Optimal Routing of Traffic Flows with Length Restrictions in Networks with Congestion

Abstract

Summary:When traffic flows are routed through a road network it is desirable to minimize the total road usage. Since a route guidance system can only recommend paths to the drivers, special care has to be taken not to route them over paths they perceive as too long. This leads in a simplified model to a nonlinear multicommodity flow problem with constraints on the available paths. In this article an algorithm for this problem is given, which combines the convex combinations algorithm by Frank and Wolfe with column generation and algorithms for the constrained shortest path problem. Computational results stemming from a cooperation with DaimlerChrysler are presented.

Smoothed penalty algorithms for optimization of nonlinear models

“…For a comparison of qualitative and quantitative properties we refer to [14]. In particular for routing problems in traffic flow networks [23,24,27] proposed efficient adapted algorithms for very large dimensions. Here, we use the traffic flow model problem just as a testcase for our general nonlinear optimization method.…”

“…We introduce the functional F : R n E → R measuring some property of the flow by This choice is motivated by the discussion in [23,27] and we recall the exact definition as given in [19]. Usually, F (q) measures the average time for passing the network and the family of functions τ e : R + → R + describes the average time for the flux q e to pass edge e. Another parameter is T > 0 which is the time horizon for the optimization.…”

CNOP - A Package for Constrained Network Optimization

“…Most of the time these are column generation methods. Examples are duty scheduling [BBKL00], traffic routing with congestion [JMS99] and scheduling switching engines [LZ00].…”

Cost-Based Filtering for Shorter Path Constraints

“…Examples range from route guidance [15] and duty scheduling in public transit [4] up to the scheduling of switching engines [19]. In [17], a general framework for constraint programming based column generation was developed that formalizes the use of optimization constraints in this context.…”