A Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Delivery Time Cost

We consider the vehicle routing problem with delivery time cost (vrpdtc) in which aims to find a set of routes of minimal total costs including the travelling cost and delivery time cost, starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. in this paper, first a mathematical model of this problem is presented. then a column generation approach is employed to obtain the lower bounds of problems. in order to solve this problem, a quantum evolutionary algorithm based on quantum computations is proposed. finally, the computational results of some instances are reported and the results of these approaches are compared. the results demonstrate the effectiveness of the quantum algorithm in solving this problem.