Volume 53, Number 3, July-September 2019
|Page(s)||1083 - 1095|
|Published online||29 July 2019|
Application of the “descent with mutations” metaheuristic to a clique partitioning problem
Telecom ParisTech, 46, rue Barrault, 75634 Paris Cedex 13, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 19 June 2018
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.
Mathematics Subject Classification: 90C27
Key words: Metaheuristics / noising methods / simulated annealing / clique partitioning of a graph / aggregation of symmetric relations into median partitions / median equivalence relations
© EDP Sciences, ROADEF, SMAI 2019
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