Kernel Search approach to solve the Minimum Spanning Tree Problem with conflicting edge pairs

The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using a tailored Kernel Search heuristic method, which consists in solving iteratively improved restrictions of the problem. The main novelty of the approach consists in using an independent set of the conflict graph within the algorithm. We test our approach on the benchmark instances and we compare our results with the ones obtained by other heuristics available in the literature.