An ant colony algorithm for time-dependent vehicle routing problem with time windows

The Vehicle Routing Problem (VRP) determines a set of vehicle routes originating and terminating at a single depot such that all customers are visited exactly once and the total demand of the customers assigned to each route does not violate the capacity of the vehicle. The objective is to minimize the total distance traveled by all vehicles. An implicit primary objective is to use the least number of vehicles. The Vehicle Routing Problem with Time Windows (VRPTW) is a variant of VRP in which lower and upper limits for delivery times for each customer are imposed. The arrival at a customer outside the specified delivery times is either penalized (soft time windows) or strictly forbidden (hard time windows). In the Stochastic Vehicle Routing problem, the customer demands and/or the travel times between the customers may vary. In this study, we address the Time-dependent Vehicle Routing Problem with hard time windows. Time-dependency is the result of different traffic conditions in different time intervals throughout the scheduling horizon. We tackle this problem using an Ant Colony Optimization approach proposing a new visibility function. This function is based on the Clark and Wright savings measure and the time compatibility between the customers. The time compatibility is measured with possible arrival times to a customer given the customers’ time-windows and the corresponding time interval(s). The performance of the proposed algorithm is tested on the well-known benchmark instances from the literature.