Numerical stability of path-based algorithms for traffic assignment

Perederieieva, Olga and Ehrgott, Matthias and Raith, Andrea and Wang, Judith Y. T. (2016) Numerical stability of path-based algorithms for traffic assignment. Optimization Methods and Software, 31 (1). pp. 53-67. ISSN 1055-6788

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In this paper we study numerical stability of path-based algorithms for the traffic assignment problem. This type of methods are based on decomposition of the original problem into smaller sub-problems which are optimised sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed fixed version of the algorithm on various benchmark instances.

Item Type:
Journal Article
Journal or Publication Title:
Optimization Methods and Software
Additional Information:
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Optimization Methods and Software on 03/06/2015, available online:
Uncontrolled Keywords:
?? traffic assignmentpath-based algorithmsconvergencenumerical stabilityfloating point arithmeticmathematics(all)control and optimizationsoftwareapplied mathematicsdiscipline-based research ??
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Deposited On:
19 Aug 2015 09:34
Last Modified:
18 Dec 2023 01:30