Freight transportation is becoming an increasingly critical activity for enterprises in a global world. Moreover, the distribution activities have a non-negligible impact on the environment, as well as on the citizens’ welfare. The classical vehicle routing problem (VRP) aims at designing routes that minimize the cost of serving customers using a given set of capacitated vehicles. Some VRP variants consider traveling times, either in the objective function (e.g., including the goal of minimizing total traveling time or designing balanced routes) or as constraints (e.g., the setting of time windows or a maximum time per route). Typically, the traveling time between two customers or between one customer and the depot is assumed to be both known in advance and static. However, in real life, there are plenty of factors (predictable or not) that may affect these traveling times, e.g., traffic jams, accidents, road works, or even the weather. In this work, we analyze the VRP with dynamic traveling times. Our work assumes not only that these inputs are dynamic in nature, but also that they are a function of the structure of the emerging routing plan. In other words, these traveling times need to be dynamically re-evaluated as the solution is being constructed. In order to solve this dynamic optimization problem, a learnheuristic-based approach is proposed. Our approach integrates statistical learning techniques within a metaheuristic framework. A number of computational experiments are carried out in order to illustrate our approach and discuss its effectiveness.
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