An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands

The traffic assignment problem (TAP) with elastic demands can be formulated as an optimization problem, the objective of which is the sum of a congestion function and a disutility function. We propose to use a variant of the analytic center cutting plane method to solve this problem. We test the method on TAP instances with the Bureau of Public Roads congestion function and different demand functions (constant elasticity and linear). The results of the numerical experiments show that it is possible to solve large instances with high accuracy.

[1]  Larry Joseph Leblanc,et al.  MATHEMATICAL PROGRAMMING ALGORITHMS FOR LARGE SCALE NETWORK EQUILIBRIUM AND NETWORK DESIGN PROBLEMS , 1973 .

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  George Karakostas,et al.  Edge Pricing of Multicommodity Networks for Selfish Users with Elastic Demands , 2006, COCOON.

[4]  Larry J. LeBlanc,et al.  A new proximal decomposition algorithm for routing in telecommunication networks , 1998 .

[5]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[6]  Anna Nagurney,et al.  NETWORK EQUILIBRIA AND DISEQUILIBRIA. , 1998 .

[7]  J. Goffin,et al.  Decomposition and nondifferentiable optimization with the projective algorithm , 1992 .

[8]  Jean-Philippe Vial,et al.  Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM , 2006, Oper. Res..

[9]  Philippe Mahey,et al.  Multicommodity Network Expansion under Elastic Demands , 2001 .

[10]  Jean-Philippe Vial,et al.  On Improvements to the Analytic Center Cutting Plane Method , 1998, Comput. Optim. Appl..

[11]  Abdel Lisser,et al.  Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems , 2002, Oper. Res..

[12]  Nathan H. Gartner,et al.  Optimal traffic assignment with elastic demands: A Review , 1980 .

[13]  M. Fukushima.  On the dual approach to the traffic assignment problem , 1984 .

[14]  Philippe Mahey,et al.  A Survey of Algorithms for Convex Multicommodity Flow Problems , 2000 .

[15]  Robert B. Dial,et al.  A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration , 2006 .

[16]  Suzanne P. Evans,et al.  DERIVATION AND ANALYSIS OF SOME MODELS FOR COMBINING TRIP DISTRIBUTION AND ASSIGNMENT , 1976 .

[17]  Jean-Philippe Vial,et al.  ACCPM with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems , 2009, Math. Program..

[18]  M. Patriksson,et al.  Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design , 2007 .

[19]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[20]  Di Yuan,et al.  An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing , 2004, Comput. Optim. Appl..

[21]  Giorgio Gallo,et al.  A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems , 1999, INFORMS J. Comput..

[22]  Michael Florian,et al.  A Method for Computing Network Equilibrium with Elastic Demands , 1974 .

[23]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[24]  M. Patriksson,et al.  An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems , 1995 .

[25]  J. E. Kelley,et al.  The Cutting-Plane Method for Solving Convex Programs , 1960 .

[26]  Nathan H. Gartner,et al.  Optimal Traffic Assignment with Elastic Demands: A Review Part I. Analysis Framework , 1980 .

[27]  Jacek Gondzio,et al.  Solving nonlinear multicommodity flow problems by the analytic center cutting plane method , 1997, Math. Program..

[28]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[29]  Larry J. LeBlanc,et al.  Efficient Algorithms for Solving Elastic Demand Traffic Assignment Problems and Mode Split-Assignment Problems , 1981 .

[30]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[31]  Jordi Castro,et al.  Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem , 2009, Comput. Optim. Appl..

[32]  Yurii Nesterov,et al.  Stable Traffic Equilibria: Properties and Applications , 2000 .

[33]  D. Hearn,et al.  A Toll Pricing Framework for Traffic Assignment Problems with Elastic Demand , 2002 .

[34]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .