A self-adaptive Armijo stepsize strategy with application to traffic assignment models and algorithms

Abstract

Stepsize determination is an important component of algorithms for solving several mathematical formulations. In this article, a self-adaptive Armijo strategy is proposed to determine an acceptable stepsize in a more efficient manner. Instead of using a fixed initial stepsize in the original Armijo strategy, the proposed strategy allows the starting stepsize per iteration to be self-adaptive. Both the starting stepsize and the acceptable stepsize are thus allowed to decrease as well as increase by making use of the information derived from previous iterations. This strategy is then applied to three well-known algorithms for solving three traffic equilibrium assignment problems with different complexity. Specifically, we implement this self-adaptive strategy in the link-based Frank–Wolfe algorithm, the route-based disaggregate simplicial decomposition algorithm and the route-based gradient projection algorithm for solving the classical user equilibrium problem, the multinomial logit-based stochastic user equilibrium (MNL SUE) and the congestion-based C-logit SUE problem, respectively. Some numerical results are also provided to demonstrate the efficiency and applicability of the proposed self-adaptive Armijo stepsize strategy implemented in traffic assignment algorithms.

Keywords:

• Armijo
• stepsize strategy
• self-adaptive
• traffic assignment

Acknowledgements

The authors are grateful to Prof. S.C. Wong (Editor of Transportmetrica) and three referees for providing useful comments and suggestions for improving the quality and clarity of this article. The work of the first author was supported by a CAREER grant from the National Science Foundation of the United States (CMS-0134161), and a Oriental Scholar Professorship Program sponsored by the Shanghai Ministry of Education in China to Tongji University, and the work of the second author was supported by the China Scholarship Council as a visiting PhD student from Southeast University in China to Utah State University in the United States.