发表机构
Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出MOSAIC框架，通过对抗性协同进化组合优化问题的专用启发式算法与问题实例，构建区域专用启发式算法池，所提取的组合在各类基准测试中均优于现有最先进的基于LLM的自动启发式设计方法。
AI 中文摘要
利用大语言模型（LLM）进行自动启发式设计（AHD）已为组合优化问题（COP）生成了强大的启发式算法。然而，现有框架针对小型固定数据集上的平均性能进行优化，并通过从标量“更好/更差”反馈中提炼出的“语言梯度”引导搜索。没有单一启发式算法能在所有实例分布中占优，且标量反馈仅能告知LLM某一启发式算法是否有所改进，无法说明在实例空间的何处改进或为何改进。我们提出MOSAIC，这是一种基于网格的框架，在由实例结构特征索引的质量多样性（QD）档案内，对问题实例和专用启发式算法进行对抗性协同进化。实例进化以暴露当前启发式算法的弱点，启发式算法则通过专门针对新暴露的区域进化以消除这些弱点。每个档案单元保存一个专用启发式算法、代表性实例以及解释该区域有效方法的见解，形成在进化搜索过程中积累的持久记忆。对于从不同网格区域采样的每对启发式算法，LLM引导的进化循环会生成判别性实例，决策树则确定每个启发式算法获胜的特征空间区域。随后，反思LLM会对比两种启发式算法，生成多方向见解，这些见解会保留在这些区域中并指导交叉和变异。该档案同时是判别性实例的协同进化基准和区域专用启发式算法的池，贪心选择从中提取紧凑的互补组合。在各类COP、测试规模和LLM主干下，该组合始终优于最先进的基于LLM的AHD方法，且协同进化的实例比进化实例生成基线实现了更高的特征空间覆盖率和更强的启发式判别能力。
英文摘要
Automated heuristic design (AHD) with large language models (LLMs) has produced strong heuristics for combinatorial optimization problems (COPs). Yet existing frameworks optimize for average performance on a small fixed dataset and steer the search with "verbal gradients" distilled from scalar better/worse feedback. No single heuristic dominates across instance distributions, and scalar feedback tells the LLM whether a heuristic improved, but not where in the instance space or why. We propose MOSAIC, a grid-based framework that adversarially co-evolves problem instances and specialist heuristics inside a Quality-Diversity (QD) archive indexed by structural instance features. Instances evolve to expose weaknesses of the current heuristics, and heuristics evolve to eliminate them by specializing to the newly exposed regions. Each archive cell keeps a specialist heuristic, representative instances, and insights explaining what works in its region, forming a persistent memory that accumulates over the evolutionary search. For each heuristic pair sampled from distant grid regions, an LLM-guided evolutionary loop generates discriminative instances, and a decision tree identifies the feature-space regions where each heuristic wins. A reflection LLM then contrasts the two heuristics to produce multi-directional insights that persist in those regions and guide crossover and mutation. The archive is simultaneously a co-evolved benchmark of discriminative instances and a pool of region specialist heuristics, from which greedy selection extracts a compact complementary portfolio. Across COPs, test sizes, and LLM backbones, the portfolio consistently outperforms state-of-the-art LLM-based AHD methods, and the co-evolved instances attain higher feature-space coverage and stronger heuristic discrimination than evolutionary instance-generation baselines.
