Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been shown to be successful to tackle these problems while single-objective formulations lead to difficulties for algorithms such as the $(1+1)$-EA due to the presence of local optima. We introduce for the first time single-objective algorithms that are provably successful for different classes of constrained submodular maximization problems. Our algorithms are variants of the $(1+\lambda)$-EA and $(1+1)$-EA and increase the feasible region of the search space incrementally in order to deal with the considered submodular problems.

翻译：约束子模优化问题在组合优化领域具有关键地位，因其涵盖了许多NP难优化问题。迄今为止，采用多目标建模的帕累托优化方法已被证明能有效处理此类问题，而单目标建模则因局部最优解的存在导致诸如$(1+1)$-EA等算法面临困难。我们首次提出了可证明适用于不同类别约束子模最大化问题的单目标算法。所提算法为$(1+\lambda)$-EA与$(1+1)$-EA的变体，通过逐步扩大搜索空间的可行区域来处理所考虑的子模优化问题。