  Theoretical studies on evolutionary algorithms have developed vigorously in
recent years. Many such algorithms have theoretical guarantees in both running
time and approximation ratio. Some approximation mechanism seems to be
inherently embedded in many evolutionary algorithms. In this paper, we identify
such a relation by proposing a unified analysis framework for a generalized
simple multi-objective evolutionary algorithm (GSEMO), and apply it on a
minimum weight general cover problem. For a wide range of problems (including
the the minimum submodular cover problem in which the submodular function is
real-valued, and the minimum connected dominating set problem for which the
potential function is non-submodular), GSEMO yields asymptotically tight
approximation ratios in expected polynomial time.
