A novel ant system with multi-layer pheromone network approach for the vehicle routing problem with time windows

Abstract

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. VRP with Time Windows (VRPTW) is a variant of VRP in which lower and upper limits are imposed to the delivery time to each customer. The arrival at a customer outside the specified delivery times is either penalized (soft time windows) or strictly forbidden (hard time windows). In this paper, we tackle VRPTW using an ant colony algorithm equipped with a multi-layer pheromone network. The performance of the proposed algorithm is tested on the well-known benchmark instances of Solomon [Algorithms for the vehicle routing and scheduling problems with time window constraints, Operations Research 1987; 35(2): 254–65] and improvements on some best-known results are reported.