The future of optical networks is focused on Wavelength Division Multiplexing (WDM) technology. WDM allows simultaneous transmissions of traffic on many non-overlapping channels (wavelengths). Since nowadays the majority of traffic requests only require a bandwidth of Mbps, there exists a waste of bandwidth in these non-overlapping channels because they support traffic in Gbps range. For exploiting the optical network resources effectively, several low-speed traffic requests can be groomed onto a wavelength channel, which is not a simple task. In fact, it is known as the Traffic Grooming problem, and is considered an optimization problem (NP-hard problem). In this work, we suggest the use of multiobjective evolutionary computation and swarm intelligence jointly for solving the Traffic Grooming problem. We have proposed the following swarm algorithms: Artificial Bee Colony, Gravitational Search Algorithm, and Firefly Algorithm; but adapted to multiobjective field: MO-ABC, MO-GSA, and MO-FA respectively. Furthermore, we have adapted the well-known Strength Pareto Evolutionary Algorithm 2, Fast Nondominated Sorting Genetic Algorithm, and Multiobjective Selection Based On Dominated Hypervolume to the Traffic Grooming problem with the aim of evaluating the quality of our swarm proposals. Finally, we present several comparisons with other heuristics and metaheuristics published in the literature by other authors. After comparing with them, we conclude that our approaches overcome the results obtained by other approaches published by other authors.