Performance analysis of (1+1)EA on the maximum independent set problem

Abstract

The maximum independent set problem (MISP) is a classic graph combinatorial optimization problem and it is known to be NP-complete. In this paper, we investigate the performance of the (1+1)EA, which is a simple evolutionary algorithm, on MISP from a theoretical point of view. We showed that the (1+1)EA can obtain an approximation ratio of Δ+1/2 on this problem in expected time O(n4), where Δ and n denote the maximum vertex degree and the number of nodes in a graph, respectively. Later on, we reveal that the (1+1)EA has better performances than the local search algorithm on an instance of MISP. We present that the local search algorithm with 3-flip neighborhood will be trapped in local optimum while the (1+1)EA can find the global optimum in expected running time O(n5).