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Title: A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models
Authors: Du, M
Tan, H
Chen, A 
Issue Date: 1-May-2021
Source: European journal of operational research, 1 May 2021, v. 290, no. 3, p. 982-999
Abstract: Step size determination (also known as line search) is an important component in effective algorithmic development for solving the traffic assignment problem. In this paper, we explore a novel step size determination scheme, the Barzilai-Borwein (BB) step size, and adapt it for solving the stochastic user equilibrium (SUE) problem. The BB step size is a special step size determination scheme incorporated into the gradient method to enhance its computational efficiency. It is motivated by the Newton-type methods, but it does not need to explicitly compute the second-order derivative. We apply the BB step size in a path-based traffic assignment algorithm to solve two well-known SUE models: the multinomial logit (MNL) and cross-nested logit (CNL) SUE models. Numerical experiments are conducted on two real transportation networks to demonstrate the computational efficiency and robustness of the BB step size. The results show that the BB step size outperforms the current step size strategies, i.e., the Armijo rule and the self-regulated averaging scheme.
Keywords: Barzilai-Borwein step size
Cross-nested logit
Path-based traffic assignment algorithm
Stochastic user equilibrium
Publisher: Elsevier
Journal: European journal of operational research 
ISSN: 0377-2217
EISSN: 1872-6860
DOI: 10.1016/j.ejor.2020.08.058
Rights: © 2020 Elsevier B.V. All rights reserved.
© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
The following publication Du, M., Tan, H., & Chen, A. (2021). A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models. European Journal of Operational Research, 290(3), 982-999 is available at
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