Organizations: School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China. · International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences, Beijing 100190, China. · Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences, Beijing 100049, China. · School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China. · Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Evolutionary program search with large language models keeps the structure of an evolutionary algorithm and uses the model as its variation operator. Typically, the model generates each candidate program in a single request from parent programs and their scores. We present AgenticEvolve, an evolutionary program search framework in which each island is run by a persistent large language model agent. Between evaluations, the agent designs and runs experiments on the candidate program. To measure the contribution of experimentation, we compare AgenticEvolve with No-analysis, an otherwise identical configuration with experiments disabled. On two heuristic design tasks with three large language models, AgenticEvolve produces better programs than No-analysis and OpenEvolve on both hidden and unseen instances. It reaches the baselines' final quality with far fewer evaluations and comparable cost. On twelve equation discovery problems, it recovers the ground-truth structure of more equations than No-analysis and existing language-model and genetic programming baselines.
Figures & tables
Fig. 1: AgenticEvolve. Left: one island, magnified. A persistent agent edits program.py and commits it for formal evaluation. Between commits, it may write and execute analysis.py to run experiments. No-analysis removes these experiments. The feedback on each commit includes a summary of the archive, and the agent can read any archived program, including those of other islands. Right: islands run concurrently and exchange migration candidates, which appear in the archive summary. The agent decides whether to use them.
Model
Input
Cached input
Output
Reasoning
DeepSeek-V4.1-Flash
0.15
0.003
0.60
high
GLM-5.3-Flash
0.15
0.03
0.50
high
Qwen3.8-Flash
0.15
0.016
0.47
medium
TABLE I: LLMs Used in the Experiments, with List Prices in USD per Million Tokens and Reasoning Effort
Fig. 2: Final program quality on the hidden evaluation set and on unseen instances. The unseen OBP instances are OR1 and fresh sequences from the training distribution, and the unseen DJSS instances are the same scenarios with fresh seeds. Each point is one run. Black squares and bars are the mean ± SD over five runs. Gray dashes mark Best Fit, the FunSearch heuristic and rule R1.
Model
Method
Hidden
Unseen
Cost ($)
p
Online bin packing (unseen: OR1)
DeepSeek
AgenticEvolve
3.42 ± 0.25
2.92 ± 0.48
1.08
–
AgenticEvolve (No-analysis)
5.54 ± 1.05
5.12 ± 0.92
0.42
< 0.01
OpenEvolve
5.74 ± 0.41
5.12 ± 0.42
3.06
< 0.01
GLM
AgenticEvolve
4.46 ± 0.80
4.14 ± 0.54
4.48
–
AgenticEvolve (No-analysis)
6.30 ± 0.19
5.61 ± 0.26
0.56
< 0.01
TABLE II: Heuristic design results: mean ± SD over five runs of the final program’s quality on the hidden set and on unseen instances (lower is better), and estimated cost per run. p : two-sided Mann–Whitney test of hidden-set quality against AgenticEvolve.
Fig. 3: Best-so-far quality against formal evaluations. Thin lines are individual runs. Bold lines and bands are the mean ± SD over the common evaluation range. The initial job-shop program scores 1.648 and lies above the plotted range.
Fig. 4: Best-so-far quality against estimated cost. Thin lines are individual runs. Bold lines and bands are the mean ± SD over the common evaluation range. Circles mark each run’s actual spend. The initial job-shop program lies above the plotted range.
Fig. 5: Estimated final waste and the optimized potential function, plotted against remaining capacity L , for the first commit of island 0 in GLM run 1 on OBP. Circles: the estimate from the agent’s seventh analysis on self-generated sequences. Line: the table U used by the committed program after coordinate descent. The dotted line marks the smallest item size, 20.
Method
Acc ID
Acc OOD
Eval.
Requests
Cost ($)
AgenticEvolve
12
12
316
4939
6.54
AgenticEvolve (No-analysis)
8
8
3988
7809
12.12
LLM-SR
3
3
12000
12000
111.34
SR-Scientist
7
8
83
5496
6.59
PySR
1
1
–
–
–
TABLE III: Symbolic regression results, totals over the twelve problems. Acc ID and Acc OOD count the problems whose selected equation is within tolerance 10−3 on the in-domain and out-of-domain test sets. For SR-Scientist, evaluations are the calls of its evaluator tool.
Problem
AgenticEvolve
AgenticEvolve (No-analysis)
LLM-SR
SR-Scientist
PySR
CRK21
∙ 6.8e-15
– 2.0e-05
– 1.2e-05
– 5.6e-07
– 4.8e-05
CRK35
∘ 3.0e-14
∙ 2.9e-14
– 9.2e-05
∙ 2.9e-14
– 3.8e-03
BPG18
∙ 1.7e-12
∙ 1.7e-12
∘ 1.7e-12
∘ 2.2e-14
– 3.4e-03
PO10
∙ 1.4e-14
– 1.8e-02
– 2.0e-02
∙ 1.4e-14
– 5.5e-04
PO0
∘ 6.8e-13
– 7.2e-05
– 6.9e-04
– 1.2e-03
– 1.1e-02
PO26
∙ 1.0e-12
∘ 1.0e-12
– 1.5e-03
– 1.1e-02
– 3.2e-02
TABLE IV: Structure of the selected equation on each problem ( ∙ exact, ∘ negligible extra terms, – not recovered) and its normalized mean squared error on the out-of-domain test set, bold when within tolerance 10−3 . The material-science problems are judged against the reduced truth.
Setting
Default
Used
Reason
num_islands
5
3
Same as AgenticEvolve.
feature_dimensions
code length, diversity
task features
Same features as AgenticEvolve.
migration_interval
50
10
Each island advances about 60 generations in a run, so the default would trigger migration at most once.
population_size
1000
50
A run produces 180 programs and would never fill the default population. Most example configurations distributed with OpenEvolve use 40 to 100.
temperature
0.7
1.0
Same as AgenticEvolve.
max_tokens
4096
model maximum
Same as AgenticEvolve.
TABLE S1: OpenEvolve settings that differ from the defaults of version 0.3.2. The evaluator timeout is given for OBP and DJSS.
Online bin packing
Dynamic job shop
Model
Method
Hidden
OR1
Fresh
Hidden
Fresh
DeepSeek
AgenticEvolve
3.42 ± 0.25
2.92 ± 0.48
3.72 ± 0.32
0.840 ± 0.063
0.846 ± 0.072
AgenticEvolve (No-analysis)
5.54 ± 1.05
5.12 ± 0.92
5.69 ± 0.95
0.970 ± 0.028
0.974 ± 0.025
OpenEvolve
5.74 ± 0.41
5.12 ± 0.42
5.85 ± 0.42
0.911 ± 0.041
0.923 ± 0.025
GLM
AgenticEvolve
4.46 ± 0.80
4.14 ± 0.54
4.72 ± 0.74
0.847 ± 0.039
0.863 ± 0.039
AgenticEvolve (No-analysis)
6.30 ± 0.19
5.61 ± 0.26
6.37 ± 0.16
0.928 ± 0.074
0.952 ± 0.069
TABLE S2: Final quality on every evaluation set, mean ± SD over five runs (lower is better). OBP quality is the excess over the L2 bound in percent, and DJSS quality is the tardiness relative to rule R1. Hidden-set values are the scores recorded during the runs. Values on OR1 and on fresh instances come from a separate evaluation of the final programs.
AgenticEvolve − No-analysis
AgenticEvolve − OpenEvolve
No-analysis − OpenEvolve
Model
Task
Set
Difference
p
Difference
p
Difference
p
DeepSeek
OBP
Hidden
− 2.12 [ − 2.93, − 1.24]
0.008
− 2.32 [ − 2.73, − 1.98]
0.008
− 0.20 [ − 1.14, 0.66]
0.917 a
OR1
− 2.20 [ − 3.00, − 1.37]
0.008
− 2.20 [ − 2.71, − 1.69]
0.012 a
0.00 [ − 0.84, 0.75]
0.916 a
Fresh
− 1.97 [ − 2.73, − 1.16]
0.008
− 2.13 [ − 2.58, − 1.75]
0.008
− 0.16 [ − 1.01, 0.62]
1.000
DJSS
Hidden
− 0.130 [ − 0.175, − 0.072]
0.016
− 0.071 [ − 0.123, − 0.006]
0.095
0.059 [0.022, 0.100]
0.056
Fresh
− 0.128 [ − 0.176, − 0.061]
0.032
− 0.077 [ − 0.124, − 0.009]
0.151
0.051 [0.025, 0.079]
0.032
TABLE S3: Differences in mean final quality between methods, with bootstrap 95% confidence intervals and two-sided Mann–Whitney p values over five runs per method. Each difference is the first method minus the second, so a negative value favors the first method. Units are those of Table S2 . The p values are not corrected for multiple comparisons. a Asymptotic approximation because of ties. All other p values are exact.
OpenEvolve
AgenticEvolve
OpenEvolve
Model
Task
final quality
Evaluations
Cost ($)
cost ($)
DeepSeek
OBP
5.74
7
0.15
3.06
GLM
OBP
5.54
17
0.96
0.69
Qwen
OBP
6.13
3
0.08
1.10
DeepSeek
DJSS
0.911
19
0.19
1.84
GLM
DJSS
0.931
26
0.20
0.48
TABLE S4: Formal evaluations and estimated cost at which the mean best-so-far curve of AgenticEvolve in Figs. 3 and 4 of the paper first reaches the mean final quality of OpenEvolve. The two budgets are read from the two curves separately and do not refer to the same point of the search. The last column is the mean cost of a complete OpenEvolve run.
Analysis
Result
1
Simulated Best Fit and Worst Fit on 400 sequences and recorded each bin’s final remaining capacity.
Best Fit excess 6.46%, compared with 6.55% in the formal evaluation. Bins with less than 20 units remaining account for 58% of the waste.
2
Scored bins using a piecewise-linear table indexed by the capacity remaining after placement. Starting from Best Fit, adjusted 13 knot values by coordinate descent on 200 sequences.
Excess 5.99% on all 400 sequences.
3
Repeated the descent with 20 knots on 400 sequences.
Exceeded the 60-second analysis limit.
4
Vectorized the simulator, repeated the 20-knot descent and tested the result on 400 sequences from a new seed.
5.99% on the training sequences and 6.19% on the new ones, where Best Fit gives 6.59%. The descent made no further progress.
5
Repeated the descent over all 131 table entries.
Exceeded the 60-second limit.
6
Counted the frequencies of the remaining capacities that would result from placing an item in each candidate bin, then repeated the descent on the eight most frequent values.
No change.
TABLE S5: The ten analyses before the first commit of island 0 in AgenticEvolve run 1 with GLM on OBP. Excess is over the L2 bound on the agent’s own sequences.
Model
Task
Offered candidates read
Commits after a read
Improved island best
Improved run best
DeepSeek
OBP
53 / 154
42
34
6
DeepSeek
DJSS
39 / 119
34
28
4
GLM
OBP
42 / 153
38
29
6
GLM
DJSS
28 / 142
25
18
5
Qwen
OBP
42 / 174
41
37
4
Qwen
DJSS
38 / 167
35
23
4
TABLE S6: Cross-island reads in the AgenticEvolve heuristic runs, five runs per row.
TABLE S7: Selected equation of every method on every problem, with its number of nodes and its structure ( ∙ exact, ∘ negligible extra terms, – not recovered). Constants are rounded to four significant digits for display. The assessment uses the full-precision values. Equations of the material-science problems are judged against the reduced truth after substituting T=273+500ε .
Problem
AgenticEvolve
AgenticEvolve (No-analysis)
LLM-SR
SR-Scientist
PySR
ID
OOD
ID
OOD
ID
OOD
ID
OOD
ID
OOD
CRK21
1.4e-15
6.8e-15
5.9e-09
2.0e-05
3.1e-09
1.2e-05
9.8e-10
5.6e-07
1.1e-07
4.8e-05
CRK35
2.0e-15
3.0e-14
2.0e-15
2.9e-14
2.6e-08
9.2e-05
2.0e-15
2.9e-14
9.6e-06
3.8e-03
BPG18
1.2e-12
1.7e-12
1.2e-12
1.7e-12
1.2e-12
1.7e-12
2.1e-14
2.2e-14
2.8e-03
3.4e-03
PO10
7.4e-15
1.4e-14
1.8e-03
1.8e-02
6.0e-03
2.0e-02
7.4e-15
1.4e-14
9.4e-05
5.5e-04
PO0
1.8e-13
6.8e-13
8.9e-05
7.2e-05
8.8e-04
6.9e-04
1.5e-03
1.2e-03
1.0e-02
1.1e-02
TABLE S8: Numerical accuracy of the selected equation per problem: normalized mean squared error on the in-domain (ID) and out-of-domain (OOD) test sets, computed locally with the shared scorer. Bold: accuracy within tolerance 10−3 on that set.
Method
Requests
Cached input (M)
Uncached input (M)
Output (M)
Reasoning (M)
Cost ($)
Wall time (min)
AgenticEvolve
4939
568.9
2.4
7.4
6.0
6.54
313
AgenticEvolve (No-analysis)
7809
1232.5
5.6
12.6
11.0
12.12
432
LLM-SR
12000
3.2
3.7
184.6
183.3
111.34
4521
SR-Scientist
5496
131.6
2.9
9.6
7.3
6.59
808
PySR
–
–
–
–
–
–
8
TABLE S9: Model usage of the symbolic-regression runs, totals over the twelve problems: completed requests, input tokens served from the provider’s cache, uncached input tokens, output tokens (of which reasoning), estimated cost at the DeepSeek-V4.1-Flash prices of the main text, and end-to-end wall time. Wall time depends on machine load and API latency and is reported for reference only.
Method
Data available to model-written code
Feedback of a failed evaluation
AgenticEvolve (v0.2.0)
training data, in analysis scripts
output and full traceback
AgenticEvolve (No-analysis, v0.2.1)
none
one-line summary
LLM-SR
none
none
SR-Scientist
training data, in its analysis tool
last line of the error output
TABLE S10: Data available to the model-written code of each symbolic-regression method and feedback of a failed evaluation in the reported runs.
Large Language Model (LLM)-guided evolutionary search is increasingly used for automated algorithm discovery, yet most current methods track search progress primarily through executable programs and scalar fitness. Even when natural-language reasoning is used through heuristic descriptions or reflection, it typically remains transient mutation context or unstructured memory, rather than organized as persistent population-level state over strategic directions. As a result, evolutionary search can struggle to distinguish syntactically different implementations of the same idea, preserve lower-fitness but strategically promising directions, or detect when an entire family of strategies has saturated. We introduce \model, a modular strategy-space layer that turns language-level strategic reasoning into first-class population-level evolutionary state in LLM-driven program search. \model represents each candidate program with an explicit natural-language strategy, clusters the archive by strategy semantics, retrieves behaviorally complementary inspirations, and periodically navigates the strategy landscape to avoid saturated directions. Without modifying the underlying evolutionary algorithms, \model improves existing evolutionary backbones across algorithm discovery, systems optimization, and agent-scaffold design tasks in most settings. Across four systems benchmarks, \model achieves a 20.6% average relative improvement, with the best single run on Prism scoring 3× higher. These results suggest that persistent strategy representations provide a practical mechanism for improving the effectiveness and cost-efficiency of LLM-guided evolutionary search, pointing toward compound AI systems whose search capabilities benefit from the structured accumulation and reuse of algorithmic strategies.
Sichun Luo, Yi Huang, Haochen Luo +7
1The University of Hong Kong · 2JIUTIAN Research, China Mobile · 3City University of Hong Kong
Agent evolvers automate the design of the prompts, skills and workflows around language model agents, yet the optimization process they follow is still designed by hand: a fixed search loop decides how candidates are evaluated, which are kept and when the search stops. We propose FREEEVOLVE, which automates this process as well. An environment specifies the goal, target agent, evaluator, data and resource limits; within these limits, the evolver itself decides what to test, how much evidence to collect, which candidates to pursue and when to stop. These decisions follow an editable evolution skill, which we improve through meta-evolution by scoring each candidate skill on the fresh target agent it produces. The optimization process thus becomes a capability learned from experience rather than a loop engineered in advance. On tau3-bench, ARC-AGI-2, ARC-AGI-3 and Terminal-Bench 2.1, FREEEVOLVE controls the evolution campaign by itself, yet improves the primary held-out metric by 13.6 points on average and matches or exceeds hand-designed evolvers. The learned process keeps improving with experience: meta-evolved skills add 6.9 points over the seed skill on fresh target agents, demonstrating transferability across environments.
Evolutionary coding agents such as AlphaEvolve are one of the notable successes in using Large Language Models (LLMs) to build AI Scientists. These agents tackle open-ended scientific problems by iteratively improving and evolving programs, leveraging the prior knowledge and reasoning capabilities of LLMs. Despite their success, mutations over programs are mostly low-level upon surface heuristics, without a persistent unit of control. In contrast, science compounds through ideas. In this work, we propose ExpEvolve, which injects idea-level extraction and control into evolution: it discovers and leverages the high-level factors from programs that explain scoring differences among different programs. We characterize theoretical conditions on when discovery with idea factors improves sample efficiency. We also build a practical framework to show that the extracted high-level idea factors are helpful for guiding exploitation from experience and exploration when discovery comes to a plateau. Across 11 open-ended mathematical tasks, ExpEvolve significantly improves the final performance and sample efficiency up to 5.0x. The improvements also transfer to 4 other LLMs and to 6 machine learning tasks from MLS-Bench. Analysis shows that ExpEvolve can discover idea-level factors to provide better exploration and exploitation for evolutionary discovery.
Yongqiang Chen, Chenxi Liu, Deyu Zou +4
MBZUAI · Carnegie Mellon University · TMLR Group, Hong Kong Baptist University +2