AI 中文总结
针对带动态背包约束的单调子模优化问题，本文提出多任务帕累托优化方法，通过任务间解共享提升性能，经理论分析与最大覆盖问题实验验证了其有效性。
AI 中文摘要
进化多任务是一种近期提出的方法，可在单次进化运行中解决多个相关优化问题，而非分别处理每个问题。本文研究带动态背包约束的单调子模优化问题，探讨一种多任务形式，其中所有任务共享同一单调子模函数f，但约束各不相同。我们聚焦于各约束内元素成本均匀的情况，证明该结构会使多任务形式下的帕累托前沿规模较小，这支持了任务间的解共享，且根据约束情况，相比独立运行标准进化方法可提升性能。通过严格的运行时间分析，我们分析了所提多任务算法为每个任务获得(1 - 1/e)近似解所需的期望时间。针对最大覆盖问题的实验结果补充了理论分析，进一步揭示了该方法在不同预算设置下的实际表现。
英文摘要
Evolutionary multitasking is a recent approach that solves multiple related optimization problems within a single evolutionary run, rather than addressing each problem separately. We consider monotone submodular optimization problems with dynamic knapsack constraints and study a multitasking formulation in which all tasks share a common monotone submodular function $f$, but differ in their constraints. We focus on the case where elements within each constraint have uniform cost and show that this structure leads to small Pareto fronts in the multitasking formulation. This enables solution sharing across tasks and can improve performance compared to running standard evolutionary approaches independently, depending on the constraint regime. Using rigorous runtime analysis, we analyze the expected time until the proposed multitasking algorithms obtain a $(1 - 1/e)$-approximation for each task. Experimental results for the Maximum Coverage problem complement the theoretical analysis and provide further insight into the practical behavior of the approach across different budget settings.
