Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function $f$ but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a $(1-1/e)$-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.

翻译：进化多目标算法通过帕累托优化已被证明能高效求解带约束的单调子模函数。传统上，当求解多个问题时，算法需针对每个问题单独运行。我们提出这些问题的多任务形式化方法，能够通过单次运行有效求解多个相关问题。在我们的设定中，给定问题共享同一个单调子模函数$f$，但具有不同的背包约束。我们研究了约束内元素具有相同成本的情况，并证明我们的多任务形式化方法能产生较小的帕累托前沿。这使得种群能够在所有问题间共享解，相较于独立运行多种经典方法，实现了显著改进。通过严格的运行时分析，我们解析了所提多任务方法为每个给定问题获得$(1-1/e)$-近似解所需的期望时间。针对最大覆盖问题的实验研究进一步揭示了该方法在元素成本差异化的实际问题中有效与失效的动力学机制。