Variable neighborhood search for the time-dependent vehicle routing problem with soft time windows

In this paper we present a variable neighborhood search for time-dependent vehicle routing problems with time windows. Unlike the well-studied routing problems with constant travel times, in the time-dependent case the travel time depends on the time of the day. This assumption approaches reality, in particular for urban areas where travel times typically vary during the day, e.g., because of traffic congestion due to rush hours. An experimental evaluation for the vehicle routing problem with soft time windows with and without time-dependent travel times is performed and it is shown that taking time-dependent travel times into account provides substantial improvements of the considered objective function.