Evolution or Illusion? Rethinking Evaluation in LLM Evolutionary Search

LLM-guided evolutionary search (Evolve systems) has reached state-of-the-art results on mathematical and combinatorial tasks, yet most existing systems report only the best of many runs and leave the run-to-run distribution undocumented. We ask how a fixed budget of LLM calls should be allocated, and how reliably a single run reaches the reported numbers. Sweeping the depth-breadth grid over five models and three tasks, we identify two empirical regularities: a fitness-compute envelope along which capability ordering largely collapses on effective FLOPs, and a bilinear depth-breadth fit with task-specific interaction; both are gated by model-task capability. Motivated by these regularities, we propose BaSE (Bandit-based Self-Evolving), a multi-armed bandit that allocates LLM calls across parallel trajectories. Without changing the model, prompt, or evaluator, BaSE improves mean fitness by 12.3% over the strongest island-protocol baseline across 8 (model, task) cells, with the largest gains on high-variance settings: a reliability gain from allocation alone.

LLM-guided evolutionary methods such as AlphaEvolve have proven effective in domains like math, systems research, and algorithmic discovery, but their reliance on frontier models makes each run expensive. We argue this is largely an artifact of how existing frameworks allocate search: archives that fail to preserve solution diversity force compensation through stronger mutation models; blind model use spends frontier dollars on local edits a smaller model could handle; and full-set evaluation wastes rollouts on redundant examples. We introduce LEVI, a harness-first evolutionary framework built on the bet that stronger search architectures can substitute for or even outperform larger LLMs in evolutionary search. LEVI improves on three core components of evolutionary search: a solution database that establishes diversity from the beginning, and then maintains it throughout the run; a smarter mutation router that plays into the strengths of large and small LLMs; and a rank-preserving proxy benchmark for rollout-heavy settings. Across systems-research benchmarks LEVI attains the highest score on a budget 3.3-6.7x smaller than the published frontier-model runs of existing frameworks like ShinkaEvolve, GEPA, and AdaEvolve; on one problem, LEVI matches the existing best at a 35x lower cost. On prompt optimization, LEVI matches or exceeds GEPA at less than half of its rollout budget on four different benchmarks. LEVI is available as an open-source framework at https://github.com/ttanv/levi.

Large language model (LLM)-driven evolution has shown promise for program search and algorithm discovery, but relying on strong models throughout long evolutionary runs is costly. A natural alternative is to combine cheap and strong models under a fixed inference budget. However, existing approaches typically allocate models at the level of individual queries or mutation steps, overlooking that evolutionary search is \textit{stateful}: each generated candidate changes the population from which subsequent mutations are produced. We empirically analyze LLM-driven evolutionary trajectories and find that search progress is strongly front-loaded, early trajectory performance is informative but noisy, and cheap models recover much of the early progress achieved by strong models at lower cost. Motivated by these findings, we propose \textbf{\model}, a training-free framework that shifts budget allocation from individual calls to evolving populations through adaptive \textit{population handoff}. A cheap model explores multiple trajectories in short blocks allocated by a bandit scheduler. Relay Gain, defined as the marginal improvement of a compact, quality-diverse candidate bank constructed for handoff, serves as the scheduler reward and determines when to hand off. The curated candidates initialize a shared strong model population for refinement. Across four benchmarks and three budgets, \model achieves the highest mean score in 11 of 12 settings, outperforming competitive baselines. Our results suggest that in stateful search, budget allocation should be organized around the population, not the individual call.