An efficient implementation of origin-destination demand adjustment problem using column generation

초록

In this paper, we propose an efficient implementation scheme for the origin-destination matrix adjustment problem (DAP). DAP is usually formulated as a bilevel optimization problem where the upper level problem is a generalized least squares problem with nonnegativity constraints and the lower level problem is formulated as a fixed demand traffic assignment problem. Typical iteration of the bilevel programming approach is that OD demand produced from the upper level is used as input to the lower level and the lower level updates the optimal link flows for the upper level. The key input data for the bilevel optimization programming approach is the link proportion parameter that is the proportion of OD demand in the current link flow. In this research, we show that a simple projected gradient approach combined with the column generation for the lower level problem can produce link proportion explicitly and converges fast using the second derivative information. Another benefit of our approach is that it provides a good feasible initial solution to the lower level problem. Using Sioux Falls network, Winnipeg network, and a large scale network having 1,859 nodes, 4,776 links, and 15,582 OD pairs, we demonstrate our algorithm. Possible extension to the real time application of our approach is introduced.