MULTIPLE ANT COLONY SYSTEM FOR A VRP WITH TIME WINDOWS AND SCHEDULED LOADING

the vehicle routing problem with time windows and scheduled loading [vrptwsl] requires not only the design of routes with time windows and capacity constraints, but also a schedule of the departures of vehicles from the depot given a load time due to the limited resources available to load the demand in the vehicles. a mathematical formulation of the vehicle routing problem with time windows and scheduled loading is presented and a metaheuristics based on multiple ant colony system is proposed and implemented where two ant colonies, each with a single objective function, are organized in a hierarchical way. a time update procedure is incorporated into the ant constructive procedure to update and schedule the departure of a vehicle from the depot when each ant moves to a new customer-node. constraint programming is used to determine a feasible move to a new customer-node. as [vrptwsl] incorporates the vehicle departure scheduling, the algorithm presented in this paper has a direct application to real problems, in this way [vrptwsl] can be taken as an important advance for practical vehicle routing problems.