Summary (Overview)

• AgenticEvolve is an evolutionary program search framework where each island is run by a persistent LLM agent that can design and execute experiments between formal evaluations, using tools to edit code, run analysis scripts, and commit candidates.
• The framework combines MAP-Elites archives, multi-island migration, and persistent conversations with self-designed experimentation capabilities.
• On two heuristic design tasks (online bin packing and dynamic job shop scheduling) across three LLMs, AgenticEvolve consistently outperforms both a No-analysis ablation and OpenEvolve on hidden and unseen instances.
• On twelve equation discovery problems, AgenticEvolve recovers more ground-truth equations than No-analysis, LLM-SR, SR-Scientist, and PySR at comparable cost.
• The paper provides a matched No-analysis configuration that isolates the contribution of experimentation, showing that agent-run experiments significantly improve program quality while keeping costs within a few USD per run.

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Introduction and Theoretical Foundation

Background and Motivation

Traditional evolutionary program search with LLMs uses the model as a variation operator within an evolutionary algorithm:

"The search maintains a population of programs, prompts the model with one or more parents and their scores, and evaluates each returned program with an automated evaluator."

In existing systems (FunSearch, AlphaEvolve, LLM-SR, LLaMEA), the model has no execution tools during candidate generation—it reasons only from parent programs, scores, and textual feedback. Empirical information enters the search only through formal evaluation, which consumes budget and often uses hidden instances.

Theoretical Foundation

The paper builds on several research threads:

• Evolutionary program search (FunSearch, AlphaEvolve, OpenEvolve) using LLMs as variation operators
• Agentic search (AlgoTune, CORAL, ReASearch) where agents interleave reasoning with tool calls
• Symbolic regression (PySR, LLM-SR, SR-Scientist) for scientific equation discovery

The key theoretical contribution is combining population-based evolutionary search with persistent agent experimentation:

"Within evolutionary search, such an agent can experiment between formal evaluations: it can generate instances, measure program behavior, fit parameters and test changes locally before submitting a candidate. These experiments can support local improvement and surrogate evaluation, both of which have long been combined with global search in evolutionary computation."

Three Main Contributions

1. A framework where persistent LLM agents conduct island-based search with self-designed experiments, plus a matched No-analysis configuration
2. Empirical evaluation on heuristic design tasks showing superior quality with fewer formal evaluations
3. Cross-task evaluation on symbolic regression showing better structure recovery than all baselines

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Methodology

Architecture: Island-Based Persistent Agents

Each island is run by a persistent LLM agent that maintains a conversation with the framework throughout the search:

Key Design Elements

• Persistent conversation: Accumulates history of revisions, experiments, and results; compaction summarizes when context window is approached
• MAP-Elites archive: Records all commits across islands, with successful programs assigned to feature-based grid cells
• Migration: Islands arranged in a ring exchange elite programs periodically; agents decide whether to adopt them
• Restricted feedback: Evaluation results return only task-defined metrics—raw output and tracebacks are withheld to prevent data leakage

The No-analysis Configuration

"No-analysis removes run_analysis from the available tools, disables access to analysis.py and removes the corresponding instructions from the system prompt. The persistent conversation, program editing, formal evaluation, archive, migration, compaction and budget remain unchanged."

This isolates the causal contribution of experimentation.

Tasks

Online Bin Packing (OBP): Items arrive sequentially with integer sizes from [20,100], bins of capacity 150. Fitness is $1/(1+e)$ where $e$ is fractional excess over the Martello–Toth $L_2$ lower bound.

Dynamic Job Shop Scheduling (DJSS): Dispatching rule scores waiting operations; quality is geometric mean of R1-normalized tardiness ratios across five scenarios.

Symbolic Regression: Twelve problems from LLM-SRBench covering chemistry, biology, physics, and material science.

Budgets and Statistics

• Each island commits 30 times → 90 evaluations per run (LLM methods)
• Five independent runs per method-model combination
• Two-sided Mann–Whitney U test at 0.05 level
• Models: DeepSeek-V4.1-Flash, GLM-5.3-Flash, Qwen3.8-Flash

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Empirical Validation / Results

Heuristic Design: Final Quality

AgenticEvolve achieves the best mean quality with every model on both tasks:

On hidden evaluation sets (lower is better):

• OBP: Excess reduced by 1.8–2.3 percentage points vs. No-analysis, 1.1–2.4 points vs. OpenEvolve
• DJSS: R1-normalized tardiness reduced by 0.08–0.16 vs. No-analysis, 0.07–0.16 vs. OpenEvolve

Generalization to unseen instances:

• On OR1 (bin packing): mean excess 2.9–4.1% vs. 5.3% for FunSearch heuristic, 5.8% for Best Fit
• On fresh DJSS seeds: R1-normalized tardiness 0.84–0.86 vs. 0.92–1.00 for baselines

Efficiency vs. Formal Evaluations

AgenticEvolve separates from baselines within the first ten evaluations and maintains its lead:

"In five of the six cases, AgenticEvolve reaches OpenEvolve's final quality within 20 evaluations, compared with OpenEvolve's 180-iteration runs."

Symbolic Regression: Structure Recovery

Case Study: BPG18 Frequency Fitting

The ground truth is a logistic growth rate with periodic forcing:

$$\dot{P} = P(a + bP + c\sin\omega t), \quad \omega \approx 0.77606$$

When $\omega$ is free, standard optimizers converge to incorrect frequencies. AgenticEvolve used analysis to scan trial frequencies, fit remaining coefficients at each, and embed the refined frequency as a literal—recovering exact structure in the first commit after ten analyses. No-analysis required repeated commits (finding $\omega = 0.77605$ at commit 107).

Cost Analysis

• Prompt caching makes persistent conversations affordable: 99% of input tokens are cached
• AgenticEvolve sends 24–164× more input tokens than OpenEvolve but costs $0.6–4.5 per run
• Without execution tools, models generate far more reasoning tokens (OpenEvolve: 15–27k output tokens/request vs. ~1k for AgenticEvolve with DeepSeek)

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Theoretical and Practical Implications

What Experiments Enable

1. Local improvement: Agents can fit parameters, test changes, and optimize locally before formal evaluation
2. Surrogate evaluation: Self-generated instances from the stated distribution allow prediction of hidden-set performance
3. Problem decomposition: The BPG18 case shows agents treating sub-problems (frequency fitting) separately from the main structure search

Transfer of Improvements

"In heuristic optimization, the evaluation instances are hidden. The agent generates its own instances from the stated distribution, and improvements on these instances must still be verified on the hidden set."

The consistent improvement across tasks demonstrates that self-designed experiments transfer reliably to held-out instances.

Security and Protocol Considerations

• Restricted feedback prevents using printed output or tracebacks to access evaluation data
• A prior vulnerability was found where a candidate located training data via an evaluator path in a traceback—leading to the feedback restriction
• Agents still attempted to access hidden data through analysis scripts; audits found no successful access (protocol-level enforcement, not OS-level sandboxing)

Archive and Migration Effects

• Every AgenticEvolve heuristic run included cross-island reads
• Of 215 commits preceded by a cross-island read, 169 improved the island's best score and 29 improved the run's best score

Open Questions

• How much of the evolutionary structure (population, archive, islands) does an agent-driven search actually need?
• Can No-analysis close the quality gap with more evaluations at AgenticEvolve's total cost?
• Does the benefit of analysis extend to stronger, non-Flash-tier models?

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Conclusion

Main Takeaways

1. Persistent agents with experimentation tools significantly improve evolutionary program search across heuristic design and scientific equation discovery
2. The benefit is causal: the matched No-analysis configuration isolates experimentation as the source of improvement
3. Efficiency gains are substantial: AgenticEvolve reaches baseline final quality with a fraction of formal evaluations
4. Cost remains practical: $0.6–4.5 USD per heuristic run,$6.54 total for twelve symbolic regression problems

Future Directions

"It remains open how much of this structure an agent-driven search needs, and how the search should be divided between the agent and the evolutionary mechanisms."

Key questions for future work:

• Which evolutionary mechanisms are essential when agents are persistent and self-directed?
• How should budget be allocated between the agent's analysis and formal evaluation?
• Does experimentation benefit scale with stronger models and more complex tasks?
• Can protocol-level restrictions be replaced by stronger OS-level sandboxes?