Abstract – The purpose of this paper is to conduct a review in the scientific literature to know the state of the art relating to a real optimization problem. This problem issues from a research project which studies the application of Operations Research methods for the optimization and upgrading of Intermodal Transportation Systems. Concretely, the problem can be classified as a VRP type. The most suitable problems and solutions were studied, but also those which would contribute to have an outlook on how to solve this kind of problems. The current document has been divided into two main groups; exact algorithms and approximated methods. In each group, the different algorithms studied were presented. Each algorithm studied were briefly explained and mentioned the where it has been applied for.

(VRPTW) is an important logistics problem which in the realworld appears to be multi-objective. Most research in this area has been carried out using classic datasets designed for the single-objective case, like the well-known Solomon’s problem instances. Some unrealistic assumptions are usually made when using these datasets in the multi-objective case (e.g. assuming that one unit of travel time corresponds to one unit of travel distance). Additionally, there is no common VRPTW multiobjective oriented framework to compare the performance of algorithms because different implementations in the literature tackle different sets of objectives. In this work, we investigate the conflicting (or not) nature of various objectives in the VRPTW and show that some of the classic test instances are not suitable for conducting a proper multi-objective study. The insights of this study have led us to generate some problem instances using data from a real-world distribution company. Experiments in these new dataset using a standard evolutionary algorithm (NSGA-II) show stronger evidence of multi-objective features. Our contribution focuses on achieving a better understanding about the multi-objective nature of the VRPTW, in particular the conflicting relationships between 5 objectives: number of vehicles, total travel distance, makespan, total waiting time, and total delay time.