Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

Zhiyuan Liu, Shuaian Wang, Bojian Zhou, Qixiu Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

79 Citations (Scopus)


After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.
Original languageEnglish
Pages (from-to)58-72
Number of pages15
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - 1 Jun 2017


  • Congestion pricing
  • Day-to-day dynamics
  • Distance-based pricing
  • Minimax regret model
  • Robust optimization

ASJC Scopus subject areas

  • Automotive Engineering
  • Transportation
  • Computer Science Applications
  • Management Science and Operations Research


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