Solving Continuous Hub Location Problems in Multiple Assignment Networks by the Hyperbolic Smoothing Approach Adilson Elias Xavier Federal University of Rio de Janeiro - Brazil e-mail: adilson@cos.ufrj.br Henrique Pacca Loureiro Luna Federal University of Alagoas - Maceio - Brazil e-mail: pacca@ic.ufal.br Claudio M Gesteira Federal University of Rio de Janeiro - Brazil e-mail: cmg@ufrj.br Abstract Hub-and-spoke (HS) network designs arise in transportation and telecom- munications systems, where items must flow among spatially separate nodes and scale economies can be attained through the shared use of high capacity links between hubs. As an alternative for the discrete approach of selecting a subset of the existing nodes as hubs, this paper explores the possibility of their continuous location. Therefore, the problem is to find the least expen- sive HS network, continuously locating hubs and assigning traffic to them, given the demands between each origin-destination pair and the respective transportation costs. The problem leads to a strongly non-differentiable min − sum − min formulation. The proposed method overcomes this difficulty with a smoothing strategy that uses a special differentiable func- tion. The approach is an application of the hyperbolic smoothing technique, 1