Evolutionary Algorithms and the Vertex Cover Problem

Experimental results have suggested that evolutionary algorithms may produce higher quality solutions for instances of vertex cover than a very well known approximation algorithm for this NP-complete problem. A theoretical analysis of the expected runtime of the (1+1)-EA on a well studied instance class confirms such a conjecture for the considered class. Furthermore, a class for which the (1+1)-EA takes exponential optimization time is examined. Nevertheless, given polynomial time, the evolutionary algorithm still produces a better solution than the approximation algorithm. Recently, the existence of an instance class has been proved for which the (1+1)-EA produces poor approximate solutions, given polynomial time. Here it is pointed out that, by using multiple runs, the (1+1)-EA finds the optimal cover of each instance of the considered graph class in polynomial time.