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Many important problems can be regarded as maximizing submodular functionsunder some constraints. A simple multi-objective evolutionary algorithm calledGSEMO has been shown to achieve good approximation for submodular functionsefficiently. While there have been many studies on the subject, most ofexisting run-time analyses for GSEMO assume a single cardinality constraint. Inthis work, we extend the theoretical results to partition matroid constraintswhich generalize cardinality constraints, and show that GSEMO can generallyguarantee good approximation performance within polynomial expected run time.Furthermore, we conducted experimental comparison against a baseline GREEDYalgorithm in maximizing undirected graph cuts on random graphs, under variouspartition matroid constraints. The results show GSEMO tends to outperformGREEDY in quadratic run time.

Maximizing Submodular or Monotone Functions under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms