A topographical method to choose optimal solutions after solving the multi-criteria urban road network design problem

The paper proposes and applies a method for systematically sorting and reducing the number of different possible solutions to a network design problem (NDP). This is achieved first by defining a topological similarity measurement and then by applying cluster analysis. The NDP can be derived from the scientific literature. In general, the method consists of some models and subsequent algorithms that generate different solutions (enumerative, branch and bound, genetic, expert panel, etc.) and evaluate for each solution an objective function (with deterministic or stochastic network assignment and with elastic or inelastic demand). The NDP, mainly in urban areas, needs multi-criteria evaluation and in each case a large set of non-dominated solutions is generated. In this paper, in order to select solutions and identify latent optimal network layouts, cluster analysis is carried out. The methodology utilises a ‘cluster’ formation in relation to the solution topology and a ‘best’ (representative) solutions extraction in relation to the criteria values. It can be utilised after solving the existing multi-criteria NDP and in other network problems, where the best solutions (for global or local network layouts) are extracted (with respect to the network topology) from a large set. The method is applied in a test system and on different real networks in two Italian towns, in order to analyse the goodness of the solution algorithm and assess its possible application to different networks.