PSO Algorithm for Bi-Level Programming Model in Urban Transportation Continuous Equilibrium Network Design

Recent developments about Bi-level programming models of urban transportation continuous equilibrium network design are briefly summarized. Taking one of usual models as example, a new algorithm is put forward. That's to say, upper level model is solved by PSO while lower level model is solved by Frank-Wolfe, then iterations are continuously progressed between them so that the best solution can be approximated. The algorithm is illustrated with a cited example and compared with other algorithms. The results demonstrate that the algorithm put forward is better in accuracy, while the iterations and extra computational burden are not so heavy. If being used in a large-scale network design, its advantage will be more prominent.