EvoX: Meta-Evolution for Automated Discovery

The paradigm of automated program generation is shifting from one-shot generation to inference-time search, where Large Language Models (LLMs) function as semantic mutation operators within evolutionary loops. While effective, these systems are currently governed by static schedules that fail to account for the non-stationary dynamics of the search process. This rigidity results in substantial computational waste, as resources are indiscriminately allocated to stagnating populations while promising frontiers remain under-exploited. We introduce AdaEvolve, a framework that reformulates LLM-driven evolution as a hierarchical adaptive optimization problem. AdaEvolve uses an "accumulated improvement signal" to unify decisions across three levels: Local Adaptation, which dynamically modulates the exploration intensity within a population of solution candidates; Global Adaptation, which routes the global resource budget via bandit-based scheduling across different solution candidate populations; and Meta-Guidance which generates novel solution tactics based on the previously generated solutions and their corresponding improvements when the progress stalls. We demonstrate that AdaEvolve consistently outperforms the open-sourced baselines across 185 different open-ended optimization problems including combinatorial, systems optimization and algorithm design problems.

Recent LLM-guided evolutionary search methods have shown that iterative program mutation can discover strong algorithms, but they typically optimize each task independently, even when related tasks share reusable structure. We study evolutionary multitask optimization (EMO) for LLM-guided program discovery and propose EMO-STA (Shared-Then-Adapt), a two-stage framework that first evolves a shared archive of executable programs across a task family and then adapts selected shared candidates to each target task. Within EMO-STA, we explore multiple adaptation strategies, including warm-starting from the shared archive, adapting the best average shared program, and adapting the shared program that performs best on each target task. Across eight task families spanning continuous optimization, geometric construction, modeling, and algorithmic optimization, EMO-STA improves over single-task evolution under matched evolutionary-iteration budgets in most settings, with STA Best-Local providing the strongest in-distribution adaptation and STA Best-Shared yielding robust transfer to unseen tasks. Iteration-allocation experiments show that devoting a substantial fraction of the family-level iteration budget to shared evolution is effective, with roughly balanced shared and aggregate adaptation budgets often yielding the best performance. ARC and time-series feature-engineering case studies further suggest that shared evolution can mitigate overfitting in low-evidence settings by favoring programs that perform well across related tasks rather than exploiting brittle task-specific artifacts.

LLM-driven program evolution can discover high-quality programs, but high API cost and run-to-run variance hinder reliable progress. We propose TurboEvolve, a multi-island evolutionary framework that improves sample efficiency and stability under matched API-cost budgets. Inspired by multiple-offspring strategies in evolutionary algorithms, TurboEvolve introduces Verbalized Sampling, which elicits K diverse candidates in one LLM call while using self-assigned probabilities only as generation signals, together with an online scheduler that adapts K to expand exploration under stagnation and reduce redundant generation during steady progress. To exploit existing solution pools, TurboEvolve further introduces island-aware initialization, which clusters seed programs into mode-specific subpopulations and applies controlled cross-cluster mixing with elitist preservation to balance diversity, sharing, and refinement. We also curate a reusable cross-task solution-pool dataset to support warm-start initialization studies and matched-resource comparisons. Across mathematical discovery and GPU-kernel optimization tasks, TurboEvolve achieves stronger cost-quality trade-offs and more stable performance than controlled baselines, while reaching competitive reported scores.