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Theoretical studies on evolutionary algorithms have developed vigorously inrecent years. Many such algorithms have theoretical guarantees in both runningtime and approximation ratio. Some approximation mechanism seems to beinherently embedded in many evolutionary algorithms. In this paper, we identifysuch a relation by proposing a unified analysis framework for a generalizedsimple multi-objective evolutionary algorithm (GSEMO), and apply it on aminimum weight general cover problem. For a wide range of problems (includingthe the minimum submodular cover problem in which the submodular function isreal-valued, and the minimum connected dominating set problem for which thepotential function is non-submodular), GSEMO yields asymptotically tightapproximation ratios in expected polynomial time.

Evolution is Still Good: Theoretical Analysis of Evolutionary Algorithms on General Cover Problems