A large neighborhood search algorithm for the vehicle routing problem with time windows

Given a fleet of vehicles assigned to a single depot, the vehicle routing problem with time windows (vrptw) consists of determining a set of feasible routes to deliver goods to a set of customers while minimizing, first, the number of vehicles used and, second, total mileage. Each customer must be visited exactly once by a vehicle within a prescribed time interval. A route starts from the depot and visits in order a sequence of customers before returning to the depot. It is feasible if the total amount of goods delivered to the visited customers does not exceed the vehicle capacity and if it respects the time window of each visited customer. The cost of a route is given by the sum of the traveling costs between the consecutive locations visited along the route.