  In a currently ongoing project, we investigate a new possibility for solving
the k-labelled spanning forest (kLSF) problem by an intelligent Variable
Neighbourhood Search (Int-VNS) metaheuristic. In the kLSF problem we are given
an undirected input graph G and an integer positive value k, and the aim is to
find a spanning forest of G having the minimum number of connected components
and the upper bound k on the number of labels to use. The problem is related to
the minimum labelling spanning tree (MLST) problem, whose goal is to get the
spanning tree of the input graph with the minimum number of labels, and has
several applications in the real world, where one aims to ensure connectivity
by means of homogeneous connections. The Int-VNS metaheuristic that we propose
for the kLSF problem is derived from the promising intelligent VNS strategy
recently proposed for the MLST problem, and integrates the basic VNS for the
kLSF problem with other complementary approaches from machine learning,
statistics and experimental algorithmics, in order to produce high-quality
performance and to completely automate the resulting strategy.
