A particle swarm optimisation for time-dependent vehicle routing problem with an efficient travel time function

Transportation plays an essential role in economic, service, and manufacturing systems. This fact has inspired a vast variety of researches to deal with different aspects of this problem. Vehicle routing problem is one of key issues in this field which has received much attention by researchers. Although there is a vast literature related to the VRP, few researches incorporate different traffic. In this paper, a mathematical model has been presented which considers variations in traffic flow based on an efficient travel time function. The proposed travel time function complies with the first‐in, first‐out (FIFO) assumption, which does not allow for surpassing. Because of the NP‐hardness of the model, a particle swarm optimisation (PSO) method has been implemented and is compared to the mathematical model for small‐ and medium‐sized instances. In addition, a set of large‐sized instances have been taken into account in order to evaluate the applicability of the model in practical applications. Experimental results show the capability of the proposed PSO to find qualified solutions in reasonable computation time.