A specialized genetic algorithm for the fuel consumption heterogeneous fleet vehicle routing problem with bidimensional packing constraints

The vehicle routing problem combined with loading of goods, considering the reduction of fuel consumption, aims at finding the set of routes that will serve the demands of the customers, arguing that the fuel consumption is directly related to the weight of the load in the paths that compose the routes. This study integrates the Fuel Consumption Heterogeneous Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-FHFVRP). To reduce fuel consumption taking the associated environmental impact into account is a classical VRP variant that has gained increasing attention in the last decade. The objective of this problem is to design the delivery routes to satisfy the customers' demands with the lowest possible fuel consumption, which depends on the distances of the paths, the assigned vehicles, the loading/unloading pattern and the load weight. In the vehicle routing problem literature, the approximate algorithms have had great success, especially the evolutionary ones, which appear in previous works with quite a sophisticated structure, obtaining excellent results, but that are difficult to implement and adapt to other variants such as the one proposed here. In this study, we present a specialized genetic algorithm to solve the design of routes, keeping its main characteristic: the easy implementation. By contrast, the loading of goods restriction is validated by means of a GRASP algorithm, which has been widely employed for solving packing problems. With a view of confirming the performance of the proposed methodology, we provide a computational study that uses all the available benchmark instances, allowing to illustrate the savings achieved in fuel consumption. In addition, the methodology suggested can be adapted to the version of solely minimizing the total distance traveled for serving the customers (without the fuel consumption) and it is compared to the best works presented in the literature. The computational results show that the methodology manages to be adequately adapted to this version and it is capable of finding improved solutions for some benchmark instances. As for future work, we propose to adjust the methodology to consider the three-dimensional loading problem so that it adapts to more reallife conditions of the industry. (C) 2021 by the authors; licensee Growing Science, Canada