Slope-Based Multipath Flow Update Algorithm for Static User Equilibrium Traffic Assignment Problem

Abstract

This paper presents a new algorithm for solving the static traffic assignment problem that operates in the space of path flows. The algorithm uses a sequential equilibration technique by which origin–destination (O-D) pairs are equilibrated one at a time iteratively. This slope-based multipath algorithm (SMPA) inherits some insights from the gradient projection (GP) algorithm of Jayakrishnan et al., Dial's Algorithm B, and the recent GP method of Florian et al. However, the flow update mechanism of the SMPA is new, with different search directions for paths with higher and lower costs than the average cost for an O-D pair. It uses the slopes of cost functions in such a way as to bring the costs of different paths closer and enable faster convergence. Further, it does not require a line search for finding the move size. Computational experiments using the Sioux Falls, South Dakota, and Borman Corridor, Indiana, networks provide insights into the SMPA and compare its performance relative to the GP algorithm of Florian et al. The results illustrate that the SMPA has a superior rate of convergence.

Slope-Based Path Shift Propensity Algorithm for the Static Traffic Assignment Problem

“…The computational experiments consider the two versions of SMPA. The first version (labeled SMPA) updates the path set and equilibrates the O-D pairs based on the sequential manner (for details see Kumar and Peeta, 2010). The second version (labeled SMPA-hybrid) was devised by Kumar and Peeta (2013) based on the insights from the experimental work done by Kumar et al (2012) The results of the computational experiment carried out for the Anaheim network are presented in Fig.…”

“…This algorithm uses the average cost for finding the search direction and does not require the second derivative information. Recently, Kumar and Peeta (2010) developed an algorithm labeled the slope-based multi-path algorithm (SMPA) that uses the slope of the cost function efficiently to shift f lows from the set of costlier paths to the set of cheaper paths simultaneously and seeks to move path costs towards the average cost for an O-D pair at each iteration to achieve faster convergence.…”

“…Second, it does not take into account the sensitivity of path costs with respect to flow. Kumar and Peeta (2010) have shown that the efficient use of the slopes of the cost function and the transfer of f lows from multiple expensive paths to multiple cheaper paths in the SMPA algorithm lead to faster convergence. The SPSA is derived by inheriting insights from the SMPA and social pressure algorithms in the flow update process.…”

“…This issue can be circumvented through approaches that ensure smoother convergence. Kumar and Peeta (2010) developed a path-based algorithm labeled the slope-based multi-path algorithm (SMPA) for the UETAP, aimed at achieving smoother and faster convergence. SMPA uses the sensitivity of the path cost with respect to f low in the form of the slopes of the path cost functions, avoids the line search by using a constant value of scaling factor and updates the flows of paths between an O-D pair simultaneously to achieve smoother and faster convergence.…”

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

“…Bekhor and Toledo (2005)), the Path Equilibrator (Dafermos and Sparrow, 1969), the Disaggregate Simplicial Decomposition (DSD, Larsson and Patriksson, 1992), the Gradient Projection (GP, Jayakrishnan et al, 1994;Chen et al, 2002b), the Social Pressure (Kupiszewska and van Vliet, 1998), the Projected Gradient (Florian et al, 2009) and the slope-based multipath flow update (Kumar and Peeta, 2010) methods. Components of these DUE solution algorithms may be modified to fit into Step 2 by applying them to the transformed costs rather than the actual costs in the inner direction finding step.…”