Optimal Toll Design in Dynamic Traffic Networks using a Pattern Search Approximation Algorithm

Ties Brands, Eric C. van Berkum, Dirk Hendrik van Amelsfort

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


    The design of an optimal road pricing scheme is not a trivial problem. Following the Dutch government's kilometer charge plans, this paper focuses on the optimization of link based toll levels differentiated in space and time. The optimal toll level design problem is formulated as a bi-level mathematical program. In the upper level we minimize an object function, e.g. the average travel time in the network, using a fixed number of price categories. At the lower level a dynamic traffic assignment model is used to determine the effects of differentiated road pricing schemes on the traffic system. Focus of the paper is on the upper-level where optimal toll levels are approximated. In the optimization procedure different variants of a pattern search algorithm are tested in a case study. Inspection of the solution space shows that many local minima exist, so the selection of the initial solution becomes important. In the case study however it appears that in all local minima the value of the objective function is almost the same, indicating the fact that many different toll schemes result in the same average travel time. The case study is also used to test the performance of the different variants of the pattern search algorithm. It appears that it is beneficial to change more variables at a time and to use a memory to remember where improvement of the objective function has been made.
    Original languageEnglish
    Title of host publication88th TRB Annual Meeting, 11-15 January 2009, Washington DC, USA.
    PublisherTransportation Research Board (TRB)
    Publication statusPublished - 11 Jan 2009
    Event88th Transportation Research Board (TRB) Annual Meeting 2009 - Washington, United States
    Duration: 11 Jan 200915 Jan 2009
    Conference number: 88


    Conference88th Transportation Research Board (TRB) Annual Meeting 2009
    Country/TerritoryUnited States


    • METIS-249577


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