A Class of Efficient Algorithms for the Bi-Level Demand Adjustment Problems in Congested Traffic Networks

Abstract

This paper studies a class of gradient-descent heuristic algorithms for the bi-level demand adjustment problem (DAP), which seeks to adjust origin-destination (OD) matrices based on observed link flows in congested transportation networks. We first present a general gradient-descent solution framework for the bi-level DAP and then examine and further develop its two building blocks, namely, the gradient approximation and stepsize calculation. This paper presents two gradient approximation and four stepsize calculation methods, of which two stepsize methods are newly developed. Similarities and differences between these algorithms, as well as the relevant implementation issues are discussed in great detail. The numerical results show that algorithms employing the new stepsize calculation strategies consistently outperform existing algorithms in terms of both computational precision and efficiency.