Graph partitioning is one of the most studied NP-complete problems. Given a graphG=(V,E) , the task is to partition the vertex setVintokdisjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this paper, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbation-based tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e., the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the graph partitioning archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithms in terms of solution quality.

The balanced graph partitioning consists in dividing the vertices of an undirected graph into a given number of subsets of approximately equal size, such that the number of edges crossing the subsets is minimized. In this work, we present a multilevel memetic algorithm for this NP-hard problem that relies on a powerful grouping recombination operator and a dedicated local search procedure. The proposed operator tends to preserve the backbone with respect to a set of parent individuals, i.e. the grouping of vertices which is same throughout each parent individual. Although our approach requires significantly longer computing time compared to some current state-of-art graph partitioning algorithms such as SCOTCH, METIS, CHACO, JOSTLE, etc., it competes very favorably with these approaches in terms of solution quality. Moreover, it easily reaches or improves on the best partitions ever reported in the literature.