ORIGINAL ARTICLE An unsupervised fuzzy clustering approach to the capacitated vehicle routing problem Henrique Ewbank 1 • Peter Wanke 1 • Abdollah Hadi-Vencheh 2,3 Received: 29 January 2014 / Accepted: 30 March 2015 Ó The Natural Computing Applications Forum 2015 Abstract 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 pro- posed heuristic to save computational time presenting op- timal results. More specifically, an assignment algorithm redistributes the demand points among the clusters based on their membership grades, observing the vehicle ca- pacity. 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 av- erage. Results also suggest a relationship between the most adequate fuzziness parameter m and the descriptive statis- tics 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. Keywords Capacitated vehicle routing problem  Homogeneous fleet  Fuzziness parameter  Clustering  Unsupervised competitive learning 1 Introduction The vehicle routing problem (VRP) is one of the most studied problems, especially regarding logistic systems [40]. It was first introduced by Dantzig and Ramser [18] as a generalization of the traveling salesman problem (TSP), presented by Flood [28]. The latter demands the vehicle to pass through all nodes once and then return to the initial point. Many clustering techniques have been applied to the TSP for solving complex instances and saving processing time [4, 12, 59]. As a matter of fact, clustering techniques have been widely used in several applications besides routing [20, 35, 52, 57], such as medical diagnostics [11, 48, 62] and social network analysis [19, 44, 64]. All of them used some kind of learn algorithm to group similar data. Traditionally, mathematical programming has been used to solve clustering issues within the ambit of vehicle routing problems [7, 24, 39, 56]. Chapleau et al. [8], for example, reexamined the school bus routing problem in an urban area and proposed building clusters to reduce the capacitated vehicle routing problem (CVRP) into smaller routing problems. They used a districting algorithm based on straight line distances and penalty factors to build the clusters. On the other hand, Novaes and Graciolli [50] used polar coordinates with districting algorithm, while Galva ˜o et al. [30] used Voronoi diagrams to separate a served re- gion into delivery zones. The use of meta-heuristics is also an emerging trend on VRP approaches as can be seen in Zarandi et al. [63], & Peter Wanke peter@coppead.ufrj.br Henrique Ewbank henrique.ewbank@coppead.ufrj.br Abdollah Hadi-Vencheh ahadi@khuisf.ac.ir 1 Center for Studies in Logistics, Infrastructure and Management, COPPEAD Graduate School of Business, Federal University of Rio de Janeiro, Rua Paschoal Lemme, 355, Rio de Janeiro, RJ 21941-918, Brazil 2 Department of Mathematics, Azad University, Mobarekeh, Isfahan, Iran 3 Islamic Azad University, Khorasgan Branch, Isfahan, Iran 123 Neural Comput & Applic DOI 10.1007/s00521-015-1901-4