Numerical solution procedures for the morning commute problem

Authors:
Yu (Marco) Nie;Michael H. Zhang
Affiliations:
Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston 60208, United States;Department of Civil and Environmental Engineering, University of California, Davis, United States
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

This paper discusses solution techniques for the morning commute problem that is formulated as a discrete variational inequality (VI). Various heuristics have been proposed to solve this problem, mostly because the analytical properties of the path travel time function have not yet been well understood. Two groups of ''non-heuristic'' algorithms for general VIs, namely projection-type algorithms and ascent direction algorithms, were examined. In particular, a new ascent direction method is introduced and implemented with a heuristic line search procedure. The performance of these algorithms are compared on simple instances of the morning commute problem. The implications of numerical results are discussed.