A Skyline Algorithm for Solving the Vehicle Routing Problem

In the last decades, many researches provided many solutions, methods and models for solving vehicle routing problem (VRP). However, they offer no reliable solution for dealing with important numbers of instances. For such a case, we already gave an algorithm using skylines to solve the VRP problem. The algorithm first determines all feasible routes with their respective costs vectors, and then the vectors are passed to the skyline operator to yield the best routes. In our previous work presenting this algorithm, we mainly focused on the novel idea on how to use skylines if such vectors are provided. In this paper, we first give a state of the art for some methods solving the vehicle routing problem. Secondly, we investigate the details regarding the first step of our algorithm regarding the determination of all feasible solutions with their associated costs vectors. We step by step consider all possible combinations of routes and reject the useless routes according to the user's needs (e.g., limited cost, limited time, limited capacity). The feasible combinations for the problem are finally passed to the skyline operator. All steps of our algorithm are illustrated through simulation examples.