Pareto optimization for subset selection with dynamic cost constraints

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