Parameterized Analysis of Multi-objective Evolutionary Algorithms and the Weighted Vertex Cover Problem

A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann [11]. In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT , where OPT is the cost of the the optimal solution for the problem. Moreover, using a diversity mechanisms, we present a multi-objective evolutionary algorithm that finds a 2−approximation in expected polynomial time and introduce a population-based evolutionary algorithm which finds a (1+ ε)−approximation in expected time O(n ·2min{n,2(1−ε)OPT}+n3).