Global Optimum of the Linearized Network Design Problem with Equilibrium Flows

The road network design problem, typically formulated as a bi-level program or a mathematical program with equilibrium constraints, is generally non-convex. The non-convexity stems from both the traffic assignment equilibrium conditions and the non-linear travel time function. In this study, we formulate the network design problem as a single-level optimization problem with equilibrium constraints, and then we transform the equilibrium constraints into a set of mixed-integer constraints and linearize the travel time function. The final result is that we cast the network design problem with equilibrium flows into a mixed-integer linear program, whose solution possesses the desirable property of global optimality, subject to the resolution of the linearization scheme adopted.

[1]  Toshihide Ibaraki,et al.  Optimal scheduling policies in time sharing service systems , 1995 .

[2]  Terry L. Friesz,et al.  Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem , 1987, Transp. Sci..

[3]  Hong Kam Lo,et al.  Reformulating the traffic equilibrium problem via a smooth gap function , 2000 .

[4]  Hong Kam Lo,et al.  Traffic equilibrium problem with route-specific costs: formulation and algorithms , 2000 .

[5]  Michael Athans,et al.  HYBRID OPTIMIZATION IN URBAN TRAFFIC NETWORKS , 1979 .

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

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

[8]  Hai Yang,et al.  An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem , 2001 .

[9]  Hai Yang,et al.  Sensitivity analysis for the elastic-demand network equilibrium problem with applications , 1997 .

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

[11]  Yang Hai,et al.  Sensitivity analysis for queuing equilibrium network flow and its application to traffic control , 1995 .

[12]  Terry L. Friesz,et al.  A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints , 1992, Transp. Sci..

[13]  Hong Kam Lo,et al.  A novel traffic signal control formulation , 1999 .

[14]  Suh-Wen Chiou,et al.  Bilevel programming for the continuous transport network design problem , 2005 .

[15]  Hong K. Lo,et al.  A Cell-Based Traffic Control Formulation: Strategies and Benefits of Dynamic Timing Plans , 2001, Transp. Sci..