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Currently, wavelength division multiplexing technology is widely used for exploiting the huge bandwidth of optical networks. It allows simultaneous transmission of traffic on many nonoverlapping channels (wavelengths). These channels support traffic demands in the gigabits per second (Gb/s) range; however, since the majority of devices or applications only require a bandwidth of megabits per second (Mb/s), this is a waste of bandwidth. This problem is efficiently solved by multiplexing a number of low-speed traffic demands (Mb/s) onto a high-speed wavelength channel (Gb/s). This is known as the traffic grooming problem. Since traffic grooming is an NP-hard problem, in this paper, we propose two novel multiobjective evolutionary algorithms for solving it. The selected algorithms are multiobjective variants of the standard differential evolution (DEPT) and variable neighborhood search. With the aim of ensuring the performance of our proposals, we have made comparisons with the well-known fast Nondominated Sort Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm 2, and other approaches published in the literature. After performing diverse comparisons, we can conclude that our novel approaches obtain promising results, highlighting in particular the performance of the DEPT algorithm.