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In literature different approaches are proposed for the solution of the transport design problem. The approaches may be classified according to the decision variables (integer, continuous and mixed integer) and according to solution algorithms used (analytical or heuristic).
The public transport network design problem is non-convex (Newell) and the best and most useful solution methods are based on heuristic procedures. This approach,followed throughout the study, concerns the minimization of an objective function (OF),including all different possible impacts of transport, but usually is limited to a combination
of operator and user’s costs.In the last years, researchers have tested new approaches based on Artificial Neural Networks, Genetic Algorithms (GAs), Simulated Annealing or Tabu Search to solve optimization problems.1 Dip. Scienze dell’Ingegneria Civile, Università di Roma Tre, eciprian@uniroma3.it 2 DITS, Università di Roma “La Sapienza”, gaetano.fusco@uniroma1.it 3 Dip. Scienze dell’Ingegneria Civile, Università di Roma Tre, sgori@uniroma3.it 4 Dip. Scienze dell’Ingegneria Civile, Università di Roma Tre, labtras@uniroma3.it 682 E. Cipriani et al.
The utilization of powerful and probabilistic optimization techniques as GAs results particularly opportune for several specific aspects: the nonlinearity and the nonconvexity of the objective functions and the discrete nature of several variables.Xiong and Schneider show that GA may efficiently solve transport network design problem. Other authors developed GAs applications to solve specific public transport network design problems (routing, scheduling, etc.). Pattnaik et al implemented a two phases procedure. First, a set of feasible routes is generated and then a GA selects the optimum routes set. Also Dhingra et al proposed an application of GAs. The solution approach provides a double application of GAs to solve separately, the routing and the scheduling problem. Ngamchai and Lovell proposed a solution model based on the use of several genetic operators designed for this specific problem. Among the most remarkable works on this matter not using GAs, it is possible to mention Mandl, Filippi and Gori, Ceder and Israeli and Baaj and Mahmassani.