Abstract
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 simple single objective evolutionary algorithm called (
) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints, we show that the GSEMO achieves a 
-approximation in expected polynomial time. For the case of monotone functions where the constraints are given by the intersection of 
matroids, we show that the (
) EA achieves a (
)-approximation in expected polynomial time for any constant 
. Turning to nonmonotone symmetric submodular functions with 
matroid intersection constraints, we show that the GSEMO achieves a 
-approximation in expected time 
.