An Ant Colony algorithm hybridized with insertion heuristics for the Time Dependent Vehicle Routing Problem with Time Windows

This paper presents an Ant Colony System algorithm hybridized with insertion heuristics for the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW). In the TDVRPTW a fleet of vehicles must deliver goods to a set of customers, time window constraints of the customers must be respected and the fact that the travel time between two points depends on the time of departure has to be taken into account. The latter assumption is particularly important in an urban context where the traffic plays a significant role.A shortcoming of Ant Colony algorithms for capacitated routing problems is that, at the final stages of the algorithm, ants tend to create infeasible solutions with unrouted clients. Hence, we propose enhancing the algorithm with an aggressive insertion heuristic relying on the minimum delay metric. Computational results confirm the benefits of more involved insertion heuristics. Moreover, the resulting algorithm turns out to be competitive, matching or improving the best known results in several benchmark problems.