多任务进化实现基于LLM的零样本跨问题泛化

中文摘要 AI 辅助

为多样化的组合优化问题设计有效启发式算法需要大量专业知识和反复搜索。大型语言模型（LLM）自动化了启发式算法的生成与改进，但启发式搜索通常依赖于被优化问题的评估反馈。因此，仅利用源任务反馈泛化到新问题定义仍然是一个核心挑战。我们提出了MECo，一个由LLM驱动的多任务进化框架，用于零样本跨问题泛化。MECo维护任务条件化的启发式种群，并利用基于跨任务种群性能的转移差距来指导它们的交互。这些交互实现了启发式算法的转移与重组。随后，一个互补的选择标准通过奖励每个成员对源组合的额外覆盖来构建紧凑的启发式集合。所选集合直接应用于目标问题，无需进一步搜索或适应。在车辆路径问题（VRP）和柔性作业车间调度（FJSP）的32个问题变体上的实验表明，在相同预算下，MECo相比八个自动化启发式设计（AHD）基线实现了最低的平均成本。在域外问题上，它优于每个系列中最强的基线。此外，将MECo框架与不同AHD方法集成，提高了两个系列中它们的ID和OOD性能，支持了其在不同方法中的有效性。

英文摘要

Designing effective heuristics for diverse combinatorial optimization problems requires substantial expertise and repeated search. Large language models (LLMs) automate heuristic generation and refinement, but heuristic search typically depends on evaluation feedback from the problem being optimized. Generalizing to new problem definitions using only source-task feedback therefore remains a central challenge. We introduce MECo, an LLM-driven multi-task evolutionary framework for zero-shot cross-problem generalization. MECo maintains task-conditioned heuristic populations and uses a transfer gap based on cross-task population performance to guide their interactions. These interactions enable the transfer and recombination of heuristics. A complementary selection criterion then constructs a compact heuristic set by rewarding each member's additional coverage of source combinations. The selected set is applied to target problems without further search or adaptation. Experiments on 32 problem variants across vehicle routing (VRP) and flexible job-shop scheduling (FJSP) show that MECo achieves the lowest mean costs compared with eight automated heuristic design (AHD) baselines under the same budgets. On out-of-domain problems, it outperforms the strongest baseline in each family. Moreover, integrating the framework of MECo with different AHD methods improves their ID and OOD performance in both families, supporting its effectiveness across different methods.

发表机构

• Southern University of Science and Technology（南方科技大学）
• Shenzhen University（深圳大学）

机构由 AI 辅助整理，请以论文原文为准。