An intelligent extension of Variable Neighbourhood Search for labelling graph problems

In this paper we describe an extension of the Variable Neighbourhood Search (VNS) which integrates the basic VNS with other complementary approaches from machine learning, statistics and experimental algorithmic, in order to produce high-quality performance and to completely automate the resulting optimization strategy. The resulting intelligent VNS has been successfully applied to a couple of optimization problems where the solution space consists of the subsets of a finite reference set. These problems are the labelled spanning tree and forest problems that are formulated on an undirected labelled graph; a graph where each edge has a label in a finite set of labels L. The problems consist on selecting the subset of labels such that the subgraph generated by these labels has an optimal spanning tree or forest, respectively. These problems have several applications in the real-world, where one aims to ensure connectivity by means of homogeneous connections.