IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v75y2020i2d10.1007_s10589-019-00160-3.html
   My bibliography  Save this article

Fast feasibility check of the multi-material vertical alignment problem in road design

Author

Listed:
  • Dominique Monnet

    (UBCO)

  • Warren Hare

    (UBCO)

  • Yves Lucet

    (UBCO)

Abstract

When building a road, it is critical to select a vertical alignment which ensures design and safety constraints. Finding such a vertical alignment is not necessarily a feasible problem, and the models describing it generally involve a large number of variables and constraints. This paper is dedicated to rapidly proving the feasibility or the infeasibility of a Mixed Integer Linear Program (MILP) modeling the vertical alignment problem. To do so, we take advantage of the particular structure of the MILP, and we prove that only a few of the MILP’s constraints determine the feasibility of the problem. In addition, we propose a method to build a feasible solution to the MILP that does not involve integer variables. This enables time saving to proving the feasibility of the vertical alignment problem and to find a feasible vertical alignment, as emphasized by numerical results. It is on average 75 times faster to prove the feasibility and 10 times faster to build a feasible solution.

Suggested Citation

  • Dominique Monnet & Warren Hare & Yves Lucet, 2020. "Fast feasibility check of the multi-material vertical alignment problem in road design," Computational Optimization and Applications, Springer, vol. 75(2), pages 515-536, March.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00160-3
    DOI: 10.1007/s10589-019-00160-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00160-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00160-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kim, Eungcheol & Jha, Manoj K. & Son, Bongsoo, 2005. "Improving the computational efficiency of highway alignment optimization models through a stepwise genetic algorithms approach," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 339-360, May.
    2. Jong, Jyh-Cherng & Schonfeld, Paul, 2003. "An evolutionary model for simultaneously optimizing three-dimensional highway alignments," Transportation Research Part B: Methodological, Elsevier, vol. 37(2), pages 107-128, February.
    3. Goh, C. J. & Chew, E. P. & Fwa, T. F., 1988. "Discrete and continuous models for computation of optimal vertical highway alignment," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 399-409, December.
    4. Moreb, Ahmad A., 1996. "Linear programming model for finding optimal roadway grades that minimize earthwork cost," European Journal of Operational Research, Elsevier, vol. 93(1), pages 148-154, August.
    5. Hare, Warren L. & Koch, Valentin R. & Lucet, Yves, 2011. "Models and algorithms to improve earthwork operations in road design using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 215(2), pages 470-480, December.
    6. Hare, Warren & Lucet, Yves & Rahman, Faisal, 2015. "A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction," European Journal of Operational Research, Elsevier, vol. 241(3), pages 631-641.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dominique Monnet & Warren Hare & Yves Lucet, 2022. "A successive relaxation algorithm to solve a MILP involving piecewise linear functions with application to road design," Computational Optimization and Applications, Springer, vol. 81(3), pages 741-767, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mukund Pratap Singh & Pitam Singh & Priyamvada Singh, 2019. "Fuzzy AHP-based multi-criteria decision-making analysis for route alignment planning using geographic information system (GIS)," Journal of Geographical Systems, Springer, vol. 21(3), pages 395-432, September.
    2. Hare, Warren & Lucet, Yves & Rahman, Faisal, 2015. "A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction," European Journal of Operational Research, Elsevier, vol. 241(3), pages 631-641.
    3. Dominique Monnet & Warren Hare & Yves Lucet, 2022. "A successive relaxation algorithm to solve a MILP involving piecewise linear functions with application to road design," Computational Optimization and Applications, Springer, vol. 81(3), pages 741-767, April.
    4. Salvatore Antonio Biancardo & Francesco Avella & Ernesto Di Lisa & Xinqiang Chen & Francesco Abbondati & Gianluca Dell’Acqua, 2021. "Multiobjective Railway Alignment Optimization Using Ballastless Track and Reduced Cross-Section in Tunnel," Sustainability, MDPI, vol. 13(19), pages 1-19, September.
    5. Pushak, Yasha & Hare, Warren & Lucet, Yves, 2016. "Multiple-path selection for new highway alignments using discrete algorithms," European Journal of Operational Research, Elsevier, vol. 248(2), pages 415-427.
    6. Eungcheol Kim & Myungseob (Edward) Kim & Gabrielle Delos & Tyler Clark, 2019. "Post-Construction Alignment Revision in Direct-Fixation Railroad Tracks," Sustainability, MDPI, vol. 11(21), pages 1-14, November.
    7. Kim, Eungcheol & Jha, Manoj K. & Son, Bongsoo, 2005. "Improving the computational efficiency of highway alignment optimization models through a stepwise genetic algorithms approach," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 339-360, May.
    8. Hare, Warren L. & Koch, Valentin R. & Lucet, Yves, 2011. "Models and algorithms to improve earthwork operations in road design using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 215(2), pages 470-480, December.
    9. Lee, Yusin & Cheng, Juey-Fu, 2001. "A model for calculating optimal vertical alignments of interchanges," Transportation Research Part B: Methodological, Elsevier, vol. 35(5), pages 423-445, June.
    10. Mohammad Mahanpoor & Saeed Monajjem & Vahid Balali, 2019. "Sustainable Highway Maintenance: Optimization of Existing Highway Vertical Alignment Considering Pavement Condition," Sustainability, MDPI, vol. 11(6), pages 1-20, March.
    11. Hüseyin Güden & Haldun Süral, 2017. "A polynomial algorithm for the earthwork allocation problem with borrow and waste site selection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(9), pages 1085-1093, September.
    12. Hao Pu & Jia Xie & Paul Schonfeld & Taoran Song & Wei Li & Jie Wang & Jianping Hu, 2021. "Railway Alignment Optimization in Mountainous Regions Considering Spatial Geological Hazards: A Sustainable Safety Perspective," Sustainability, MDPI, vol. 13(4), pages 1-22, February.
    13. García-Chan, N. & Alvarez-Vázquez, L.J. & Martínez, A. & Vázquez-Méndez, M.E., 2021. "Designing an ecologically optimized road corridor surrounding restricted urban areas: A mathematical methodology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 745-759.
    14. Jha, Manoj K. & Schonfeld, Paul, 2004. "A highway alignment optimization model using geographic information systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(6), pages 455-481, July.
    15. Benjamin Faber, 2014. "Trade Integration, Market Size, and Industrialization: Evidence from China's National Trunk Highway System," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1046-1070.
    16. Burdett, R.L. & Kozan, E., 2014. "An integrated approach for earthwork allocation, sequencing and routing," European Journal of Operational Research, Elsevier, vol. 238(3), pages 741-759.
    17. Yu, Shiwei & Zheng, Shuhong & Gao, Shiwei & Yang, Juan, 2017. "A multi-objective decision model for investment in energy savings and emission reductions in coal mining," European Journal of Operational Research, Elsevier, vol. 260(1), pages 335-347.
    18. Mauro Dell’Amico & Guenther Fuellerer & Gerhard Höfinger & Manuel Iori & Stefano Novellani, 2016. "A Decision Support System for Highway Construction: The Autostrada Pedemontana Lombarda," Interfaces, INFORMS, vol. 46(3), pages 245-263, April.
    19. Wu, Fei & Schonfeld, Paul, 2022. "Optimized two-directional phased development of a rail transit line," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 424-447.
    20. Zhong, Tao & Young, Rhonda, 2010. "Multiple Choice Knapsack Problem: Example of planning choice in transportation," Evaluation and Program Planning, Elsevier, vol. 33(2), pages 128-137, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00160-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.