A memetic algorithm for the weighted feedback vertex set problem

Given an undirected and vertex weighted graph G=(V,E,w), the Weighted Feedback Vertex Set Problem consists of finding the subset F⊆V of vertices, with minimum weight, whose removal results in an acyclic graph. Finding the minimum feedback vertex set in a graph is an important combinatorial problem that has a variety of real applications. In this article, we introduce a memetic algorithm for this problem. We propose an efficient greedy procedure that quickly generates chromosomes with specific characteristics and a wise application of recent local search procedures based on k‐diamonds. Computational results show that the proposed algorithm outperforms the effectiveness of two other metaheuristics recently proposed in the literature for this problem.