A hybrid metaheuristic for the minimum labeling spanning tree problem

An edge-labeled graph (ELG) is a graph in which each edge has a label associated. Given G, an ELG, the minimum labeling spanning tree problem (MLSTP) is an NP-hard problem that consists in finding a spanning tree in G by using a minimum number of labels. The MLSTP has applications in areas such as computer networks, multimodal transportation networks, and data compression. This paper introduces new concepts, presents a revised version of the maximum vertex covering algorithm and provides a tighter bound to its time complexity. Further, a new MIP-based metaheuristic is proposed for solving the MLSTP, the multi-start local branching (MSLB). It combines the efficiency of the proposed constructive heuristics with the capacity of exploration of a new local search method based on MIP. The computational experiments performed show that the MSLB is superior to the current state-of-the-art metaheuristics in respect to quality of the solutions and processing times. (C) 2018 Elsevier B.V. All rights reserved.