Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve, have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. In this article, we present ImprovEvolve, a simple yet effective technique for enhancing LLM-based evolutionary approaches such as AlphaEvolve. Given an optimization problem, the standard approach is to evolve program code that, when executed, produces a solution close to the optimum. We propose an alternative program parameterization that maintains the ability to construct optimal solutions while reducing the cognitive load on the LLM. Specifically, we evolve a program (implementing, e.g., a Python class with a prescribed interface) that provides the following functionality: (1) propose a valid initial solution, (2) improve any given solution in terms of fitness, and (3) perturb a solution with a specified intensity. The optimum can then be approached by iteratively applying improve() and perturb() with a scheduled intensity. We evaluate ImprovEvolve on challenging problems from the AlphaEvolve paper: hexagon packing in a hexagon and the second autocorrelation inequality. For hexagon packing, the evolved program achieves new state-of-the-art results for 11, 12, 15, and 16 hexagons; a lightly human-edited variant further improves results for 14, 17, and 23 hexagons. For the second autocorrelation inequality, the human-edited program achieves a new state-of-the-art lower bound of 0.96258, improving upon AlphaEvolve's 0.96102.

翻译：近期，基于大语言模型（LLM）引导的进化计算，特别是AlphaEvolve，在发现新颖数学构造和解决具有挑战性的优化问题方面取得了显著成功。本文提出ImprovEvolve，这是一种用于增强诸如AlphaEvolve等基于LLM的进化方法的简单而有效的技术。给定一个优化问题，标准方法是进化一段程序代码，该代码在执行时能产生接近最优解的方案。我们提出了一种替代性的程序参数化方法，它在保持构建最优解能力的同时，降低了对LLM的认知负荷。具体来说，我们进化一个程序（例如，实现一个具有规定接口的Python类），该程序提供以下功能：(1) 提出一个有效的初始解，(2) 在适应度方面改进任何给定的解，以及(3) 以指定的强度扰动一个解。然后，可以通过按计划强度迭代应用improve()和perturb()来逼近最优解。我们在AlphaEvolve论文中的两个具有挑战性的问题上评估了ImprovEvolve：正六边形内的正六边形填充问题和二阶自相关不等式。对于正六边形填充问题，进化出的程序在填充11、12、15和16个正六边形时取得了新的最优结果；经过轻微人工编辑的变体进一步提升了填充14、17和23个正六边形时的结果。对于二阶自相关不等式，经过人工编辑的程序取得了新的最优下界0.96258，优于AlphaEvolve的0.96102。