Continuous Network Design Using Partial Linearized Subgradient Methods

Abstract

Although demand management has shown to be a vital tool in managing congestion, many metropolitan planning organizations (MPOs) and departments of transportation (DOTs) still pursue network modification and capacity increase as a congestion relief and a mitigation measure. The network design problem (NDP) still has, therefore, an essential and significant role in shaping and sizing urban transportation networks. The literature has traditionally treated the NDP as a bi-level mathematical programming problem or a mathematical program with equilibrium constraints (MPEC). In the bi-level optimization setting, the problem is approached as a leader-follower problem in which the lower level is a user equilibrium (UE) assignment problem as the follower, and the upper level is the network sizing problem as the leader problem. NDP has long been known as a challenging problem, and many solution algorithms have been proposed to solve it. This study proposed an efficient solution algorithm for the continuous network design problem (CNDP). The solution algorithm has been shown empirically to solve the CNDP in a shorter time using partial linearized subgradient methods. The proposed method was applied to a small network that was traditionally used to evaluate the performance of solution algorithms versus Braess’s paradox. It was then applied to the Sioux Falls network as a well-known benchmark network to compare the results with previous studies. The proposed method has been shown to run much faster than all the previous studies reviewed in this paper with minimal degradation of accuracy (0.52% lower than the best solution).