Solving the bandwidth coloring problem applying constraint and integer programming techniques ✩ Bruno Dias a , Rosiane de Freitas a,b,∗ , Nelson Maculan c , Philippe Michelon d a ProgramadeP´os-Gradua¸ c˜aoemInform´ atica (PPGI/UFAM), Universidade Federal do Amazonas, Manaus, Brazil b Instituto de Computa¸ c˜ao (IComp/UFAM), Universidade Federal do Amazonas, Manaus, Brazil c PESC/COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro - RJ, Brazil d Centre d’Enseignement et de Recherche en Informatique, Universit´ e d’Avignon et des Pays de Vaucluse, Avignon, France Abstract In this paper, constraint and integer programming formulations are applied to solve Bandwidth Coloring Problem (BCP) and Bandwidth Multicoloring Problem (BMCP). The problems are modeled using distance geometry (DG) approaches, which are then used to construct the constraint programming for- mulation. The integer programming formulation is based on a previous for- mulation for the related Minimum Span Frequency Assignment Problem (MS- FAP), which is modified in order to reduce its size and computation time. The two exact approaches are implemented with available solvers and applied to well-known sets of instances from the literature, GEOM and Philadelphia-like problems. Using these models, some heuristic solutions from previous works are proven to be optimal, a new upper bound for an instance is given and all optimal solutions for the Philadelphia-like problems are presented. A discussion is also made on the performance of constraint and integer programming for each considered coloring problem, and the best approach is suggested for each one of ✩ Supported by CAPES (Coordena¸ c˜ao de Aperfei¸coamento de Pessoal de Ensino Supe- rior), CNPq (Conselho Nacional de Desenvolvimento Cient´ ıfico e Tecnol´ ogico and FAPEAM (Funda¸c˜ao de Amparo a Pesquisa do Estado do Amazonas) - Brazil. * Corresponding author Email addresses: bruno.dias@icomp.ufam.edu.br (Bruno Dias), rosiane@icomp.ufam.edu.br (Rosiane de Freitas), maculan@cos.ufrj.br (Nelson Maculan), philippe.michelon@univ-avignon.fr (Philippe Michelon) Preprint submitted to Computers and Operations Research June 27, 2016