Joint optimization for area traffic control and network flow

A joint optimization problem for solving area traffic control and network flow is investigated. A bilevel programming is used to formulate this joint optimization problem where the network flow following Wardrop's principles can be obtained by solving traffic assignment problems. In this paper, we present a solution approach for jointly optimizing the area traffic control and network flow on the basis of a newly presented algorithm for concurrent flow (Comput. Oper. Res. (2004) in press). We propose three kinds of formulations for this joint optimization problem and present a gradient-based method to effectively solve this problem via a mixture of locally optimal search and global search heuristic where a near global optimum may be found. Numerical comparisons are made for the values of performance index achieved by the joint optimization problem with system optimal flow and those did by equilibrium flow at various sets of initial signal settings. Substantially good results have demonstrated the robustness of the proposed algorithm in solving both system optimal and user equilibrium flow for the joint optimization problem at large-scale networks.

[1]  D I Robertson,et al.  TRANSYT: A TRAFFIC NETWORK STUDY TOOL , 1969 .

[2]  Terry L. Friesz,et al.  Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints , 1990, Math. Program..

[3]  Nathan H. Gartner,et al.  Area Traffic Control and Network Equilibrium , 1976 .

[4]  Terry L. Friesz,et al.  Sensitivity Analysis for Equilibrium Network Flow , 1988, Transp. Sci..

[5]  J. Bard,et al.  Nondifferentiable and Two-Level Mathematical Programming , 1996 .

[6]  Michal Kočvara,et al.  Nonsmooth approach to optimization problems with equilibrium constraints : theory, applications, and numerical results , 1998 .

[7]  P. Marcotte.  Network Optimization with Continuous Control Parameters , 1983 .

[8]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[9]  Suh-Wen Chiou.  TRANSYT derivatives for area traffic control optimisation with network equilibrium flows , 2003 .

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

[11]  Tschangho John Kim,et al.  Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review , 1992, Ann. Oper. Res..

[12]  R E Allsop,et al.  TRAFFIC IN A SIGNAL-CONTROLLED ROAD NETWORK: AN EXAMPLE OF DIFFERENT SIGNAL TIMINGS INCLUDING DIFFERENT ROUTEING , 1977 .

[13]  Suh-Wen Chiou,et al.  Optimization of Area Traffic Control for Equilibrium Network Flows , 1999, Transp. Sci..

[14]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

[15]  Benjamin Heydecker.  A decomposition approach for signal optimisation in road networks , 1996 .

[16]  Hai Yang,et al.  Transport bilevel programming problems: recent methodological advances , 2001 .

[17]  Shing Chung Josh Wong,et al.  Group-based optimisation of signal timings using the TRANSYT traffic model , 1996 .

[18]  Hai Yang,et al.  Models and algorithms for road network design: a review and some new developments , 1998 .

[19]  J. Clegg,et al.  Bilevel programming applied to optimising urban transportation , 2001 .

[20]  Mike Smith,et al.  Bilevel And Other Modelling Approaches to Urban Traffic Management and Control , 1998 .

[21]  R E Allsop.  SOME POSSIBILITIES FOR USING TRAFFIC CONTROL TO INFLUENCE TRIP DISTRIBUTION AND ROUTE CHOICE , 1974 .

[22]  Michael Florian,et al.  Traffic Equilibrium Methods , 1976 .

[23]  Patrice Marcotte,et al.  Exact and inexact penalty methods for the generalized bilevel programming problem , 1996, Math. Program..

[24]  Mike Smith,et al.  Traffic control and route-choice; a simple example , 1979 .

[25]  Shing Chung Josh Wong,et al.  Derivatives of the performance index for the traffic model from TRANSYT , 1995 .

[26]  Patrice Marcotte,et al.  Efficient implementation of heuristics for the continuous network design problem , 1992, Ann. Oper. Res..

[27]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

[28]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[29]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[30]  Suh-Wen Chiou.  A combinatorial approximation algorithm for concurrent flow problem and its application , 2005, Comput. Oper. Res..

[31]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .