A hybrid genetic algorithm for the static and dynamic vehicle routing problem with soft time windows

In this paper, we are interested in vehicle routing optimization which is an important problem in the fields of transportation. We will introduce the Vehicle Routing Problem with soft time windows, in both cases: static (VRPSTW) and dynamic (D-VRPSTW). Input information changes dynamically over time with the appearance of new customer requests at any point during the vehicle's route, that include real-life assumptions. On the other hand, soft time windows allow deliveries outside the boundaries against a penalty cost. This paper proposes the hybridization of the genetic method and the variable neighborhood search method to solve the two version of the problem. This algorithm reduces the transportation costs by using a fleet of vehicles, improves the quality of service by reducing the delay time for each customer and increase the stopping time for each vehicle. The solution quality of this method has been compared against existing results on benchmark problems.