AI 中文总结
本文提出结合进化多任务与EAX的MT-EAX算法，经三种缩放方法对比实验，证实其在TSP求解中可节省大量计算量，且早期搜索阶段性能显著优于标准EAX。
AI 中文摘要
进化多任务技术可让算法在单次运行中求解多个相关问题。本文研究将进化多任务与边组装交叉（Edge Assembly Crossover, EAX）相结合，提出MT-EAX算法以求解经典旅行商问题（TSP）。为在严格计算预算下公平对比MT-EAX与标准EAX的性能，评估了三种缩放方法：世代缩放、种群缩放和平衡缩放。结果表明，按世代缩放的MT-EAX在搜索初期的计算效率极高，在达到同等或更优解质量的同时，可节省60%至90%的计算量。研究发现，实例几何结构对性能影响显著，聚类型、正态分布实例的性能提升大于均匀分布实例。但按种群缩放或采用显式解迁移时，因种群匮乏和跨实例父代选择不兼容，结果为负。研究证实，MT-EAX的优势源于早期世代并行搜索带来的多样性提升，通过解耦配置可成功保留该优势，最终收敛时其性能通常严格优于或匹配标准EAX。
英文摘要
Evolutionary multitasking allows several related problems to be solved in a single run of an algorithm. In this paper, we investigate integrating evolutionary multitasking with Edge Assembly Crossover (MT-EAX) to solve the classical Travelling Salesperson Problem (TSP). To fairly compare MT-EAX against standard EAX under strict compute budgets, we evaluate three scaling methods: generation scaling, population scaling, and balanced scaling. Our results show that generationally scaled MT-EAX is highly effective compute-wise in the early stages of the search, saving $60\%$ to $90\%$ of compute for equal or better solution quality. We observe that instance geometry has a significant impact, with clustered, normally distributed instances securing larger improvements than uniformly distributed ones. However, when scaling by population or utilising explicit solution transfer, the results are negative due to population starvation and incompatible cross-instance parent selection. We demonstrate that the advantage of MT-EAX derives from increased diversity through parallel search in early generations, which can be successfully preserved using a decoupled configuration to often strictly outperform or match standard EAX performance at final convergence.
