A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models

Muqing Du, Heqing Tan and Anthony Chen

European Journal of Operational Research, 2021, vol. 290, issue 3, 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: Transportation; Stochastic user equilibrium; Barzilai-Borwein step size; Path-based traffic assignment algorithm; Cross-nested logit (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:290:y:2021:i:3:p:982-999

DOI: 10.1016/j.ejor.2020.08.058

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