Heuristics for the Network Design Problem

The concentration of human activities in urban areas has induced an increase in travel demand. This has brought urban transport systems to considerable levels of congestion, with negative environmental effects and external diseconomies leading to a poor quality of life. Therefore quantitative methods for urban network design have been developed in order to assure more effective results. The network design problem (reviews in Magnanti and Wong 1984, Cascetta 2001) has recently been treated in the literature using different models and algorithms. The proposed algorithms in the literature can first of all be classified according to type of decision variables: integer (Branch and Bound, Billheimer and Gray, Poorzahedy and Turnquist), continuous (Marcotte, Davis, Friesz and Shah, Clegg et al.) and mixed integer (Cantarella and Vitetta). In relation to solution algorithms, network design can be divided into heuristic (Billheimer and Gray, Cantarella and Vitetta, Friesz and Shah, etc.), exact (brute force, Branch and Bound, etc.) and local convergent (Davis, Clegg et al.). This article deals with the problem of urban road network design, with the hypothesis of a congested network and rigid travel demand. The decision variables are the network layout and the signal settings at the junctions; the objective is the minimization of the user total travel time. The users’ behaviour is simulated with a deterministic user equilibrium model. Solution algorithms proposed in this paper are based on heuristic methods with mixed integer variables. The network design problem has been variously formulated in the literature. Its more consolidated formulation is (Cascetta, 1999):