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

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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
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    References listed on IDEAS

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    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.
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    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.
    2. Qi, Weiwei & Zou, Zhenyu & Ruan, Lianjie & Wu, Jiabin, 2024. "Method for designing fuel-efficient highway longitudinal slopes for intelligent vehicles in eco-driving scenarios," Applied Energy, Elsevier, vol. 368(C).

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