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A dual decomposition method for sector capacity constrained traffic flow optimization

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  • Sun, D.
  • Clinet, A.
  • Bayen, A.M.

Abstract

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.

Suggested Citation

  • Sun, D. & Clinet, A. & Bayen, A.M., 2011. "A dual decomposition method for sector capacity constrained traffic flow optimization," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 880-902, July.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:6:p:880-902
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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. Gosling, Geoffrey D., 1999. "Aviation System Performance Measures," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2xw9204x, Institute of Transportation Studies, UC Berkeley.
    3. Hanif D. Sherali & Raymond W. Staats & Antonio A. Trani, 2006. "An Airspace-Planning and Collaborative Decision-Making Model: Part II---Cost Model, Data Considerations, and Computations," Transportation Science, INFORMS, vol. 40(2), pages 147-164, May.
    4. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    5. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    6. Lisa Navazio & Giorgio Romanin-Jacur, 1998. "The Multiple Connections Multi-Airport Ground Holding Problem: Models and Algorithms," Transportation Science, INFORMS, vol. 32(3), pages 268-276, August.
    7. Mostafa Terrab & Amedeo R. Odoni, 1993. "Strategic Flow Management for Air Traffic Control," Operations Research, INFORMS, vol. 41(1), pages 138-152, February.
    8. Dimitris Bertsimas & Sarah Stock Patterson, 1998. "The Air Traffic Flow Management Problem with Enroute Capacities," Operations Research, INFORMS, vol. 46(3), pages 406-422, June.
    9. Peter B. Vranas & Dimitris J. Bertsimas & Amedeo R. Odoni, 1994. "The Multi-Airport Ground-Holding Problem in Air Traffic Control," Operations Research, INFORMS, vol. 42(2), pages 249-261, April.
    10. Hanif D. Sherali & J. Cole Smith & Antonio A. Trani, 2002. "An Airspace Planning Model for Selecting Flight-plans Under Workload, Safety, and Equity Considerations," Transportation Science, INFORMS, vol. 36(4), pages 378-397, November.
    11. Michael O. Ball & Robert Hoffman & Avijit Mukherjee, 2010. "Ground Delay Program Planning Under Uncertainty Based on the Ration-by-Distance Principle," Transportation Science, INFORMS, vol. 44(1), pages 1-14, February.
    12. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    13. Thomas W. M. Vossen & Michael O. Ball, 2006. "Slot Trading Opportunities in Collaborative Ground Delay Programs," Transportation Science, INFORMS, vol. 40(1), pages 29-43, February.
    14. Guglielmo Lulli & Amedeo Odoni, 2007. "The European Air Traffic Flow Management Problem," Transportation Science, INFORMS, vol. 41(4), pages 431-443, November.
    15. Robert Hoffman & Michael O. Ball, 2000. "A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints," Operations Research, INFORMS, vol. 48(4), pages 578-590, August.
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    Cited by:

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    3. Wei, P. & Cao, Y. & Sun, D., 2013. "Total unimodularity and decomposition method for large-scale air traffic cell transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 1-16.
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    5. Xiao, Mingming & Cai, Kaiquan & Abbass, Hussein A., 2018. "Hybridized encoding for evolutionary multi-objective optimization of air traffic network flow: A case study on China," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 35-55.

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