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

Multi-objective Evolutionary Algorithms are Generally Good: Maximizing Monotone Submodular Functions over Sequences