A heuristic method for a congested capacitated transit assignment model with strategies

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algorithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtaining capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested networks. A set of computational tests on realistic small- and large-scale transit networks under various congestion levels are reported, and the characteristics of the proposed method are analyzed.

[1]  J. Elíasson,et al.  A dynamic stochastic model for evaluating congestion and crowding effects in transit systems , 2016 .

[2]  Esteve Codina,et al.  A Variational Inequality Reformulation of a Congested Transit Assignment Model by Cominetti, Correa, Cepeda, and Florian , 2013, Transp. Sci..

[3]  Yu Jiang,et al.  Reliability-Based Transit Assignment for Congested Stochastic Transit Networks , 2011, Comput. Aided Civ. Infrastructure Eng..

[4]  Michael Florian,et al.  Optimal strategies: A new assignment model for transit networks , 1989 .

[5]  M. Maiti,et al.  Approximating fixed points by ishikawa iterates , 1989, Bulletin of the Australian Mathematical Society.

[6]  E. Codina,et al.  A model for setting services on auxiliary bus lines under congestion , 2013 .

[7]  I. Ömer Verbas,et al.  Gap-based transit assignment algorithm with vehicle capacity constraints: Simulation-based implementation and large-scale application , 2016 .

[8]  José Eugenio Leal,et al.  ALOCAÇÃO DE FLUXOS DE PASSAGEIROS EM UMA REDE DE TRANSPORTE PÚBLICO DE GRANDE PORTE FORMULADO COMO UM PROBLEMA DE INEQUAÇÕES VARIACIONAIS , 2003 .

[9]  Henry X. Liu,et al.  Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem , 2009 .

[10]  Krzysztof C. Kiwiel,et al.  Proximity control in bundle methods for convex nondifferentiable minimization , 1990, Math. Program..

[11]  Abbas Babazadeh,et al.  Algorithm for Equilibrium Transit Assignment Problem , 2005 .

[12]  Ioannis Kaparias,et al.  Dynamic User Equilibrium in Public Transport Networks with Passenger Congestion and Hyperpaths , 2013 .

[13]  H. W. Ho,et al.  Schedule-based transit assignment model with vehicle capacity and seat availability , 2011 .

[14]  Claude Lemaréchal,et al.  An Algorithm for Minimizing Convex Functions , 1974, IFIP Congress.

[15]  M. Patriksson,et al.  Equilibrium characterizations of solutions to side constrained asymmetric traffic assignment models , 1995 .

[16]  Fumitaka Kurauchi,et al.  A quasi-dynamic capacity constrained frequency-based transit assignment model , 2008 .

[17]  C. Daganzo.  On the traffic assignment problem with flow dependent costs—II , 1977 .

[18]  Federico Malucelli,et al.  A Modeling Framework for Passenger Assignment on a Transport Network with Timetables , 1998, Transp. Sci..

[19]  Fumitaka Kurauchi,et al.  Capacity Constrained Transit Assignment with Common Lines , 2003, J. Math. Model. Algorithms.

[20]  Stefano Pallottino,et al.  Equilibrium traffic assignment for large scale transit networks , 1988 .

[21]  P. Robillard,et al.  Common Bus Lines , 1975 .

[22]  Roberto Cominetti,et al.  A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria , 2006 .

[23]  J. Dunn,et al.  Iterative construction of fixed points for multivalued operators of the monotone type , 1978 .

[24]  Esteve Codina Sancho,et al.  Applying Projection‐Based Methods to the Asymmetric Traffic Assignment Problem , 2015, Comput. Aided Civ. Infrastructure Eng..

[25]  Michael Florian,et al.  L’Optimisation Des Fréquences D’un Réseau De Transport En Commun Moyennement Congestionné , 2003 .

[26]  H. M. Zhang,et al.  Models and algorithms for the traffic assignment problem with link capacity constraints , 2004 .

[27]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[28]  Jia Hao Wu,et al.  A simplicial decomposition method for the transit equilibrium assignment problem , 1993, Ann. Oper. Res..

[29]  Siriphong Lawphongpanich,et al.  Schedule-based transit assignment model with travel strategies and capacity constraints , 2008 .

[30]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[31]  José R. Correa,et al.  Common-Lines and Passenger Assignment in Congested Transit Networks , 2001, Transp. Sci..

[32]  Michel Gendreau,et al.  Modeling Bus Stops in Transit Networks: A Survey and New Formulations , 2001, Transp. Sci..

[33]  J. Blum.  Multidimensional Stochastic Approximation Methods , 1954 .

[34]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[35]  S. Ishikawa.  Fixed points by a new iteration method , 1974 .

[36]  Enrique Fernández,et al.  Transit Assignment for Congested Public Transport Systems: An Equilibrium Model , 1993, Transp. Sci..