An unsupervised fuzzy clustering approach to the capacitated vehicle routing problem

This paper analyzes and predicts the fuzziness parameter from a fuzzy clustering technique applied to the vehicle routing problem with homogeneous fleet. It uses unsupervised fuzzy clustering as the cornerstone of a proposed heuristic to save computational time presenting optimal results. More specifically, an assignment algorithm redistributes the demand points among the clusters based on their membership grades, observing the vehicle capacity. When compared to the optimal values of the 85 known instances in the literature, the results found in terms of the total distance travelled indicate a 5 % error in average. Results also suggest a relationship between the most adequate fuzziness parameter m and the descriptive statistics of the demands of each point and their distances to the central depot within each instance. The neural network trained to predict the most adequate fuzziness parameter based on these descriptives reported a pseudo R ² of 90.6 %. This would allow shorter computational times, as the initial search for the most adequate fuzziness parameter could be abbreviated. This analysis would be recommended for e-commerce companies and home appliance markets.