Résumé (EN)

This paper presents a multi-start iterated local search (MS-ILS), an exact approach based on an improved integer linear programming (ILP) model, and a matheuristic combining the ILP approach with MS-ILS through solution merging for the minimum capacitated dominating set (CAPMDS) problem for undirected graphs. This problem is an extension of the well-known minimum dominating set problem, where there is a cap on the number of nodes that each node can dominate, and the goal is to find a dominating set of minimum cardinality where the number of dominated nodes for each dominating node is within this cap. This -hard problem has several real world applications in resource constrained environments such as clustering of wireless sensor networks along with selection of cluster heads, document summarization in information retrieval. Computational results on the standard benchmark instances of this problem show the superiority of our approaches over state-of-the-art approaches available in the literature in their respective categories.