Technical Papers
Nov 25, 2021

Robust Optimization Method for Mountain Railway Alignments Considering Preference Uncertainty for Costs and Seismic Risks

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8, Issue 1

Abstract

Railways are vital infrastructures whose design is complex and time-consuming. In addition to multiple conflicting objectives and highly-constrained search spaces, their design also faces great uncertainties. The aim of this study is to optimize railway alignments considering decision-makers’ preference uncertainty for multiple objectives, which can influence the alignment determination macroscopically and fundamentally. First, a multiobjective model is built by integrating costs (including construction and operation costs) and seismic risks (including direct and indirect losses) for mountain railway optimization. To solve this model, a particle swarm algorithm is improved by incorporating a multicriteria tournament decision (MTD). Then, a robust optimization MTD (RO-MTD) method is developed to find cost-risk tradeoffs by addressing the uncertainty of decision-makers’ preferences. The major steps of the RO-MTD include (1) treating uncertain preferences as variables, (2) sampling the uncertain space of preferences, (3) analyzing all possible preference scenarios, and (4) integrating those analyses to achieve a robust evaluation. Finally, the preceding approaches are applied to a complicated real-world case. By comparing the RO-MTD and MTD as well as the computer-generated alignment and the best manually-designed one, the effectiveness of the proposed method is confirmed.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions. All design data for the case study presented here, such as the railway location, manually-design solution, and topographic and seismic information of the study area, are provided by the China Railway Eryuan Engineering Group. These data were provided to support this research but detailed information cannot be presented in this paper because the proprietary rights belong to that company.
However, some alternative topography data can be downloaded from the Geospatial Data Cloud website (http://www.gscloud.cn) and the PGA data can be referred to the Seismic Ground Motion Parameter Zonation Map of China (China Earthquake Administration 2016). These data are available from the corresponding author upon reasonable request.

Acknowledgments

This work is partially funded by the National Science Foundation of China (NSFC) with Award Nos. 51778640 and 52078497, the Project of Science and Technology Research and Development Plan of China National Railway Group with Award No. P2019G003, and the Central South University Special Scholarship for Study Abroad. The authors are grateful to the China Railway Eryuan Engineering Group for supporting them with many real cases.

References

Andreotti, G., and C. G. Lai. 2019. “Use of fragility curves to assess the seismic vulnerability in the risk analysis of mountain tunnels.” Tunnelling Underground Space Technol. 91 (Sep): 103008. https://doi.org/10.1016/j.tust.2019.103008.
Argyroudis, S., and A. M. Kaynia. 2015. “Analytical seismic fragility functions for highway and railway embankments and cuts.” Earthquake Eng. Struct. Dyn. 44 (11): 1863–1879. https://doi.org/10.1002/eqe.2563.
Babapour, R., R. Naghdi, I. Ghajar, and Z. Mortazavi. 2018. “Forest road profile optimization using meta-heuristic techniques.” Appl. Soft Comput. 64 (Mar): 126–137. https://doi.org/10.1016/j.asoc.2017.12.015.
China Ministry of Railways. 2017. Code for design of railway line. TB 10098-2017. Beijing: China Railway Publishing House.
Conca, D., F. Bozzoni, and C. Lai. 2020. “Interdependencies in seismic risk assessment of seaport systems: Case study at largest commercial port in Italy.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 6 (2): 04020006. https://doi.org/10.1061/AJRUA6.0001043.
Costa, A. L., M. D. C. Cunha, P. A. L. F. Coelho, and H. H. Einstein. 2018. “Planning for natural hazards: Robust approach for high-speed rail infrastructure.” Nat. Hazard. Rev. 19 (1): 04017025. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000277.
Deb, K., and H. Gupta. 2006. “Introducing robustness in multi-objective optimization.” Evol. Comput. 14 (4): 463–494. https://doi.org/10.1162/evco.2006.14.4.463.
Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan. 2002. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput. 6 (2): 182–197. https://doi.org/10.1109/4235.996017.
de Smith, M. J. 2006. “Determination of gradient and curvature constrained optimal paths.” Comput.-Aided Civ. Infrastruct. Eng. 21 (1): 24–38. https://doi.org/10.1111/j.1467-8667.2005.00414.x.
Easa, S. M., and A. Mehmood. 2008. “Optimizing design of highway horizontal alignments: New substantive safety approach.” Comput.-Aided Civ. Infrastruct. Eng. 23 (7): 560–573. https://doi.org/10.1111/j.1467-8667.2008.00560.x.
Espinet, X., A. Schweikert, and P. Chinowsky. 2017. “Robust prioritization framework for transport infrastructure adaptation investments under uncertainty of climate change.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 3 (1): E4015001. https://doi.org/10.1061/AJRUA6.0000852.
FEMA (Federal Emergency Management Agency). 2003. HAZUS-MH technical manual. Washington, DC: Federal Emergency Management Agency.
Gao, T., Z. Li, Y. Gao, P. Schonfeld, X. Feng, Q. Wang, and Q. He. 2021. “A deep reinforcement learning approach to mountain railway alignment optimization.” Comput.-Aided Civ. Infrastruct. Eng. 2021 (May): 7. https://doi.org/10.1111/mice.12694.
Han, R., Y. Li, and J. van de Lindt. 2016. “Seismic loss estimation with consideration of aftershock hazard and post-quake decisions.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 2 (4): 04016005. https://doi.org/10.1061/AJRUA6.0000875.
Hare, W., S. Hossain, Y. Lucet, and F. Rahman. 2014. “Models and strategies for efficiently determining an optimal vertical alignment of roads.” Comput. Oper. Res. 44 (Apr): 161–173. https://doi.org/10.1016/j.cor.2013.11.005.
Hirpa, D., W. Hare, Y. Lucet, Y. Pushak, and S. Tesfamariam. 2016. “A bi-objective optimization framework for three-dimensional road alignment design.” Transp. Res. Part C: Emerging Technol. 65 (Apr): 61–78. https://doi.org/10.1016/j.trc.2016.01.016.
Jha, M. K., and P. Schonfeld. 2004. “A highway alignment optimization model using geographic information systems.” Transp. Res. Part A: Policy Pract. 38 (6): 455–481. https://doi.org/10.1016/j.tra.2004.04.001.
Jha, M. K., P. Schonfeld, and S. Samanta. 2007. “Optimizing rail transit routes with genetic algorithms and geographic information system.” J. Urban Plann. Dev. 133 (3): 161–171. https://doi.org/10.1061/(ASCE)0733-9488(2007)133:3(161).
Jong, J. C., M. K. Jha, and P. Schonfeld. 2000. “Preliminary highway design with genetic algorithms and geographic information systems.” Comput.-Aided Civ. Infrastruct. Eng. 15 (4): 261–271. https://doi.org/10.1111/0885-9507.00190.
Jong, J. C., and P. Schonfeld. 2003. “An evolutionary model for simultaneously optimizing three-dimensional highway alignments.” Transp. Res. Part B: Methodol. 37 (2): 107–128. https://doi.org/10.1016/S0191-2615(01)00047-9.
Kang, M., M. Jha, and P. Schonfeld. 2012. “Applicability of highway alignment optimization models.” Transp. Res. Part C: Emerging Technol. 21 (1): 257–286. https://doi.org/10.1016/j.trc.2011.09.006.
Kang, M., and P. Schonfeld. 2020. Artificial intelligence in highway location and alignment optimization. Singapore: World Scientific Publishing.
Kang, M., P. Schonfeld, and N. Yang. 2009. “Prescreening and repairing in a genetic algorithm for highway alignment optimization.” Comput.-Aided Civ. Infrastruct. Eng. 24 (2): 109–119. https://doi.org/10.1111/j.1467-8667.2008.00574.x.
Kennedy, J., and R. Eberhart. 1995. “Particle swarm optimization.” In Proc., IEEE Int. Conf. on Neural Networks. Piscataway, NJ: IEEE.
Kim, E., M. Jha, D. Lovell, and P. Schonfeld. 2004. “Intersections modeling for highway alignment optimization.” Comput.-Aided Civ. Infrastruct. Eng. 19 (Mar): 119–129. https://doi.org/10.1111/j.1467-8667.2004.00342.x.
Kim, E., M. Jha, P. Schonfeld, and H. S. Kim. 2007. “Highway alignment optimization incorporating bridges and tunnels.” J. Transp. Eng. 133 (2): 71–81. https://doi.org/10.1061/(ASCE)0733-947X(2007)133:2(71).
Kim, M., P. Schonfeld, and E. Kim. 2013. “Comparison of vertical alignments for rail transit.” J. Transp. Eng. 139 (2): 230–238. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000476.
Kruissebrink, J., M. Emmerich, A. Deutz, and T. Back. 2010. “Exploiting overlap when searching for robust optima.” In Parallel problem solving from nature, PPSN XI, 63–72. Berlin: Springer.
Lai, X., and P. Schonfeld. 2016. “Concurrent optimization of rail transit alignments and station locations.” Urban Rail Transit 2 (1): 1–15. https://doi.org/10.1007/s40864-016-0033-1.
Lee, K. H., and G. J. Park. 2001. “Robust optimization considering tolerances of design variables.” Comput. Struct. 79 (1): 77–86. https://doi.org/10.1016/S0045-7949(00)00117-6.
Lemonge, A., J. Carvalho, P. H. Hallak, and D. Vargas. 2020. “Multi-objective truss structural optimization considering natural frequencies of vibration and global stability.” Expert Syst. Appl. 165 (Mar): 113777. https://doi.org/10.1016/j.eswa.2020.113777.
Li, C., L. Ding, and B. Zhong. 2019a. “Highway planning and design in the Qinghai-Tibet Plateau of China: A cost-safety balance perspective.” Engineering 5 (2): 337–349. https://doi.org/10.1016/j.eng.2018.12.008.
Li, W., H. Pu, P. Schonfeld, J. Yang, H. Zhang, L. Wang, and J. Xiong. 2017. “Mountain railway alignment optimization with bidirectional distance transform and genetic algorithm.” Comput.-Aided Civ. Infrastruct. Eng. 32 (8): 691–709. https://doi.org/10.1111/mice.12280.
Li, W., H. Pu, P. Schonfeld, H. Zhang, and X. Zheng. 2016. “Methodology for optimizing constrained 3-dimensional railway alignments in mountainous terrain.” Transp. Res. Part C: Emerging Technol. 68 (Jul): 549–565. https://doi.org/10.1016/j.trc.2016.05.010.
Liu, K., Q. Li, and Z. H. Zhang. 2019. “Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints.” Transp. Res. Part B: Methodol. 119 (Jan): 79–101. https://doi.org/10.1016/j.trb.2018.11.012.
Maji, A., and M. K. Jha. 2009. “Multi-objective highway alignment optimization using a genetic algorithm.” J. Adv. Transp. 43 (4): 481–504. https://doi.org/10.1002/atr.5670430405.
Mulvey, J., R. Vanderbei, and S. Zenios. 1995. “Robust optimization of large-scale systems.” Oper. Res. 43 (2): 264–281. https://doi.org/10.1287/opre.43.2.264.
Paenke, I., J. Branke, and Y. Jin. 2006. Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation. New York: IEEE.
Papadimitriou, D., and C. Papadimitriou. 2016. “Robust and reliability-based structural topology optimization using a continuous adjoint method.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 2 (3): B4016002. https://doi.org/10.1061/AJRUA6.0000869.
Parreiras, R. O., and J. A. Vasconcelos. 2009. “Decision making in multi-objective optimization aided by the bi-objective tournament decision method.” Nonlinear Anal.: Theory Methods Appl. 71 (12): 191–198. https://doi.org/10.1016/j.na.2008.10.060.
Pu, H., Z. Liang, P. Schonfeld, W. Li, J. Wang, H. Zhang, T. Song, J. Wang, J. Hu, and X. Peng. 2021a. “Optimization of grade-separated road and railway crossings based on a distance transform algorithm.” Eng. Optim. 2021 (Jan): 1–20. https://doi.org/10.1080/0305215X2020.1861264.
Pu, H., T. Song, P. Schonfeld, W. Li, H. Zhang, J. Hu, X. Peng, and J. Wang. 2019a. “Mountain railway alignment optimization using stepwise & hybrid particle swarm optimization incorporating genetic operators.” Appl. Soft Comput. 78 (May): 41–57. https://doi.org/10.1016/j.asoc.2019.01.051.
Pu, H., T. Song, P. Schonfeld, W. Li, H. Zhang, J. Wang, J. Hu, and X. Peng. 2019b. “A three-dimensional distance transform for optimizing constrained mountain railway alignments.” Comput.-Aided Civ. Infrastruct. Eng. 34 (11): 972–990. https://doi.org/10.1111/mice.12475.
Pu, H., J. Xie, P. Schonfeld, T. Song, W. Li, J. Wang, and J. Hu. 2021b. “Railway alignment optimization in mountainous regions considering spatial geological hazards: A sustainable safety perspective.” Sustainability 13 (4): 1661. https://doi.org/10.3390/su13041661.
Pu, H., H. Zhang, W. Li, J. Xiong, J. Hu, and J. Wang. 2019c. “Concurrent optimization of mountain railway alignment and station locations using a distance transform algorithm.” Comput. Ind. Eng. 127 (Jan): 1297–1314. https://doi.org/10.1016/j.cie.2018.01.004.
Rakshit, P., A. Konar, and S. Das. 2017. “Noisy evolutionary optimization algorithms—A comprehensive survey.” Swarm Evol. Comput. 33 (Jan): 18–45. https://doi.org/10.1016/j.swevo.2016.09.002.
Shafahi, Y., and M. Bagherian. 2013. “A customized particle swarm method to solve highway alignment optimization problem.” Comput.-Aided Civ. Infrastruct. Eng. 28 (1): 52–67. https://doi.org/10.1111/j.1467-8667.2012.00769.x.
Shi, Y., and R. Eberhart. 1998. “A modified particle swarm optimizer.” In Proc., IEEE Int. Conf. on Evolutionary Computation. IEEE World Congress on Computational Intelligence, 69–73. New York: IEEE. https://doi.org/10.1109/ICEC.1998.699146.
Song, T., H. Pu, P. Schonfeld, W. Li, H. Zhang, Y. Ren, J. Wang, J. Hu, and X. Peng. 2020a. “Parallel three-dimensional distance transform for railway alignment optimization using OpenMP.” J. Transp. Eng. Part A: Syst. 146 (5): 04020029. https://doi.org/10.1061/JTEPBS.0000344.
Song, T., H. Pu, P. Schonfeld, H. Zhang, W. Li, and J. Hu. 2021a. “Simultaneous optimization of 3D alignments and station locations for dedicated high-speed railways.” Comput.-Aided Civ. Infrastruct. Eng. 2021 (Jun): 22. https://doi.org/10.1111/mice.12739.
Song, T., H. Pu, P. Schonfeld, H. Zhang, W. Li, J. Hu, and J. Wang. 2020b. “Mountain railway alignment optimization considering geological impacts: A cost-hazard bi-objective model.” Comput.-Aided Civ. Infrastruct. Eng. 35 (12): 1365–1386. https://doi.org/10.1111/mice.12571.
Song, T., H. Pu, P. Schonfeld, H. Zhang, W. Li, J. Hu, and J. Wang. 2021b. “Bi-objective mountain railway alignment optimization incorporating seismic risk assessment.” Comput.-Aided Civ. Infrastruct. Eng. 36 (2): 143–163. https://doi.org/10.1111/mice.12607.
Song, T., H. Pu, P. Schonfeld, H. Zhang, W. Li, X. Peng, J. Hu, and W. Liu. 2021c. “GIS-based multi-criteria railway design with spatial environmental considerations.” Appl. Geogr. 2021 (Apr): 102449. https://doi.org/10.1016/j.apgeog.2021.102449.
Sushma, M. B., and A. Maji. 2020. “A modified motion planning algorithm for horizontal highway alignment development.” Comput.-Aided Civ. Infrastruct. Eng. 35 (8): 818–831. https://doi.org/10.1111/mice.12534.
Walter, G., and F. Coolen. 2018. “Robust Bayesian reliability for complex systems under prior-data conflict.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 4 (3): 04018025. https://doi.org/10.1061/AJRUA6.0000974.
Wright, P. H. 1996. Highway engineering. New York: Wiley.
Yang, N., M. W. Kang, P. Schonfeld, and M. K. Jha. 2014. “Multi-objective highway alignment optimization incorporating preference information.” Transp. Res. Part C: Emerging Technol. 40 (Mar): 36–48. https://doi.org/10.1016/j.trc.2013.12.010.
Yu, S., S. Zheng, and X. Li. 2018. “The achievement of the carbon emissions peak in China: The role of energy consumption structure optimization.” Energy Econ. 74 (Aug): 693–707. https://doi.org/10.1016/j.eneco.2018.07.017.
Yuan, Y., Z. Li, and B. Huang. 2016. “Robust optimization under correlated uncertainty: Formulations and computational study.” Comput. Chem. Eng. 85 (Feb): 58–71. https://doi.org/10.1016/j.compchemeng.2015.10.017.
Zeferino, J. A., M. C. Cunha, and A. P. Antunes. 2012. “Robust optimization approach to regional wastewater system planning.” J. Environ. Manage. 109 (Oct): 113–122. https://doi.org/10.1016/j.jenvman.2012.05.008.
Zhang, H., H. Pu, P. Schonfeld, T. Song, W. Li, J. Wang, X. Peng, and J. Hu. 2020. “Multi-objective railway alignment optimization considering costs and environmental impacts.” Appl. Soft Comput. 89 (Apr): 106105. https://doi.org/10.1016/j.asoc.2020.106105.

Information & Authors

Information

Published In

Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8Issue 1March 2022

History

Received: Jun 10, 2021
Accepted: Oct 6, 2021
Published online: Nov 25, 2021
Published in print: Mar 1, 2022
Discussion open until: Apr 25, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Candidate, School of Civil Engineering, National Engineering Laboratory for High Speed Railway Construction, Central South Univ., Changsha 410075, China. ORCID: https://orcid.org/0000-0002-7663-2042. Email: [email protected]
Professor, School of Civil Engineering, National Engineering Laboratory for High Speed Railway Construction, Central South Univ., Changsha 410075, China (corresponding author). Email: [email protected]
Paul Schonfeld, F.ASCE [email protected]
Professor, Dept. of Civil and Environmental Engineering, Univ. of Maryland, College Park, MD 20742. Email: [email protected]
Jianping Hu [email protected]
Professorate Senior Engineer, China Railway Eryuan Engineering Group Co. Ltd., No. 3, Tongjin Rd., Chengdu 610031, China. Email: [email protected]
Jiangtao Liu [email protected]
Senior Engineer, China Railway Eryuan Engineering Group Co. Ltd., No. 3, Tongjin Rd., Chengdu 610031, China. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Modeling Earthquake-Induced Landslide Risk for Mountain Railway Alignment Optimization, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 10.1061/AJRUA6.RUENG-1179, 10, 2, (2024).
  • Modeling and application of a customized knowledge graph for railway alignment optimization, Expert Systems with Applications, 10.1016/j.eswa.2023.122999, 244, (122999), (2024).
  • Optimizing net present values of risk avoidance for mountain railway alignments with seismic performance evaluation, Computer-Aided Civil and Infrastructure Engineering, 10.1111/mice.13125, 39, 7, (944-962), (2023).
  • A Review of Alignment Optimization Research for Roads, Railways and Rail Transit Lines, IEEE Transactions on Intelligent Transportation Systems, 10.1109/TITS.2023.3235685, 24, 5, (4738-4757), (2023).
  • Three-dimensional subway alignment recreation considering tunnel construction gauges, Tunnelling and Underground Space Technology, 10.1016/j.tust.2023.105347, 141, (105347), (2023).
  • Minimizing costs and carbon emissions in railway alignment optimization: A bi-objective model, Transportation Research Part D: Transport and Environment, 10.1016/j.trd.2023.103615, 116, (103615), (2023).
  • A geographic information model for 3-D environmental suitability analysis in railway alignment optimization, Integrated Computer-Aided Engineering, 10.3233/ICA-220692, 30, 1, (67-88), (2022).
  • Mountain railway alignment optimization integrating layouts of large‐scale auxiliary construction projects, Computer-Aided Civil and Infrastructure Engineering, 10.1111/mice.12839, 38, 4, (433-453), (2022).
  • Modelling and optimization of constrained alignments for existing railway reconstruction, International Journal of Rail Transportation, 10.1080/23248378.2022.2081878, 11, 3, (428-447), (2022).
  • Optimization of metro vertical alignment for minimized construction costs and traction energy: A dynamic programming approach, Tunnelling and Underground Space Technology, 10.1016/j.tust.2022.104722, 129, (104722), (2022).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share