Exploiting Tree Decomposition for Guiding Neighborhoods Exploration for VNS

Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an acyclic graph. There are works exploiting tree decomposition for complete search methods. In this paper, we show how tree decomposition can be used to efficiently guide local search methods that use large neighborhoods like VNS. We propose DGVNS (Decomposition Guided VNS) which uses the graph of clusters in order to build neighborhood structures enabling better diversification and intensification. Second, we introduce tightness dependent tree decomposition which allows to take advantage of both the structure of the problem and the constraints tightness. Third, experiments performed on random instances (GRAPH) and real life instances (CELAR, SPOT5 and tagSNP) show the appropriateness and the efficiency of our approach. Moreover, we study and discuss the influence of the width of the tree decomposition on our approach and the relevance of removing clusters with very few proper variables from the tree decomposition.