Comparison of Exact and Approximate methods for the Vehicle Routing Problem with Time Windows

This paper presents a comparison of two approaches for solving the vehicle routing problem with time windows (VRPTW). Scheduling of vehicles for pickup and delivery is a common problem in logistics and may be expressed as VRPTW, for which both exact and approximate techniques are available. It is therefore interesting to compare such techniques to evaluate their performance and figure what is the best option based on the instance features and size. In this work, we compared Mixed Integer Linear Programming (MILP) with Set-Based Particle Swarm optimization (S-PSO). Both algorithms are tested on the full 56 instances of the Solomon dataset. The results show that the two algorithms perform similarly for lower number of customers while there are significant differences for the cases with higher number of customers. For higher number of customers MILP consistently performs as good as or better than S-PSO for the clustered data, both with short and long scheduling horizons, while the S-PSO outperforms MILP in most cases with random and mixed random clustered data with long scheduling horizons. Furthermore when the algorithms perform the same with regards to the main objective (number of vehicles), MILP generally achieves a better result in the second objective (distance traveled).