Application of the “descent with mutations” metaheuristic to a clique partitioning problem

Abstract

We study here the application of the “descent with mutations” metaheuristic to a problem arising from the field of classification and cluster analysis (dealing more precisely with the aggregation of symmetric relations) and which can be represented as a clique partitioning of a weighted graph. In this problem, we deai with a complete undirected graphe G; the edges of G have weights which can be positive, negative or equal to 0; the aim is to partition the vertices of G into disjoint cliques (whose number depends on G in order to minimize the sum of the weights of the edges with their two extremities in a same clique; this problem is NP-hard. The “descent with mutations” is a local search metaheuristic, of which the design is very simple and is based on local transformation. It consists in randomly performing random elementary transformations, irrespective improvement or worsening with respect to the objective function. We compare it with another very efficient metaheuristic, which is a simulated annealing method improved by the addition of some ingredients coming from the noising methods. Experiments show that the descent with mutations is at least as efficient for the studied problem as this improved simulated annealing, usually a little better, while it is much easier to design and to tune.