Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good approximations is the population size of the algorithms which grows with the number of trade-offs that the algorithms encounter. In this paper, we introduce a sliding window speed up technique for recently introduced algorithms. We prove that our technique eliminates the population size as a crucial factor negatively impacting the runtime and achieves the same theoretical performance guarantees as previous approaches within less computation time. Our experimental investigations for the classical maximum coverage problem confirms that our sliding window technique clearly leads to better results for a wide range of instances and constraint settings.

翻译：帕累托优化通过进化多目标算法已被广泛应用于求解带约束的子模优化问题。决定所用进化算法获得良好近似解运行时间的一个关键因素是算法的种群规模，该规模随算法遇到的权衡数量增长。本文针对近期提出的算法引入了一种滑动窗口加速技术。我们证明该技术消除了种群规模对运行时间的负面影响，并在更短的计算时间内实现了与先前方法相同的理论性能保证。针对经典最大覆盖问题的实验研究证实，我们的滑动窗口技术在一系列实例和约束设置下均能显著取得更优结果。