用LLM演化三类子程序，实现更高效的问题求解
ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search
- 将优化过程拆解为初始化、局部改进和扰动三类子程序
- 在六边形排列等任务中发现新最优解，部分提升超2.4%
- 适合需要高效探索复杂解空间的研究者
LLM引导的进化计算在解决复杂优化问题并发现新型数学构造方面表现卓越。传统方法是让LLM生成一个完整的端到端优化程序。本文提出ImprovEvolve，通过演化三个专用子程序（初始化、局部改进、扰动）来降低对LLM的认知负担。算法通过迭代应用局部改进和强度调度的扰动，实现基于盆地跳跃的搜索。在六边形嵌套问题中，ImprovEvolve发现了11、12、15、16个六边形的新最优排列；对14、17、23个六边形，在极少量人工调优后也获得新解。在第二自相关不等式中，程序将下界从0.96102提升至0.96258。在球码问题上，对90个随机选取的先进球码，该方法降低了多数已知最大余弦值，相对改进最高达2.4%。
原文摘要 · Abstract (English)
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%.
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