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

Mojgan Pourhassan, Feng Shi, Frank Neumann

Abstract: 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 [1]. In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of the optimal solution for the problem. Moreover, using a diversity mechanism, we present a multi-objective evolutionary algorithm that finds a $$2-$$ approximation in expected polynomial time.