Automating Parent Selection Configuration in Genetic Programming with Agentic AI

Parent selection significantly affects exploration, exploitation, and complexity control in genetic programming (GP) for symbolic regression. It is unclear whether large language models (LLMs) can synthesize effective operators in a zero-shot setting without iterative meta-evolution. Here, zero-shot means that the model receives only the task description, with no reference operators or iterative feedback. In this work, we benchmark zero-shot synthesis of parent-selection operators across eight LLMs within a standard GP framework for symbolic regression. Each model receives the same natural-language prompt to generate a parent-selection operator, which is then evaluated in a standard GP framework with only the parent-selection operator replaced, while all other components and the evolutionary-search budget are held constant. For each LLM, ten independent zero-shot operators are evaluated on twelve OpenML regression benchmarks and compared against automatic lexicase and tournament selection baselines. Claude Sonnet4.6 and Gemini3.1 Pro stand out for consistently strong performance on both training and held-out test $R^2$. The strongest operator in our benchmark---a Kimi~K2.5 zero-shot synthesis---surpasses the automatic lexicase and tournament baselines in search effectiveness. These results suggest that zero-shot LLM synthesis is a viable approach to generating competitive GP selection operators. Analysis shows that many generated operators use semantics to guide selection, suggesting that LLMs can produce non-trivial search heuristics from the task description alone. We also examine the relationship between public LLM leaderboard rankings and GP performance. Widely used benchmarks, such as Humanity's Last Exam and SWE-bench Verified, strongly correlate with training $R^2$, while their relationship to held-out test $R^2$ is weaker and less clear.

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.

2026 has brought an explosion of interest in LLM-guided evolution of agentic artifacts, with systems like GEPA and Autoresearch demonstrating that LLMs can iteratively improve prompts, code, and agent architectures across diverse domains. As adoption accelerates, a central question emerges: given the same information, the same seed agent, and the same objective, which optimization algorithm yields the best results under the same evaluation budget? This question becomes critical when evaluations are expensive, such as when they require human judgment or multiple LLM calls. We present the first systematic comparison of three optimization paradigms -- Elo tournament selection (RoboPhD), Pareto-based selection (GEPA), and greedy hill-climbing (Autoresearch) -- across four benchmarks spanning abstract reasoning, cloud scheduling, SQL generation, and financial QA, all under a fixed budget of 1,500 evaluations. RoboPhD introduces validation-free evolution: instead of splitting the budget between training and validation, it uses Elo competition on training data to simultaneously evaluate agents and drive evolution. All three systems receive seed agents with diagnostic print() statements that evolution can grow, enabling self-instrumenting agents that develop increasingly informative diagnostics for the benefit of their evolutionary successors. Using a single default configuration, RoboPhD outperforms both GEPA and Autoresearch on three of four benchmarks, losing only on the simplest task, where the winning solution (from our Autoresearch adaptation) required under 90 lines of code. On ARC-AGI, RoboPhD evolves a 22-line seed agent into a 1,013-line multi-strategy system, improving accuracy from 27.8% to 65.8% using Gemini 3.1 Flash Lite as the solver. We release RoboPhD as a versatile toolkit under the MIT license with a simple optimize_anything() API for evolving diverse complex agents.