Authors: Nico Pelleriti, Sree Harsha Nelaturu, Zhanke Zhou, Zongze Li, Max Zimmer, Bo Han, Sebastian Pokutta
Organizations: 1Zuse Institute Berlin · 2Technical University of Berlin · 3Hong Kong Baptist University · 4RIKEN Center for Advanced Intelligence Project
Abstract
Recent work pairs LLMs with evolutionary search to iteratively generate, modify, and select code using task-specific feedback. These systems have produced strong results in mathematical discovery and algorithm design, yet a fundamental question remains: what do they actually evolve? Progress is typically summarized by the best score a run reaches under a task-specific evaluator, but that score can reflect several different mechanisms: new algorithmic structure, re-tuning an existing strategy, recombining ideas already in the model's internal knowledge, or overfitting to the evaluator. Distinguishing these mechanisms requires inspecting the search process itself, not only its final outcome. We introduce EvoTrace, a dataset of evolutionary coding traces spanning four evolutionary frameworks, reasoning and non-reasoning models, and 16 tasks across mathematics and algorithm design. To analyze these traces, we develop EvoReplay, a replay-based methodology that reconstructs the local search states behind high-scoring solutions and tests controlled interventions, including adjusting constants, removing program components and substituting models or prompting contexts. We annotate every code edit in EvoTrace with one of nine recurring edit types using an LLM-as-judge pipeline validated against blind human re-annotation. Across EvoTrace, most score gains come from a small subset of these edit types. We further find a deterministic cycling pattern: about 30% of code lines added during search are byte-identical re-introductions of previously-deleted lines, present throughout nearly every run. These results show that benchmark gains in evolutionary coding agents can arise from qualitatively different mechanisms, only some of which correspond to new algorithmic structure. EvoTrace enables more diagnostic evaluation of evolutionary coding agents beyond final benchmark scores.
We introduce Evolutionary Ensemble (EvE), a decentralized framework that organizes existing, highly capable coding agents into a live, co-evolving system for algorithmic discovery. Rather than reinventing the wheel within the "LLMs as optimizers" paradigm, EvE fixes the base agent substrate and focuses entirely on evolving the cumulative guidance and skills that dictate agent behaviors. By maintaining two co-evolving populations, namely functional code solvers and agent guidance states, the system evaluates agents through a synchronous race, updating their empirical Elo ratings based on the marginal gains they contribute to the current solver state. When applied to a research bottleneck in In-Context Operator Networks (ICON), EvE autonomously discovered a robust rescale-then-interpolate mechanism that enables reliable example-count generalization. Crucially, controlled ablations reveal the absolute necessity of stage-dependent agent adaptation to navigate the shifting search landscapes of complex codebases. Compared to variants driven by a fixed initial agent or even a frozen "best-evolved" agent, EvE uniquely avoids phase mismatch, demonstrating that organizing agents into a self-revising ensemble is the fundamental driver for breaking through static performance ceilings.
AlphaEvolve and FunSearch have demonstrated the potential of combining large language models (LLMs) with evolutionary search for automated algorithm discovery. However, discovery success is shaped not only by model capability but also significantly by the design of the execution infrastructure, i.e., the harness. This paper investigates effective harness design through three questions: under a fixed token budget, is it better to produce many algorithms with brief thought or fewer algorithms with deeper thought? How should the harness handle evaluation hacks, where generated programs exploit the scoring function? And how can agents that require full filesystem access execute safely in parallel? Using Vesper, an algorithm discovery framework that incorporates harness improvements addressing these questions, we evaluate on Circle Packing under the same token budget. Interestingly, generating fewer algorithms while thinking more deeply about each one achieved higher scores. That is, scaling the quality of each individual is more budget-efficient than scaling the number of evolutionary generations. Surprisingly, more capable models produced evaluation hacks at higher rates, making hack detection increasingly necessary as models scale.
LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4%.
Alexey Kravatskiy, Valentin Khrulkov, Ivan Oseledets