We consider the subset selection problem for function f with constraint bound B that changes over time. Within the area of submodular optimization, various greedy approaches are commonly used. For dynamic environments we observe that the adaptive variants of these greedy approaches are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a $\varphi =({\alpha }_f/2)(1-\frac{1}{e^{{\alpha }_f}})$-approximation, where ${\alpha }_f$ is the submodularity ratio of f, for each possible constraint bound $b\le B$. Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that B increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms. We also consider EAMC, a new evolutionary algorithm with polynomial expected time guarantee to maintain ϕ approximation ratio, and NSGA-II with two different population sizes as advanced multi-objective optimization algorithm, to demonstrate their challenges in optimizing the maximum coverage problem. Our empirical analysis shows that, within the same number of evaluations, POMC is able to perform as good as NSGA-II under linear constraint, while EAMC performs significantly worse than all considered algorithms in most cases.

我们考虑约束边界B随时间变化的函数f的子集选择问题。在子模块优化领域，通常使用各种贪婪方法。对于动态环境，我们观察到这些贪婪方法的自适应变体无法保持其近似质量。调查最近引入的 POMC 帕累托优化方法，我们表明该算法有效地计算了$\phi =({\alpha }_F/2)(1-\frac{1}{{\mathrm{电子}}^{{\alpha }_F}})$-近似，其中 ${\alpha }_F$是f的子模比，对于每个可能的约束边界$乙\le 乙$. 此外，我们表明 POMC 能够在B增加的情况下快速调整其解决方案集。我们对社交网络中影响最大化的实验研究表明 POMC 优于广义贪婪算法。我们还考虑了 EAMC，一种具有多项式预期时间保证以保持ϕ近似比的新进化算法，以及具有两种不同种群规模的 NSGA-II 作为高级多目标优化算法，以证明它们在优化最大覆盖问题方面的挑战。我们的实证分析表明，在相同数量的评估中，POMC 在线性约束下的性能与 NSGA-II 一样好，而 EAMC 在大多数情况下的性能明显低于所有考虑的算法。