Intelligent Optimization for the Minimum Labelling Spanning Tree Problem

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective heuristics have been proposed and analysed. In this paper we present preliminary results of a currently ongoing project regarding the implementation of an intelligent optimization algorithm to solve the MLST problem. This algorithm is obtained by the basic Variable Neighbourhood Search heuristic with the integration of other complements from machine learning, statistics and experimental algorithmics, in order to produce high-quality performance and to completely automate the resulting optimization strategy.