Numerical solution procedures for the morning commute problem

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.