This paper presents a hybrid algorithm for solving the Capacitated VehicleRouting Problem with practical three-dimensional loading constraint. This problem is known as 3L-CVRP (Three-dimensional Loading Capacitated Vehicle Routing Problem). The proposed methodology consists of two phases. The first phase uses an optimization procedure based on cuts to obtain solutions for the well-known Capacitated Vehicle Routing Problem (CVRP). The second phase validates the results of the first phase of a GRASP algorithm (Greedy Randomized Adaptive Search Procedure). In particular, the GRASP approach evaluates the packing constraints for each performed route of the CVRP. The proposed hybrid algorithm uses a relaxation of the classical model of two sub-indices for the vehicle routing problem. Specifically different types of cuts are added: subtour elimination, capacity-cut constraints, and packing-cut constrains. The proposed algorithm is compared with the most efficient approaches for the 3L-CVRP on the set of benchmark instances considered in the literature. The computational results indicate that the proposed approach is able to obtain good solutions, improving some of the best-known solutions from the literature.
RESUMEN:En este artículo se presenta un algoritmo híbrido para resolver el problema de ruteo de vehículos con restricciones de capacidad y restricciones prácticas de empaquetamiento tridimensional, este problema en la literatura es conocido como 3L-CVRP (Capacitated Vehicle Routing Problem and Container Loading Problem). La metodología de solución propuesta en este trabajo consiste de dos fases. La primera utiliza un procedimiento de optimización basado en cortes para el Problema de Rutas de Vehículos Capacitados (CVRP). La segunda valida las soluciones de la fase anterior a través de un algoritmo GRASP (Greedy Randomized Adaptive Search Procedure), el cual evalúa las restricciones de empaquetamiento de cada una de las rutas. Para el algoritmo híbrido se utiliza la relajación del modelo clásico de dos subíndices para el problema de ruteo de vehículos. En particular diferentes tipos de cortes son adicionados: eliminación de subtours, cortes debido a las restricciones de capacidad y cortes para restricciones de empaquetamiento. El algoritmo propuesto ha sido comparado con los algoritmos más eficaces para el 3L-CVRP en el conjunto clásico de instancias presentadas en la literatura. Los resultados computacionales muestran que el método propuesto es capaz de obtener buenos resultados perfeccionando algunas de las mejores soluciones conocidas propuestas en la literatura.
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 real-life conditions of the industry.
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