Existing approaches to traffic assignment focus mainly on approximating the user equilibrium. However, nowadays, with the increasing number of traffic information reaching drivers, traffic authorities have a unique opportunity to try to recommend route choices that are as much as possible aligned with the system optimum. In this paper, we formulate traffic assignment as a multi-objective optimization problem and engage an evolutionary approach to find route solutions for all users in the network. The aim is to discover a good approximation of an optimal distribution of vehicles to alternative routes between their origin and destination, from the perspective of the overall system, while still considering individual needs. Several multi-objective models are defined for this purpose and integrated in a nondominated sorting genetic algorithm. Computational experiments performed support the ability of the proposed approach to detect efficient route assignments in terms of network performance, while also considering the user perspective. efficient route assignments in terms of network performance, while also considering the user perspective.