A Hybrid Cross Entropy Algorithm for Solving Dynamic Transit Network Design Problem

This paper proposes a hybrid multiagent learning algorithm for solving the dynamic simulation-based bilevel network design problem. The objective is to determine the op-timal frequency of a multimodal transit network, which minimizes total users' travel cost and operation cost of transit lines. The problem is formulated as a bilevel programming problem with equilibrium constraints describing non-cooperative Nash equilibrium in a dynamic simulation-based transit assignment context. A hybrid algorithm combing the cross entropy multiagent learning algorithm and Hooke-Jeeves algorithm is proposed. Computational results are provided on the Sioux Falls network to illustrate the perform-ance of the proposed algorithm.

[1]  Jean-Patrick Lebacque,et al.  A Cross Entropy Based Multi-Agent Approach to Traffic Assignment Problems , 2009 .

[2]  Andreas Voellmy,et al.  Large-scale multi-agent transportation simulations , 2002 .

[3]  Hani S. Mahmassani,et al.  Dynamic models of commuter behavior: Experimental investigation and application to the analysis of planned traffic disruptions , 1990 .

[4]  Patrice Marcotte,et al.  Network design problem with congestion effects: A case of bilevel programming , 1983, Math. Program..

[5]  Shing Chung Josh Wong,et al.  A predictive dynamic traffic assignment model in congested capacity-constrained road networks , 2000 .

[6]  Michael Florian,et al.  Optimizing frequencies in a transit network: a nonlinear bi-level programming approach , 1995 .

[7]  Michael Florian,et al.  Application of a simulation-based dynamic traffic assignment model , 2008, Eur. J. Oper. Res..

[8]  Warrren B Powell,et al.  The Convergence of Equilibrium Algorithms with Predetermined Step Sizes , 1982 .

[9]  Hani S. Mahmassani,et al.  Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem , 2009 .

[10]  Larry J. LeBlanc,et al.  Transit system network design , 1988 .

[11]  Huijun Sun,et al.  A continuous equilibrium network design model and algorithm for transit systems , 2004 .

[12]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[13]  Larry J. LeBlanc,et al.  CONTINUOUS EQUILIBRIUM NETWORK DESIGN MODELS , 1979 .

[14]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[15]  Mike Smith,et al.  A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks , 1993 .

[16]  Kenneth A. Small,et al.  THE SCHEDULING OF CONSUMER ACTIVITIES: WORK TRIPS , 1982 .

[17]  Shing Chung Josh Wong,et al.  A dynamic schedule-based model for congested transit networks , 2004 .