Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints we show that GSEMO achieves a (1 − 1/e)-approximation in expected time O(n2 (log n + k)), where k is the value of the given constraint. For the case of non-monotone submodular functions with k matroid intersection constraints, we show that GSEMO achieves a 1/(k +2+1/k + ε)-approximation in expected time O(nk+5 log(n)/ε).
CITATION STYLE
Friedrich, T., & Neumann, F. (2014). Maximizing submodular functions under matroid constraints by multi-objective evolutionary algorithms. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8672, 922–931. https://doi.org/10.1007/978-3-319-10762-2_91
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