP with different base LLMs demonstrates nearly identical performance. Does this imply that different LLMs are making the same configuration decisions? Why would LLMs of varying scales and capabilities take identical actions?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The algorithm configuration process is decomposed into several steps with detailed descriptions, which significantly enhances interpretability. Users can deeply analyze why the LLM makes a particular decision and how the framework achieves SOTA performance, providing insights for future algorithm design.\n\n2. The plug-and-play approach is adaptive and generalizable, enabling application across broader optimization scenarios and enhancing the interpretability and performance of LLMs in diverse applications.\n\n3. The experimental results validate the SOTA performance of the proposed method on three combinatorial optimization tasks.", "weaknesses": "1. The strategist LLM requires users to provide the name of the target algorithm and its hyperparemeters. It demands users' expert knowledge requirement on the target optimization tasks. For optimization tasks where users lack familiarity or no known promising algorithms exist, specifying a suitable algorithm becomes challenging.\n\n2. Furthermore, the algorithmic knowledge embedded in LLMs is inherently limited and potentially outdated. Consequently, LLMs may struggle to accurately analyze the qualitative effects of hyperparameters in complex, advanced algorithms, which could hinder the framework's generalization across diverse optimization tasks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jOGQSKEkZj", "reviewer": "Reviewer_yTaP", "summary": "This paper proposes AutoEP, an LLM-driven framework for automating hyperparameter evolution in metaheuristic algorithms.The core idea is to replace static control rules or reinforcement-learning-based policies with quantitative reasoning driven by LLMs, thereby enabling adaptive, interpretable hyperparameter control without additional training.AutoEP incorporates an exploratory landscape analysis (ELA) module that extracts numerical descriptors from the ongoing optimization process, and a chain-of-reasoning (CoR) framework consisting of three agents (Strategist, Analyst, Actuator) to translate ELA features into parameter updates.\nExperimental results across multiple metaheuristic algorithms (GA, PSO, ACO) and optimization problems (TSP, CVRP, FSSP, UAV trajectory optimization) demonstrate that AutoEP improves performance and runtime efficiency compared to classical adaptive heuristics and recent LLM-enhanced approaches.\nAblation studies further support the importance of ELA grounding and CoR decomposition.", "questions": "1. Since all historical records are kept, how large does the Experience Pool grow during long optimization runs, and how is memory or context length managed?\n2. Is there any mechanism (e.g., damping or adaptive scaling) to prevent over-adjustment of hyperparameters?\n3. Can AUTOEP adapt to new algorithm families (e.g., DE or CMA-ES) without additional human intervention?\n4. Could you report sensitivity analyses for Experience Pool size and CoR decision frequency?\n5. Could you also report per-component latency breakdown (Strategist/Analyst/Actuator) to substantiate the 30 ms decision claim?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Introducing an ELA-grounded, LLM-reasoning framework for online parameter control is conceptually new and methodologically sound.\n2. The CoR structure (Strategist–Analyst–Actuator) provides interpretability and modularity while reducing reliance on very large proprietary models.\n3. The paper evaluates across four distinct problem domains and three algorithmic backbones, demonstrating versatility. Ablation and sensitivity analyses are included and substantiate the key design choices.", "weaknesses": "1. Section 3.2 states that all historical states, actions, and outcomes are stored in the Experience Pool.While this guarantees completeness, it also raises concerns about prompt bloat and redundant context as optimization proceeds over hundreds of generations.In large-scale or long-horizon runs, this could degrade inference efficiency and increase context noise for the LLM.\n2. The framework claims that the CoR pipeline ensures stable exploration–exploitation balancing, but no mathematical or empirical justification is provided for convergence.\n3. Visualizing how LLM decisions evolve (e.g., parameter adjustment curves or attention to specific ELA features) would substantiate the interpretability claim.\n4. AutoEP is compared to ReEvo and EoH but not to more recent LLM-based black-box optimizers such as EvoLLM.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BQwa0cmws4", "reviewer": "Reviewer_xA6g", "summary": "This paper introduces a new framework called AutoEP, which aims to optimize the performance of metaheuristic algorithms by using LLMs to automatically adjust the algorithm's hyperparameters. The main contribution of the paper is the proposal of a novel framework that does not require training and can dynamically adjust the algorithm's hyperparameters through the zero-shot reasoning ability of LLMs.", "questions": "Just a kind discussion:\nIn this framework, do you think the algorithm relies more on the reasoning ability of the LLM, the experience (historical knowledge of the search space), or memory (rote learning)?\nMy essential question is whether the algorithm can solve a completely new combinatorial optimization task (one that is not TSP, for example) by solely depending on its reasoning ability.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1) The paper is organized and easy to follow, with a clear presentation of the problem, methodology, and results.\n2) The experiments are thorough, using multiple benchmarks and reliable comparisons to validate the proposed method.\n3) The method of using LLMs for zero-shot reasoning to adjust hyperparameters is novel and offers a fresh perspective in automated algorithm design.", "weaknesses": "1) Dependency on LLM Performance: AutoEP’s effectiveness relies on the capabilities of the underlying LLM, which may vary in accuracy and efficiency, affecting consistency.\n2) The current tests focus on standard benchmarks. Broader testing on more complex or dynamic problems would offer better insights into its robustness and scalability. Some Case study will be good.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Oral)