Cost scaling based successive approximation algorithm for the traffic assignment problem

Hong Zheng and Srinivas Peeta

Transportation Research Part B: Methodological, 2014, vol. 68, issue C, 17-30

Abstract: This paper presents a cost scaling based successive approximation algorithm, called ε-BA (ε-optimal bush algorithm), to solve the user equilibrium traffic assignment problem by successively refining ε-optimal flows. As ε reduces to zero, the user equilibrium solution is reached. The proposed method is a variant of bush-based algorithms, and also a variant of the min-mean cycle algorithm to solve the min-cost flow by successive approximation. In ε-BA, the restricted master problem, implying traffic equilibration restricted on a bush, is solved to ε-optimality by cost scaling before bush reconstruction. We show that ε-BA can reduce the number of flow operations substantially in contrast to Dial’s Algorithm B, as the former operates flows on a set of deliberately selected cycles whose mean values are sufficiently small. Further, the bushes can be constructed effectively even if the restricted master problem is not solved to a high level of convergence, by leveraging the ε-optimality condition. As a result, the algorithm can solve a highly precise solution with faster convergence on large-scale networks compared to our implementation of Dial’s Algorithm B.

Keywords: Traffic assignment; Successive approximation; Cost scaling; Min-mean cycle; Bush (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.trb.2014.05.016

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