Abstract
Traditionally, traffic congestion was alleviated through significantly upgrading the infrastructure of transportation networks. However, building new roads or adding more lanes to a main road needs huge expenses. A better cost-effective approach is to redesign and fine-tune transportation networks by closing and reversing existing lanes. This paper aims at developing an optimal scheme for lane-level closure and reversal to improve the performance of existing transportation networks with a fairly tight budget. We call this new problem Lane-level Closure and Reversal Problem (LCRP). By considering the capacities of all lanes of a road, two different bi-objective bi-level programs (called the arc-based and lane-based models) are developed to formulate the LCRP. Furthermore, our proposed formulations consider the elastic traffic demand and the elimination of conflict points resulting from reversing lanes. A hybrid machine learning and bi-objective optimization (MLBO) algorithm is developed to overcome the curse of dimensionality of the bi-level programs, especially for the land-based model that is more general but with higher computational complexity. The proposed methodology is illustrated by a small-size numerical example and verified by a real-world case study from Winnipeg (i.e., a benchmark transportation network). Computational results show that the integrated lane-level closure and reversal model can achieve a 0.52% reduction in the total travel time, which is significantly better than the 0.05% reduction individually obtained by arc-level closure or the 0.10% reduction obtained by arc-level reversal. The proposed methodology is beneficial for the traffic management bureau to make a more precise decision in redesigning transportation networks in practice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Babonneau F, Vial J-P (2008) An efficient method to compute traffic assignment problems with elastic demands. Transp Sci 42(2):249–260. https://doi.org/10.1287/trsc.1070.0208
Bagloee SA, Ceder A, Tavana M, Bozic C (2014) A heuristic methodology to tackle the Braess Paradox detecting problem tailored for real road networks. Transpo A Transp Sci 10(5):437–456. https://doi.org/10.1080/23249935.2013.787557
Bagloee SA, Sarvi M, Patriksson M (2017) A hybrid branch-and-bound and Benders decomposition algorithm for the network design problem. Comput Aided Civil Infrastruct Eng 32(4):319–343. https://doi.org/10.1111/mice.12224
Bagloee SA, Asadi M, Patriksson M (2018) Minimization of water pumps’ electricity usage: a hybrid approach of regression models with optimization. Expert Syst Appl 107:222–242. https://doi.org/10.1016/j.eswa.2018.04.027
Bagloee SA, Asadi M, Sarvi M, Patriksson M (2018) A hybrid machine-learning and optimization method to solve bi-level problems. Expert Syst Appl 95:142–152. https://doi.org/10.1016/j.eswa.2017.11.039
Bagloee SA, Ceder AA, Sarvi M, Asadi M (2019) Is it time to go for no-car zone policies? Braess Paradox Detection. Transp Res Part A Policy Pract 121:251–264. https://doi.org/10.1016/j.tra.2019.01.021
Bagloee SA, Johansson KH, Asadi M (2019) A hybrid machine-learning and optimization method for contraflow design in post-disaster cases and traffic management scenarios. Expert Syst Appl 124:67–81. https://doi.org/10.1016/j.eswa.2019.01.042
Balas E, Jeroslow R (1972) Canonical cuts on the unit hypercube. SIAM J Appl Math 23(1):61–69. https://doi.org/10.1137/0123007
Bani Younes M, Boukerche A (2015) A performance evaluation of an efficient traffic congestion detection protocol (ECODE) for intelligent transportation systems. Ad Hoc Netw 24:317–336. https://doi.org/10.1016/j.adhoc.2014.09.005
Batista SFA, Leclercq L (2019) Regional dynamic traffic assignment framework for macroscopic fundamental diagram multi-regions models. Transp Sci 53(6):1563–1590. https://doi.org/10.1287/trsc.2019.0921
Beckmann M, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Technical report
Bengio Y, Lodi A, Prouvost A (2021) Machine learning for combinatorial optimization: a methodological tour d’horizon. Eur J Oper Res 290(2):405–421. https://doi.org/10.1016/j.ejor.2020.07.063
Bonami P, Lodi A, Zarpellon G (2018) Learning a classification of mixed-integer quadratic programming problems. In W.-J. van Hoeve, editor, Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Lecture Notes in Computer Science, pp. 595–604, Cham, Springer International Publishing. https://doi.org/10.1007/978-3-319-93031-2_43
Braess D (1968) Über ein paradoxon aus der verkehrsplanung. Unternehm Oper Res Rech Opérationnelle 12(1):258–268. https://doi.org/10.1007/BF01918335
Braess D, Nagurney A, Wakolbinger T (2005) On a paradox of traffic planning. Transp Sci 39(4):446–450. https://doi.org/10.1287/trsc.1050.0127
Chen X, Liu Z, Zhang K, Wang Z (2020) A parallel computing approach to solve traffic assignment using path-based gradient projection algorithm. Transp Res Part C Emerg Technol 120:102809. https://doi.org/10.1016/j.trc.2020.102809
Chen S, Wang H, Meng Q (2022) An optimal dynamic lane reversal and traffic control strategy for autonomous vehicles. IEEE Trans Intell Transp Syst 23(4):3804–3815. https://doi.org/10.1109/TITS.2021.3074011
Cheng Q, Chen Y, Liu Z (2022) A bi-level programming model for the optimal lane reservation problem. Expert Syst Appl 189:116147. https://doi.org/10.1016/j.eswa.2021.116147
Cova TJ, Johnson JP (2003) A network flow model for lane-based evacuation routing. Transp Res Part A Policy Pract 37(7):579–604. https://doi.org/10.1016/S0965-8564(03)00007-7
Dafermos S, Nagurney A (1984) On some traffic equilibrium theory paradoxes. Transp Res Part B Methodol 18(2):101–110. https://doi.org/10.1016/0191-2615(84)90023-7
Di Z, Yang L (2020) Reversible lane network design for maximizing the coupling measure between demand structure and network structure. Transp Res Part E Logist Transp Rev 141:102021. https://doi.org/10.1016/j.tre.2020.102021
Du M, Tan H, Chen A (2021) A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models. Eur J Oper Res 290(3):982–999. https://doi.org/10.1016/j.ejor.2020.08.058
Easley D, Kleinberg J (2010) Networks, crowds, and markets, vol 8. Cambridge University Press, Cambridge
Fang Y, Chu F, Mammar S, Zhou M (2012) Optimal lane reservation in transportation network. IEEE Trans Intell Transp Syst 13(2):482–491. https://doi.org/10.1109/TITS.2011.2171337
Fang Y, Chu F, Mammar S, Shi Q (2015) A new cut-and-solve and cutting plane combined approach for the capacitated lane reservation problem. Comput Ind Eng 80:212–221. https://doi.org/10.1016/j.cie.2014.12.014
Farvaresh H, Sepehri MM (2013) A branch and bound algorithm for bi-level discrete network design problem. Netw Spat Econ 13(1):67–106. https://doi.org/10.1007/s11067-012-9173-3
Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res Logist Q 3(1–2):95–110. https://doi.org/10.1002/nav.3800030109
Gao Z, Wu J, Sun H (2005) Solution algorithm for the bi-level discrete network design problem. Transp Res Part B Methodol 39(6):479–495. https://doi.org/10.1016/j.trb.2004.06.004
He X, Zheng H, Peeta S, Li Y (2018) Network design model to integrate shelter assignment with contraflow operations in emergency evacuation planning. Netw Spat Econ 18(4):1027–1050. https://doi.org/10.1007/s11067-017-9381-y
He Z, Zheng L, Lu L, Guan W (2018) Erasing lane changes from roads: a design of future road intersections. IEEE Trans Intell Veh 3(2):173–184. https://doi.org/10.1109/TIV.2018.2804164
Hosseininasab S-M, Shetab-Boushehri S-N (2015) Integration of selecting and scheduling urban road construction projects as a time-dependent discrete network design problem. Eur J Oper Res. https://doi.org/10.1016/j.ejor.2015.05.039
Hosseininasab S-M, Shetab-Boushehri S-N, Hejazi SR, Karimi H (2018) A multi-objective integrated model for selecting, scheduling, and budgeting road construction projects. Eur J Oper Res 271(1):262–277. https://doi.org/10.1016/j.ejor.2018.04.051
Islam KA, Moosa IM, Mobin J, Nayeem MA, Rahman MS (2019) A heuristic aided Stochastic Beam Search algorithm for solving the transit network design problem. Swarm Evol Comput 46:154–170. https://doi.org/10.1016/j.swevo.2019.02.007
Jeroslow RG (1985) The polynomial hierarchy and a simple model for competitive analysis. Math Program 32(2):146–164. https://doi.org/10.1007/BF01586088
Karakitsiou A, Migdalas A (2016) Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method. Oper Res Int J 16(3):401–421. https://doi.org/10.1007/s12351-015-0205-x
Karoonsoontawong A, Lin D-Y (2011) Time-varying lane-based capacity reversibility for traffic management. Comput Aided Civil Infrastruct Eng 26(8):632–646. https://doi.org/10.1111/j.1467-8667.2011.00722.x
Köhler E, Möhring RH, Nökel K, Wünsch G (2008)Optimization of signalized traffic networks. In Krebs H-J, Jäger W, (eds), Mathematics – Key Technology for the Future, pages 179–188. Springer Berlin Heidelberg, Berlin, Heidelberg, https://doi.org/10.1007/978-3-540-77203-3_13
Lindsay. (2021a) Road zipper. https://www.lindsay.com/usca/en/infrastructure/brands/road-zipper/
Lindsay. (2021b) US I-75 Pavement rehabilitation. https://www.lindsay.com/usca/en/infrastructure/brands/road-zipper/case-studies/?page=2 &per-page=12
Liu SQ, Huang X, Li X, Masoud M, Chung S-H, Yin Y (2021) How is China’s energy security affected by exogenous shocks? Evidence of China-US trade dispute and COVID-19 pandemic. Discov Energy 1(1):2. https://doi.org/10.1007/s43937-021-00002-6
Liu SQ, Kozan E, Corry P, Masoud M, Luo K (2022) A real-world mine excavators timetabling methodology in open-pit mining. Optim Eng. https://doi.org/10.1007/s11081-022-09741-4
Lu H, Freund RM (2021) Generalized stochastic Frank-Wolfe algorithm with stochastic “substitute’’ gradient for structured convex optimization. Math Program 187(1):317–349. https://doi.org/10.1007/s10107-020-01480-7
Ma J, Li D, Cheng L, Lou X, Sun C, Tang W (2018) Link restriction: methods of testing and avoiding braess paradox in networks considering traffic demands. J Transp Eng Part A Syst 144(2):04017076. https://doi.org/10.1061/JTEPBS.0000111
Mathew TV, Sharma S (2009) Capacity expansion problem for large urban transportation networks. J Transp Eng 135(7):406–415. https://doi.org/10.1061/(ASCE)0733-947X(2009)135:7(406)
Miandoabchi E, Daneshzand F, Szeto WY, Farahani RZ (2013) Multi-objective discrete urban road network design. Comput Oper Res 40(10):2429–2449. https://doi.org/10.1016/j.cor.2013.03.016
Miandoabchi E, Daneshzand F, Zanjirani Farahani R, Szeto WY (2015) Time-dependent discrete road network design with both tactical and strategic decisions. J Oper Res Soc 66(6):894–913. https://doi.org/10.1057/jors.2014.55
Pan W, Liu SQ (2022) Deep reinforcement learning for the dynamic and uncertain vehicle routing problem. Appl Intell. https://doi.org/10.1007/s10489-022-03456-w
Poorzahedy H, Rouhani OM (2007) Hybrid meta-heuristic algorithms for solving network design problem. Eur J Oper Res 182(2):578–596. https://doi.org/10.1016/j.ejor.2006.07.038
Requia WJ, Higgins CD, Adams MD, Mohamed M, Koutrakis P (2018) The health impacts of weekday traffic: a health risk assessment of PM2.5 emissions during congested periods. Environ Int 111:164–176. https://doi.org/10.1016/j.envint.2017.11.025
Rinaldi M, Picarelli E, D’Ariano A, Viti F (2020) Mixed-fleet single-terminal bus scheduling problem: modelling, solution scheme and potential applications. Omega 96:102070. https://doi.org/10.1016/j.omega.2019.05.006
Roughgarden T (2006) On the severity of Braess’s Paradox: designing networks for selfish users is hard. J Comput Syst Sci 72(5):922–953. https://doi.org/10.1016/j.jcss.2005.05.009
Roughgarden T, Tardos É (2002) How bad is selfish routing? J ACM (JACM) 49(2):236–259. https://doi.org/10.1145/506147.506153
Said R, Elarbi M, Bechikh S, Ben Said L (2021) Solving combinatorial bi-level optimization problems using multiple populations and migration schemes. Oper Res. https://doi.org/10.1007/s12351-020-00616-z
Sando T, Mbatta G, Moses R (2014) Lane width crash modification factors for curb-and-gutter asymmetric multilane roadways: statistical modeling. J Transp Stat 10(1):61–78
Stabler B, Bar-Gera H, Sall E (2020) Transportation Networks for Research. https://github.com/bstabler/TransportationNetworks
Szeto WY, Wang Y, Wong SC (2014) The chemical reaction optimization approach to solving the environmentally sustainable network design problem: the CRO approach to solving the environmentally sustainable NDP. Comput Aided Civil Infrastruct Eng 29(2):140–158. https://doi.org/10.1111/mice.12033
Tuydes H, Ziliaskopoulos A (2004) Network re-design to optimize evacuation contraflow. In 83rd Annual Meeting of the Transportation Research Board, Washington, DC
Wang S, Meng Q, Yang H (2013) Global optimization methods for the discrete network design problem. Transp Res Part B Methodol 50:42–60. https://doi.org/10.1016/j.trb.2013.01.006
Wang Y, Szeto WY, Han K, Friesz TL (2018) Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications. Transp Res Part B Methodol 111:370–394. https://doi.org/10.1016/j.trb.2018.03.011
Wu P, Che A, Chu F, Fang Y (2017) Exact and heuristic algorithms for rapid and station arrival-time guaranteed bus transportation via lane reservation. IEEE Trans Intell Transp Syst 18(8):2028–2043. https://doi.org/10.1109/TITS.2016.2631893
Wu Y, Chu C, Chu F, Wu N (2009) Heuristic for lane reservation problem in time constrained transportation. In: 2009 IEEE International Conference on Automation Science and Engineering, pp. 543–548, Bangalore, India, IEEE. https://doi.org/10.1109/COASE.2009.5234190
Wu P, Xu L, D’Ariano A, Zhao Y, Chu C (2022) Novel formulations and improved differential evolution algorithm for optimal lane reservation with task merging. IEEE Transactions on Intelligent Transportation Systems, pp. 1–16, https://doi.org/10.1109/TITS.2022.3175010
Xie C, Lin D-Y, Travis Waller S (2010) A dynamic evacuation network optimization problem with lane reversal and crossing elimination strategies. Transp Res Part E Logist Transp Rev 46(3):295–316. https://doi.org/10.1016/j.tre.2009.11.004
Xin J, Yu B, D’Ariano A, Wang H, Wang M (2021) Time-dependent rural postman problem: time-space network formulation and genetic algorithm. Oper Res. https://doi.org/10.1007/s12351-021-00639-0
Xu Z, Xie J, Liu X, Nie YM (2020) Hyperpath-based algorithms for the transit equilibrium assignment problem. Transp Res Part E Logist Transp Rev 143:102102. https://doi.org/10.1016/j.tre.2020.102102
Yin J, D’Ariano A, Wang Y, Yang L, Tang T (2021) Timetable coordination in a rail transit network with time-dependent passenger demand. Eur J Oper Res. https://doi.org/10.1016/j.ejor.2021.02.059
Yu H, Ma R, Zhang M (2018) Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network. Transp Res Part B Methodol 110:302–325. https://doi.org/10.1016/j.trb.2018.02.009
Yu Y, Han K, Ochieng W (2020) Day-to-day dynamic traffic assignment with imperfect information, bounded rationality and information sharing. Transp Res Part C Emerg Technol 114:59–83. https://doi.org/10.1016/j.trc.2020.02.004
Zeng L, Liu SQ, Kozan E, Corry P, Masoud M (2021) A comprehensive interdisciplinary review of mine supply chain management. Resour Policy 74:102274. https://doi.org/10.1016/j.resourpol.2021.102274
Zhang H, Gao Z (2007) Two-way road network design problem with variable lanes. J Syst Sci Syst Eng 16(1):50–61. https://doi.org/10.1007/s11518-007-5034-x
Zhang Q, Liu SQ, Masoud M (2022) A traffic congestion analysis by user equilibrium and system optimum with incomplete information. J Comb Optim 43(5):1391–1404. https://doi.org/10.1007/s10878-020-00663-4
Zhao P, Hu H (2019) Geographical patterns of traffic congestion in growing megacities: big data analytics from Beijing. Cities 92:164–174. https://doi.org/10.1016/j.cities.2019.03.022
Zhao J, Ma W, Liu Y, Yang X (2014) Integrated design and operation of urban arterials with reversible lanes. Transp B Transp Dyn 2(2):130–150. https://doi.org/10.1080/21680566.2014.908751
Funding
This work was supported by the National Natural Science Foundation of China under Grant No. 71871064.
Author information
Authors and Affiliations
Contributions
Conceptualization: Qiang Zhang (QZ), Shi Qiang Liu (SQL), Andrea D’Ariano (AD); Methodology: QZ, SQL, AD; Formal analysis and investigation: QZ, SQL, AD; Writing - original draft preparation: QZ; Writing - review and editing: SQL, AD; Funding acquisition: SQL; Resources: SQL; Supervision: SQL, AD.
Corresponding author
Ethics declarations
Conflict of interest
No potential conflict of interest was reported by the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, Q., Liu, S.Q. & D’Ariano, A. Bi-objective bi-level optimization for integrating lane-level closure and reversal in redesigning transportation networks. Oper Res Int J 23, 23 (2023). https://doi.org/10.1007/s12351-023-00756-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12351-023-00756-y
Keywords
- Transportation
- Traffic congestion
- Lane-level closure and reversal problem
- Bi-level programming
- Integer linear programming