An Adaptive Neighborhood Search for k-Clustering Minimum Bi-clique Completion Problems

Abstract

In this paper, we propose to solve the k-clustering minimum bi-clique completion problem by using an adaptive neighborhood search. An instance of the problem is defined by a bipartite graph G(V = (S,T),E), where V (resp. E) denotes the set of vertices (resp. edges) and the goal of the problem is to determine the partition of the set S of V into k clusters (disjoint subsets) such that the number of the edges that complete each cluster into a bi-clique, according to the vertices of T, should be minimized. The adaptive search is based upon three complementary steps: (i) a starting step that provides an initial solution by applying an adaptation of Johnson’s principle, (ii) an intensification step in which both exchanging and k-opt strategies are introduced and, (iii) a diversification step that tries to explore unvisited solutions’ space. The method is evaluated on benchmark instances taken from the literature, where the provided results are compared to those reached by recent methods available in the literature. The proposed method remains competitive and it yields new results.