Computation and application of the paired combinatorial logit stochastic user equilibrium problem

The paired combinatorial logit (PCL) model is one of the recent extended logit models adapted to resolve the overlapping problem in the route choice problem, while keeping the analytical tractability of the logit choice probability function. However, the development of efficient algorithms for solving the PCL model under congested and realistic networks is quite challenging, since it has large-dimensional solution variables as well as a complex objective function. In this paper, we examine the computation and application of the PCL stochastic user equilibrium (SUE) problem under congested and realistic networks. Specifically, we develop an improved path-based partial linearization algorithm for solving the PCL SUE problem by incorporating recent advances in line search strategies to enhance the computational efficiency required to determine a suitable stepsize that guarantees convergence. A real network in the city of Winnipeg is applied to examine the computational efficiency of the proposed algorithm and the robustness of various line search strategies. In addition, in order to acquire the practical implications of the PCL SUE model, we investigate the effectiveness of how the PCL model handles the effects of congestion, stochasticity, and similarity in comparison with the multinomial logit stochastic traffic equilibrium problem and the deterministic traffic equilibrium problem.

[1]  P. Hughes,et al.  A PROBIT-BASED STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL , 1997 .

[2]  E. Cascetta,et al.  STOCHASTIC USER EQUILIBRIUM ASSIGNMENT WITH EXPLICIT PATH ENUMERATION: COMPARISON OF MODELS AND ALGORITHMS , 1997 .

[3]  M. Bell.  Alternatives to Dial's logit assignment algorithm , 1995 .

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

[5]  Xiangdong Xu,et al.  Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models , 2012 .

[6]  C. Chu.  A PAIRED COMBINATORIAL LOGIT MODEL FOR TRAVEL DEMAND ANALYSIS , 1989 .

[7]  Michael Patriksson,et al.  An algorithm for the stochastic user equilibrium problem , 1996 .

[8]  C. Fisk.  Some developments in equilibrium traffic assignment , 1980 .

[9]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[10]  S. Bekhor,et al.  Route Choice Models Used in the Stochastic User Equilibrium Problem: A Review , 2004 .

[11]  Wilfred W. Recker,et al.  Improved Path Flow Estimator for Origin-Destination Trip Tables , 2005 .

[12]  Mike Maher,et al.  Algorithms for logit-based stochastic user equilibrium assignment , 1998 .

[13]  Anthony Chen,et al.  C-logit stochastic user equilibrium model: formulations and solution algorithm , 2012 .

[14]  Y. She.  Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods , 1985 .

[15]  Michael G.H. Bell,et al.  A STOCHASTIC USER EQUILIBRIUM PATH FLOW ESTIMATOR , 1997 .

[16]  D. Bertsekas.  On the Goldstein-Levitin-Polyak gradient projection method , 1974, CDC 1974.

[17]  Michael Patriksson,et al.  The Traffic Assignment Problem: Models and Methods , 2015 .

[18]  Anthony Chen,et al.  L-Norm Path Flow Estimator for Handling Traffic Count Inconsistencies: Formulation and Solution Algorithm , 2010 .

[19]  Hai-Jun Huang,et al.  A study on logit assignment which excludes all cyclic flows , 1998 .

[20]  Anthony Chen,et al.  Examining the Quality of Synthetic Origin-Destination Trip Table Estimated by Path Flow Estimator , 2005 .

[21]  Carlos F. Daganzo,et al.  On Stochastic Models of Traffic Assignment , 1977 .

[22]  Shlomo Bekhor,et al.  Path-Based Algorithms to Solve C-Logit Stochastic User Equilibrium Assignment Problem , 2012 .

[23]  F. Leurent.  Curbing the computational difficulty of the logit equilibrium assignment model , 1997 .

[24]  Shlomo Bekhor,et al.  EFFECTS OF CHOICE SET SIZE AND ROUTE CHOICE MODELS ON PATH-BASED TRAFFIC ASSIGNMENT , 2008 .

[25]  Anthony Chen,et al.  ADAPTATION OF THE PAIRED COMBINATORIAL LOGIT MODEL TO THE ROUTE CHOICE PROBLEM , 2005 .

[26]  D. M. Deighton,et al.  Computers in Operations Research , 1977, Aust. Comput. J..

[27]  J. Wielinski,et al.  Annual Meeting of the Transportation Research Board , 2010 .

[28]  Mike Maher,et al.  ALGORITHMS FOR SOLVING THE PROBIT PATH-BASED STOCHASTIC USER EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM WITH ONE OR MORE USER CLASSES , 2002 .

[29]  Warren B. Powell,et al.  An algorithm for the equilibrium assignment problem with random link times , 1982, Networks.

[30]  Anthony Chen,et al.  Norm approximation method for handling traffic count inconsistencies in path flow estimator , 2009 .

[31]  Shlomo Bekhor,et al.  A Path-Based Algorithm for the Cross-Nested Logit Stochastic User Equilibrium Traffic Assignment , 2009, Comput. Aided Civ. Infrastructure Eng..

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

[33]  M G H Bell.  STOCHASTIC USER EQUILIBRIUM ASSIGNMENT AND ITERATIVE BALANCING. , 1993 .

[34]  Zhaowang Ji,et al.  Solving the Overlapping Problem in Route Choice with Paired Combinatorial Logit Model , 2003 .

[35]  A. Alfa,et al.  Algorithms for solving fisk's stochastic traffic assignment model , 1991 .

[36]  Xiangdong Xu,et al.  A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem , 2012, Comput. Oper. Res..

[37]  Robert B. Dial,et al.  A PROBABILISTIC MULTIPATH TRAFFIC ASSIGNMENT MODEL WHICH OBVIATES PATH ENUMERATION. IN: THE AUTOMOBILE , 1971 .

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

[39]  Shlomo Bekhor,et al.  FORMULATIONS OF EXTENDED LOGIT STOCHASTIC USER EQUILIBRIUM ASSIGNMENTS , 1999 .

[40]  Carlo G. Prato,et al.  Route choice modeling: past, present and future research directions , 2009 .

[41]  M J Maher.  SAM - A STOCHASTIC ASSIGNMENT MODEL , 1992 .

[42]  F. Koppelman,et al.  The paired combinatorial logit model: properties, estimation and application , 2000 .

[43]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .