Efficient heuristics for the minimum labeling global cut problem Thiago Gouveia da Silva a,1 Gilberto F. de Sousa Filho b Igor A. M. Barbosa b Nenad Mladenovic d Lucidio A. F. Cabral b Luiz Satoru Ochi c Daniel Aloise e a Instituto Federal de Educa¸c˜ ao, Ciˆ encia e Tecnologia da Para´ ıba, Brazil b Universidade Federal da Para´ ıba, Brazil c Universidade Federal Fluminense, Brazil d Serbian Academy of Sciences and Arts, Serbia e ´ Ecole Polytechnique de Montr´ eal, Qu´ ebec, Canada Abstract Let G =(V,E,L) be an edge-labeled graph. Let V be the set of vertices of G, E the set of edges, L the set of labels (colors) such that each edge e ∈ E has an associated label L(e). The goal of the minimum labeling global cut problem (MLGCP) is to find a subset L ′ ⊆ L of labels such that G ′ =(V,E ′ ,L\L ′ ) is not connected and |L ′ | is minimized. In this work, we generate random instances for the MLGCP to perform empirical tests. Also propose a set of heuristics using concepts of Genetic Algorithm and metaheuristic VNS, including some of their procedures, like two local search moves, and an auxiliary data structure to speed up the local search. Computational experiments show that the metaheuristic VNS outperforms other methods with respect to solution quality. Keywords: Edge-Labeled Graphs, Variable Neighborhood Search, Connectivity 1 Introduction In the last few years, several papers have addressed problems defined over an edge-labeled graph (ELG). As opposed to weighted graphs, every edge of an 1 Email: thiago.gouveia.da.silva@gmail.com Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 66 (2018) 23–30 1571-0653/© 2018 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm https://doi.org/10.1016/j.endm.2018.03.004