On the Use of the Dual Formulation for Minimum Weighted Vertex Cover in Evolutionary Algorithms

We consider the weighted minimum vertex cover problem and investigate how its dual formulation can be exploited to design evolutionary algorithms that provably obtain a 2-approximation. Investigating multi-valued representations, we show that variants of randomized local search and the (1+1)EA achieve this goal in expected pseudo-polynomial time. In order to speed up the process, we consider the use of step size adaptation in both algorithms and show that RLS obtains a 2-approximation in expected polynomial time while the one+one still encounters a pseudo-polynomial lower bound.