Traffic assignment aims to assign trips in a road network such that the travel time of each car is minimized given multiple alternative routes and origin-destination pairs. The number of alternative routes between two points considered in traffic assignment is an important factor in discovering an optimal distribution of cars to routes. This paper investigates the influence of using different number of routes in traffic assignment modeled as a multi-objective optimization problem. An evolutionary algorithm is used to find route solutions for all users in the network considering a different set of best possible routes between origin and destination points. The performance of the multi-objective evolutionary models considered is assessed using several parameter settings for a non-trivial road network. Results show the limitations and advantages of different settings to detect efficient route assignments in terms of network performance.