Abstract
ABSTRACT The Vehicle Routing Problem (VRP) is a classical problem, and when the number of customers is very large, the task of finding the optimal solution can be extremely complex. It is still necessary to find an effective way to evaluate the quality of solutions when there is no known optimal solution. This work presents a suggestion to analyze the quality of vehicle routes, based only on their geometric properties. The proposed descriptors aim to be invariants in relation to the amount of customers, vehicles and the size of the covered area. Applying the methodology proposed in this work it is possible to obtain the route and, then, to evaluate the quality of solutions obtained using computer vision. Despite considering problems with different configurations for the number of customers, vehicles and service area, the results obtained with the experiments show that the proposal is useful for classifying the routes into good or bad classes. A visual analysis was performed using the Parallel Coordinates and Viz3D techniques and then a classification was performed by a Backpropagation Neural Network, which indicated an accuracy rate of 99.87%.
Highlights
The vehicle routing problem (VRP) has important applications in many areas with different characteristics
We propose that the descriptors presented in Subsection 2.1 and descriptors in Equations 10 and 11 may be applied to assess the quality of the solutions to the vehicle routing problem by means of a geometrical analysis of routes
It is not a simple task to find optimal solutions to the vehicle routing problem, when there are a large number of customers and vehicles, as well as different sizes and shapes of the assisted areas
Summary
The vehicle routing problem (VRP) has important applications in many areas with different characteristics. The VRP is an NP-hard problem, thereby if the number of costumers is too large, it is very difficult to find the best solution, either by heuristic methods as exact methods. This work presents a proposal to analyze the quality of vehicle routes, based only on their geometric shapes analysis. Are presented the techniques of information visualization, used in visual analysis of data, and a technique for attributes selection, based on analysis of variance; Section 3 presents the methodology, proposed in this work, to evaluate the quality of solutions for the vehicle routing problem, based on the geometric analysis of the route shapes; In Section 4 are presented some results using the instances type “A” from Augerat et al (1998)[4]; Section 5 presents the conclusions and future works
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