  Evolutionary algorithms (EAs) are general-purpose optimization algorithms,
inspired by natural evolution. Recent theoretical studies have shown that EAs
can achieve good approximation guarantees for solving the problem classes of
submodular optimization, which have a wide range of applications, such as
maximum coverage, sparse regression, influence maximization, document
summarization and sensor placement, just to name a few. Though they have
provided some theoretical explanation for the general-purpose nature of EAs,
the considered submodular objective functions are defined only over sets or
multisets. To complement this line of research, this paper studies the problem
class of maximizing monotone submodular functions over sequences, where the
objective function depends on the order of items. We prove that for each kind
of previously studied monotone submodular objective functions over sequences,
i.e., prefix monotone submodular functions, weakly monotone and strongly
submodular functions, and DAG monotone submodular functions, a simple
multi-objective EA, i.e., GSEMO, can always reach or improve the best known
approximation guarantee after running polynomial time in expectation. Note that
these best-known approximation guarantees can be obtained only by different
greedy-style algorithms before. Empirical studies on various applications,
e.g., accomplishing tasks, maximizing information gain, search-and-tracking and
recommender systems, show the excellent performance of the GSEMO.
