A hybrid inverse optimization-stochastic programming framework for network protection

References

• Abpeykar, S., & Ghatee, M. (2014). Supervised and unsupervised learning dss for incident management in intelligent tunnel: A case study in Tehran Niayesh tunnel. Tunnelling and Underground Space Technology, 42, 293–306. https://doi.org/10.1016/j.tust.2014.03.008
   Web of Science ®Google Scholar
• Ahuja, R. K., & Orlin, J. B. (2001). Inverse optimization. Operations Research, 49(5), 771–783. https://doi.org/10.1287/opre.49.5.771.10607
   Web of Science ®Google Scholar
• Allen, S., Gabriel, S. A., & Dickerson, J. P. (2022). Using inverse optimization to learn cost functions in generalized Nash games. Computers & Operations Research, 142, 105721. https://doi.org/10.1016/j.cor.2022.105721
   Web of Science ®Google Scholar
• Alvear, D., Abreu, O., Cuesta, A., & Alonso, V. (2013). Decision support system for emergency management: Road tunnels. Tunnelling and Underground Space Technology, 34, 13–21. https://doi.org/10.1016/j.tust.2012.10.005
   Web of Science ®Google Scholar
• Asadabadi, A., & Miller-Hooks, E. (2017). Optimal transportation and shoreline infrastructure investment planning under a stochastic climate future. Transportation Research Part B: Methodological, 100, 156–174. https://doi.org/10.1016/j.trb.2016.12.023
   Web of Science ®Google Scholar
• Aswani, A., Shen, Z.-J., & Siddiq, A. (2018). Inverse optimization with noisy data. Operations Research, 66(3), 870–892. https://doi.org/10.1287/opre.2017.1705
   Web of Science ®Google Scholar
• Babier, A., Chan, T. C., Lee, T., Mahmood, R., & Terekhov, D. (2020). An ensemble learning framework for model fitting and evaluation in inverse linear optimization. Informs Journal on Optimization, 3(2), 119–138.
   Google Scholar
• Ban, X. J. (2005). Quasi-variational inequality formulations and solution approaches for dynamic user equilibria. The University of Wisconsin-Madison.
   Google Scholar
• Ban, J. X., Liu, H. X., Ferris, M. C., & Ran, B. (2006). A general mpcc model and its solution algorithm for continuous network design problem. Mathematical and Computer Modelling, 43(5–6), 493–505. https://doi.org/10.1016/j.mcm.2005.11.001
   Web of Science ®Google Scholar
• Barbarosoǧlu, G., & Arda, Y. (2004). A two-stage stochastic programming framework for transportation planning in disaster response. Journal of the Operational Research Society, 55(1), 43–53. https://doi.org/10.1057/palgrave.jors.2601652
   Web of Science ®Google Scholar
• Bertsimas, D., Gupta, V., & Paschalidis, I. C. (2015). Data-driven estimation in equilibrium using inverse optimization. Mathematical Programming, 153(2), 595–633. https://doi.org/10.1007/s10107-014-0819-4
   Web of Science ®Google Scholar
• Branston, D. (1976). Link capacity functions: A review. Transportation Research, 10(4), 223–236. https://doi.org/10.1016/0041-1647(76)90055-1
   Google Scholar
• Cantillo, V., Macea, L. F., & Jaller, M. (2019). Assessing vulnerability of transportation networks for disaster response operations. Networks and Spatial Economics, 19(1), 243–273. https://doi.org/10.1007/s11067-017-9382-x
   Web of Science ®Google Scholar
• Carpentier, P.-L., Gendreau, M., & Bastin, F. (2013). Long-term management of a hydroelectric multireservoir system under uncertainty using the progressive hedging algorithm. Water Resources Research, 49(5), 2812–2827. https://doi.org/10.1002/wrcr.20254
   Web of Science ®Google Scholar
• Chan, T. C., & Kaw, N. (2020). Inverse optimization for the recovery of constraint parameters. European Journal of Operational Research, 282(2), 415–427. https://doi.org/10.1016/j.ejor.2019.09.027
   Web of Science ®Google Scholar
• Chan, T. C., Lee, T., & Terekhov, D. (2019). Inverse optimization: Closed-form solutions, geometry, and goodness of fit. Management Science, 65(3), 1115–1135. https://doi.org/10.1287/mnsc.2017.2992
   Web of Science ®Google Scholar
• Chen, Y., & Florian, M. (1998). Congested O-D trip demand adjustment problem: Bilevel programming formulation and optimality conditions. In A. Migdalas, P.M. Pardalos, & P. Värbrand (eds.), Multilevel optimization: Algorithms and applications. Nonconvex optimization and its applications (pp. 1–22). Boston, MA: Springer.
   Google Scholar
• Chow, J. Y., Ritchie, S. G., & Jeong, K. (2014). Nonlinear inverse optimization for parameter estimation of commodity-vehicle-decoupled freight assignment. Transportation Research Part E: Logistics and Transportation Review, 67, 71–91. https://doi.org/10.1016/j.tre.2014.04.004
   Web of Science ®Google Scholar
• Chu, J. C., & Chen, S. (2016). Optimization of transportation-infrastructure-system protection considering weighted connectivity reliability. Journal of Infrastructure Systems, 22(1), 04015008. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000264
   Web of Science ®Google Scholar
• Cioca, M., Cioca, L., Buraga, S. (2007). Spatial [elements] decision support system used in disaster management. In 2007 Inaugural Ieee-Ies Digital Ecosystems and Technologies Conference (pp. 607–612). https://doi.org/10.1109/DEST.2007.372045
   Google Scholar
• Crainic, T. G., Fu, X., Gendreau, M., Rei, W., & Wallace, S. W. (2011). Progressive hedging-based metaheuristics for stochastic network design. Networks, 58(2), 114–124. https://doi.org/10.1002/net.20456
   Web of Science ®Google Scholar
• Cuesta, A., Alvear, D., Abreu, O., & Silió, D. (2014). Real-time stochastic evacuation models for decision support in actual emergencies. Fire Safety Science, 11, 1063–1076. https://doi.org/10.3801/IAFSS.FSS.11-1063
   Google Scholar
• Dafermos, S. C., & Sparrow, F. T. (1969). The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, 73B(2), 91–118. https://doi.org/10.6028/jres.073B.010
   Google Scholar
• Daganzo, C. F., & Sheffi, Y. (1977). On stochastic models of traffic assignment. Transportation Science, 11(3), 253–274. https://doi.org/10.1287/trsc.11.3.253
   Google Scholar
• Department of Homeland Security. (2013). National infrastructure protection plan: Partnering for critical infrastructure security and resilience. https://www.cisa.gov/sites/default/files/publications/national-infrastructure-protection-plan-2013-508.pdf.
   Google Scholar
• Dial, R. B. (1971). A probabilistic multipath traffic assignment model which obviates path enumeration. Transportation Research, 5(2), 83–111. https://doi.org/10.1016/0041-1647(71)90012-8
   Google Scholar
• Dirkse, S. P., & Ferris, M. C. (1995). The path solver: A nommonotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, 5(2), 123–156. https://doi.org/10.1080/10556789508805606
   Google Scholar
• Döyen, A., & Aras, N. (2019). An integrated disaster preparedness model for retrofitting and relief item transportation. Networks and Spatial Economics, 19(4), 1031–1068. https://doi.org/10.1007/s11067-019-9441-6
   Web of Science ®Google Scholar
• Du, M., Tan, H., & Chen, A. (2021). A faster path-based algorithm with barzilai-borwein step size for solving stochastic traffic equilibrium models. European Journal of Operational Research, 290(3), 982–999. https://doi.org/10.1016/j.ejor.2020.08.058
   Web of Science ®Google Scholar
• Eguchi, R. T., Goltz, J. D., Seligson, H. A., Flores, P. J., Blais, N. C., Heaton, T. H., & Bortugno, E. (1997). Real-time loss estimation as an emergency response decision support system: The early post-earthquake damage assessment tool (EPEDAT). Earthquake Spectra, 13(4), 815–832. https://doi.org/10.1193/1.1585982
   Google Scholar
• Facchinei, F., & Pang, J.-S. (2007). Finite-dimensional variational inequalities and complementarity problems. Springer Science & Business Media.
   Google Scholar
• Fan, Y., & Liu, C. (2010). Solving stochastic transportation network protection problems using the progressive hedging-based method. Networks and Spatial Economics, 10(2), 193–208. https://doi.org/10.1007/s11067-008-9062-y
   Web of Science ®Google Scholar
• Faturechi, R., Isaac, S., Miller-Hooks, E., & Feng, L. (2018). Risk-based models for emergency shelter and exit design in buildings. Annals of Operations Research, 262(1), 185–212. https://doi.org/10.1007/s10479-016-2223-3
   Web of Science ®Google Scholar
• Faturechi, R., & Miller-Hooks, E. (2014). Travel time resilience of roadway networks under disaster. Transportation Research Part B: Methodological, 70, 47–64. https://doi.org/10.1016/j.trb.2014.08.007
   Web of Science ®Google Scholar
• FEMA. (2019, October 28). National response framework: Fourth edition. https://www.fema.gov/sites/default/files/2020-04/NRF_FINALApproved_2011028.pdf.
   Google Scholar
• Ferris, M. C., & Munson, T. S. (2000). Complementarity problems in gams and the path solver. Journal of Economic Dynamics and Control, 24(2), 165–188. https://doi.org/10.1016/S0165-1889(98)00092-X
   Web of Science ®Google Scholar
• Ferris, M. C., & Munson, T. S. (2020). Path 4.7. https://www.gams.com/latest/docs/S_PATH.html,
   Google Scholar
• Fertier, A., Barthe-Delanoë, A.-M., Montarnal, A., Truptil, S., & Bénaben, F. (2020). A new emergency decision support system: The automatic interpretation and contextualisation of events to model a crisis situation in real-time. Decision Support Systems, 133, 113260. https://doi.org/10.1016/j.dss.2020.113260
   Web of Science ®Google Scholar
• Fikar, C., Gronalt, M., & Hirsch, P. (2016). A decision support system for coordinated disaster relief distribution. Expert Systems with Applications, 57, 104–116. https://doi.org/10.1016/j.eswa.2016.03.039
   Web of Science ®Google Scholar
• Fisk, C. (1980). Some developments in equilibrium traffic assignment. Transportation Research Part B: Methodological, 14(3), 243–255. https://doi.org/10.1016/0191-2615(80)90004-1
   Web of Science ®Google Scholar
• Fortuny-Amat, J., & McCarl, B. (1981). A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society, 32(9), 783–792. https://doi.org/10.1057/jors.1981.156
   Web of Science ®Google Scholar
• Gabriel, S. A., & Bernstein, D. (1997). The traffic equilibrium problem with nonadditive path costs. Transportation Science, 31(4), 337–348. https://doi.org/10.1287/trsc.31.4.337
   Web of Science ®Google Scholar
• Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2012). Complementarity modeling in energy markets (Vol. 180). Springer Science & Business Media.
   Google Scholar
• GAMS Development Corporation. (2021). General algebraic modeling system (gams) release 34.1.0. https://www.gams.com/download/,
   Google Scholar
• Geweke, J. (1986). Exact inference in the inequality constrained normal linear regression model. Journal of Applied Econometrics, 1(2), 127–141. https://doi.org/10.1002/jae.3950010203
   Google Scholar
• Ghobadi, K., & Mahmoudzadeh, H. (2021). Inferring linear feasible regions using inverse optimization. European Journal of Operational Research, 290(3), 829–843. https://doi.org/10.1016/j.ejor.2020.08.048
   Web of Science ®Google Scholar
• Gonçalves, R. E., Finardi, E. C., & da Silva, E. L. (2012). Applying different decomposition schemes using the progressive hedging algorithm to the operation planning problem of a hydrothermal system. Electric Power Systems Research, 83(1), 19–27. https://doi.org/10.1016/j.epsr.2011.09.006
   Web of Science ®Google Scholar
• Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press. http://www.deeplearningbook.org
   Google Scholar
• Grass, E., & Fischer, K. (2016). Two-stage stochastic programming in disaster management: A literature survey. Surveys in Operations Research and Management Science, 21(2), 85–100. https://doi.org/10.1016/j.sorms.2016.11.002
   Google Scholar
• Gul, S., Denton, B. T., & Fowler, J. W. (2015). A progressive hedging approach for surgery planning under uncertainty. INFORMS Journal on Computing, 27(4), 755–772. https://doi.org/10.1287/ijoc.2015.0658
   Web of Science ®Google Scholar
• Guo, A., Liu, Z., Li, S., & Li, H. (2017). Seismic performance assessment of highway bridge networks considering post-disaster traffic demand of a transportation system in emergency conditions. Structure and Infrastructure Engineering, 13(12), 1523–1537. https://doi.org/10.1080/15732479.2017.1299770
   Web of Science ®Google Scholar
• Guo, R., Yang, H., & Huang, H. (2018). Are we really solving the dynamic traffic equilibrium problem with a departure time choice? Transportation Science, 52(3), 603–620. https://doi.org/10.1287/trsc.2017.0764
   Web of Science ®Google Scholar
• Gurobi Optimization. (2021). Gurobi optimizer reference manual. http://www.gurobi.com.
   Google Scholar
• Hart, W. E., Laird, C. D., Watson, J., Woodruff, D. L., Hackebeil, G. A., Nicholson, B. L., & Siirola, J. D. (2017a). Pyomo–optimization modeling in python (2nd ed., Vol. 67). Springer Science & Business Media.
   Google Scholar
• Hart, W. E., Laird, C. D., Watson, J., Woodruff, D. L., Hackebeil, G. A., Nicholson, B. L., & Siirola, J. D. (2017b). Pyomo–optimization modeling in python: Second edition (Vol. 67). Springer Optimization and Its Applications.
   Google Scholar
• Hart, W. E., Watson, J., & Woodruff, D. L. (2011). Pyomo: Modeling and solving mathematical programs in python. Mathematical Programming Computation, 3(3), 219–260. https://doi.org/10.1007/s12532-011-0026-8
   Google Scholar
• Hong, S., Kim, K., Byeon, G., & Min, Y. (2017). A method to directly derive taste heterogeneity of travellers’ route choice in public transport from observed routes. Transportation Research Part B: Methodological, 95, 41–52. https://doi.org/10.1016/j.trb.2016.10.012
   Web of Science ®Google Scholar
• Hong, S., Kim, K., & Ko, S. (2021). Estimating heterogeneous agent preferences by inverse optimization in a randomized nonatomic game. Annals of Operations Research, 307(1–2), 207–228. https://doi.org/10.1007/s10479-021-04270-2
   Web of Science ®Google Scholar
• Horita, F. E., de Albuquerque, J. P., Degrossi, L. C., Mendiondo, E. M., & Ueyama, J. (2015). Development of a spatial decision support system for flood risk management in brazil that combines volunteered geographic information with wireless sensor networks. Computers & Geosciences, 80, 84–94. https://doi.org/10.1016/j.cageo.2015.04.001
   Web of Science ®Google Scholar
• Horita, F., & de Albuquerque, J. (2013). An approach to support decision-making in disaster management based on volunteer geographic information (VGI) and spatial decision support systems (SDSS). In Iscram.
   Google Scholar
• Hunter, J. D. (2007). Matplotlib: A 2d graphics environment. Computing in Science & Engineering, 9(3), 90–95. https://doi.org/10.1109/MCSE.2007.55
   Web of Science ®Google Scholar
• Hvattum, L. M., & Løkketangen, A. (2009). Using scenario trees and progressive hedging for stochastic inventory routing problems. Journal of Heuristics, 15(6), 527–557. https://doi.org/10.1007/s10732-008-9076-0
   Web of Science ®Google Scholar
• Kaviani, A., Thompson, R. G., Rajabifard, A., Griffin, G., & Chen, Y. (2015). A decision support system for improving the management of traffic networks during disasters. In 37th Australasian Transport Research Forum (ATRF).
   Google Scholar
• Keshavarz, A., Wang, Y., & Boyd, S. (2011). Imputing a convex objective function. In 2011 IEEE International Symposium on Intelligent Control (pp. 613–619).
   Google Scholar
• Kureshi, I., Theodoropoulos, G., Mangina, E., O’Hare, G., & Roche, J. (2015). Towards an info-symbiotic decision support system for disaster risk management. In 2015 IEEE/ACM 19th International Symposium on Distributed Simulation and Real Time Applications (DS-RT) (pp. 85–91).
   Google Scholar
• Lamghari, A., & Dimitrakopoulos, R. (2016). Progressive hedging applied as a metaheuristic to schedule production in open-pit mines accounting for reserve uncertainty. European Journal of Operational Research, 253(3), 843–855. https://doi.org/10.1016/j.ejor.2016.03.007
   Web of Science ®Google Scholar
• Li, J. Y.-M. (2021). Inverse optimization of convex risk functions. Management Science, 67(11), 7113–7141. https://doi.org/10.1287/mnsc.2020.3851
   Web of Science ®Google Scholar
• Liew, C. K. (1976). Inequality constrained least-squares estimation. Journal of the American Statistical Association, 71(355), 746–751. https://doi.org/10.1080/01621459.1976.10481560
   Web of Science ®Google Scholar
• Lu, J., Atamturktur, S., & Huang, Y. (2016). Bi-level resource allocation framework for retrofitting bridges in a transportation network. Transportation Research Record: Journal of the Transportation Research Board, 2550(1), 31–37. https://doi.org/10.3141/2550-05
   Google Scholar
• Luathep, P., Sumalee, A., Lam, W. H., Li, Z., & Lo, H. K. (2011). Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach. Transportation Research Part B: Methodological, 45(5), 808–827. https://doi.org/10.1016/j.trb.2011.02.002
   Web of Science ®Google Scholar
• Lu, J., Gupte, A., & Huang, Y. (2018). A mean-risk mixed integer nonlinear program for transportation network protection. European Journal of Operational Research, 265(1), 277–289. https://doi.org/10.1016/j.ejor.2017.07.025
   Web of Science ®Google Scholar
• Lu, Z., Meng, Q., & Gomes, G. (2016). Estimating link travel time functions for heterogeneous traffic flows on freeways. Journal of Advanced Transportation, 50(8), 1683–1698. https://doi.org/10.1002/atr.1423
   Web of Science ®Google Scholar
• Marcotte, P., & Patriksson, M. (2007). Traffic equilibrium. In Handbooks in operations research and management science (Vol. 14, pp. 623–713).
   Google Scholar
• MATLAB. (2020). Version 9.8.0.1417392 (R2020a) Update 4. The MathWorks, Inc.
   Google Scholar
• McKinney, W. (2010). Data structures for statistical computing in python. In Proceedings of the 9th Python in Science Conference (Vol. 445, pp. 51–56).https://doi.org/10.25080/Majora-92bf1922-00a
   Google Scholar
• Mohajerin Esfahani, P., Shafieezadeh-Abadeh, S., Hanasusanto, G. A., & Kuhn, D. (2018). Data-driven inverse optimization with imperfect information. Mathematical Programming, 167(1), 191–234. https://doi.org/10.1007/s10107-017-1216-6
   Web of Science ®Google Scholar
• Mohammadi, R., Ghomi, S. F., & Jolai, F. (2016). Prepositioning emergency earthquake response supplies: A new multi-objective particle swarm optimization algorithm. Applied Mathematical Modelling, 40(9–10), 5183–5199. https://doi.org/10.1016/j.apm.2015.10.022
   Web of Science ®Google Scholar
• Mulvey, J. M., & Vladimirou, H. (1991). Applying the progressive hedging algorithm to stochastic generalized networks. Annals of Operations Research, 31(1), 399–424. https://doi.org/10.1007/BF02204860
   Google Scholar
• Murty, K. G. (1983). Linear programming. Springer.
   Google Scholar
• NCEI. (2021). U.S. billion-dollar weather and climate disasters. https://www.ncdc.noaa.gov/billions/, https://doi.org/10.25921/stkw-7w73
   Google Scholar
• Nguyen, S., & Dupuis, C. (1984). An efficient method for computing traffic equilibria in networks with asymmetric transportation costs. Transportation Science, 18(2), 185–202. https://doi.org/10.1287/trsc.18.2.185
   Web of Science ®Google Scholar
• Noyan, N. (2012). Risk-averse two-stage stochastic programming with an application to disaster management. Computers & Operations Research, 39(3), 541–559. https://doi.org/10.1016/j.cor.2011.03.017
   Web of Science ®Google Scholar
• Oliphant, T. E. (2006). A guide to NumPy. Trelgol Publishing.
   Google Scholar
• Otsuka, R. P., Work, D. B., & Song, J. (2016). Estimating post-disaster traffic conditions using real-time data streams. Structure and Infrastructure Engineering, 12(8), 904–917. https://doi.org/10.1080/15732479.2015.1054293
   Web of Science ®Google Scholar
• Palsson, O. P., & Ravn, H. F. (1994). Stochastic heat storage problem—Solved by the progressive hedging algorithm. Energy Conversion and Management, 35(12), 1157–1171. https://doi.org/10.1016/0196-8904(94)90019-1
   Web of Science ®Google Scholar
• Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
   Web of Science ®Google Scholar
• Ratliff, L. J., Jin, M., Konstantakopoulos, I. C., Spanos, C., & Sastry, S. S. (2014). Social game for building energy efficiency: Incentive design. In 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton) (pp. 1011–1018). https://doi.org/10.1109/ALLERTON.2014.7028565
   Google Scholar
• Rockafellar, R. T., & Wets, R. J. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16(1), 119–147. https://doi.org/10.1287/moor.16.1.119
   Web of Science ®Google Scholar
• Rodríguez-Espíndola, O., Albores, P., & Brewster, C. (2018). Disaster preparedness in humanitarian logistics: A collaborative approach for resource management in floods. European Journal of Operational Research, 264(3), 978–993. https://doi.org/10.1016/j.ejor.2017.01.021
   Web of Science ®Google Scholar
• Ryan, S. M., Wets, R. J., Woodruff, D. L., Silva-Monroy, C., & Watson, J. (2013). Toward scalable, parallel progressive hedging for stochastic unit commitment. In Power and Energy Society General Meeting (PES), 2013 IEEE (pp. 1–5).
   Google Scholar
• Sahebjamnia, N., Torabi, S. A., & Mansouri, S. A. (2017). A hybrid decision support system for managing humanitarian relief chains. Decision Support Systems, 95, 12–26. https://doi.org/10.1016/j.dss.2016.11.006
   Web of Science ®Google Scholar
• Schult, D. A., Swart, P. (2008). Exploring network structure, dynamics, and function using networkx. In Proceedings of the 7th Python in Science Conferences (SciPy 2008) (Vol. 2008, pp. 11–16).
   Google Scholar
• Shahmoradi, Z., & Lee, T. (2022). Quantile inverse optimization: Improving stability in inverse linear programming. Operations Research, 70(4), 2538–2562. https://doi.org/10.1287/opre.2021.2143
   Web of Science ®Google Scholar
• Sheffi, Y. (1985). Urban transportation networks: Equilibrium analysis with mathematical programming methods. Prentice-Hall, Inc.
   Google Scholar
• Siri, E., Siri, S., & Sacone, S. (2020). A progressive traffic assignment procedure on networks affected by disruptive events. In 2020 European Control Conference (ECC) (pp. 130–135). https://doi.org/10.23919/ECC51009.2020.9143945
   Google Scholar
• Stoer, J. (1971). On the numerical solution of constrained least-squares problems. SIAM Journal on Numerical Analysis, 8(2), 382–411. https://doi.org/10.1137/0708038
   Web of Science ®Google Scholar
• Tai, K., Kizhakkedath, A., Lin, J., Tiong, R., & Sim, M. (2013). Identifying extreme risks in critical infrastructure interdependencies. In Proceedings of the International Symposium of Next Generation Infrastructure (pp. 1–4).
   Google Scholar
• Thai, J., & Bayen, A. M. (2018). Imputing a variational inequality function or a convex objective function: A robust approach. Journal of Mathematical Analysis and Applications, 457(2), 1675–1695. https://doi.org/10.1016/j.jmaa.2016.09.031
   Web of Science ®Google Scholar
• Thai, J., Hariss, R., & Bayen, A. (2015). A multi-convex approach to latency inference and control in traffic equilibria from sparse data. In 2015 American Control Conference (ACC) (pp. 689–695). https://doi.org/10.1109/ACC.2015.7170815
   Google Scholar
• Todini, E. (1999). An operational decision support system for flood risk mapping, forecasting and management. Urban Water, 1(2), 131–143. https://doi.org/10.1016/S1462-0758(00)00010-8
   Google Scholar
• US Department of Commerce. (1964). Bureau of public roads: Traffic assignment manual.
   Google Scholar
• Van Der Walt, S., Colbert, S. C., & Varoquaux, G. (2011). The NumPy array: A structure for efficient numerical computation. Computing in Science & Engineering, 13(2), 22–30. https://doi.org/10.1109/MCSE.2011.37
   Web of Science ®Google Scholar
• van Zuilekom, K., van Maarseveen, M., & van der Doef, M. (2005). A decision support system for preventive evacuation of people. In P. van Oosterom, S. Zlatanova, & E. M. Fendel (eds), Geo-information for disaster management (pp. 229–253). Berlin, Heidelberg: Springer.
   Google Scholar
• Veliz, F. B., Watson, J., Weintraub, A., Wets, R. J., & Woodruff, D. L. (2014). Stochastic optimization models in forest planning: A progressive hedging solution approach. Annals of Operations Research, 232(1), 259–274. https://doi.org/10.1007/s10479-014-1608-4
   Web of Science ®Google Scholar
• Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., & van der Walt, S. J. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in python. Nature Methods, 17(3), 261–272. doi:https://doi.org/10.1038/s41592-019-0686-2
   PubMed Web of Science ®Google Scholar
• Vovsha, P. (1997). The cross-nested logit model: Application to mode choice in the Tel-Aviv metropolitan area. Transportation Research Board.
   Google Scholar
• W. F. Programme. (2019). 2.3 Nepal road network. https://dlca.logcluster.org/display/public/DLCA/2.3+Nepal+Road+Network,
   Google Scholar
• Wächter, A., & Biegler, L. T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1), 25–57. https://doi.org/10.1007/s10107-004-0559-y
   Web of Science ®Google Scholar
• Wallace, W. A., & De Balogh, F. (1985). Decision support systems for disaster management. Public Administration Review, 45, 134–146. https://doi.org/10.2307/3135008
   Web of Science ®Google Scholar
• Wang, J., Peeta, S., & He, X. (2019). Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles. Transportation Research Part B: Methodological, 126, 139–168. https://doi.org/10.1016/j.trb.2019.05.022
   Web of Science ®Google Scholar
• Wardrop, J. G. (1952). Road paper. Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, 1(3), 325–362. https://doi.org/10.1680/ipeds.1952.11259
   Google Scholar
• Watson, J., & Woodruff, D. L. (2011). Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Computational Management Science, 8(4), 355–370. https://doi.org/10.1007/s10287-010-0125-4
   Google Scholar
• Watson, J., Woodruff, D. L., & Hart, W. E. (2012). Pysp: Modeling and solving stochastic programs in python. Mathematical Programming Computation, 4(2), 109–149. https://doi.org/10.1007/s12532-012-0036-1
   Google Scholar
• Winston, W. L. (1994). Operations research: Applications and algorithms. Wadsworth Inc.
   Google Scholar
• Wolfram—Alpha. (2021). Wolframalpha computational intelligence. https://www.wolframalpha.com/,
   Google Scholar
• Wong, W., & Wong, S. (2016). Network topological effects on the macroscopic bureau of public roads function. Transportmetrica A: Transport Science, 12(3), 272–296. https://doi.org/10.1080/23249935.2015.1129650
   Web of Science ®Google Scholar
• Yang, Z., Guo, L., & Yang, Z. (2019). Emergency logistics for wildfire suppression based on forecasted disaster evolution. Annals of Operations Research, 283(1–2), 917–937. https://doi.org/10.1007/s10479-017-2598-9
   Web of Science ®Google Scholar
• Yilmaz, Z., Aydemir-Karadag, A., & Erol, S. (2019). Finding optimal depots and routes in sudden-onset disasters: An earthquake case for erzincan. Transportation Journal, 58(3), 168–196. https://doi.org/10.5325/transportationj.58.3.0168
   Web of Science ®Google Scholar
• Zhang, J., Jian, J., & Tang, C. (2011). Inverse problems and solution methods for a class of nonlinear complementarity problems. Computational Optimization and Applications, 49(2), 271–297. https://doi.org/10.1007/s10589-009-9294-x
   Web of Science ®Google Scholar
• Zhang, J., Paschalidis, I. C. (2017). Data-driven estimation of travel latency cost functions via inverse optimization in multi-class transportation networks. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC) (pp. 6295–6300). https://doi.org/10.1109/CDC.2017.8264608
   Google Scholar
• Zhang, J., Pourazarm, S., Cassandras, C. G., & Paschalidis, I. C. (2018). The price of anarchy in transportation networks: Data-driven evaluation and reduction strategies. Proceedings of the IEEE, 106(4), 538–553. https://doi.org/10.1109/JPROC.2018.2790405
   Web of Science ®Google Scholar
• Zhang, H., & Ritchie, S. G. (1994). Real-time decision-support system for freeway management and control. Journal of Computing in Civil Engineering, 8(1), 35–51. https://doi.org/10.1061/(ASCE)0887-3801(1994)8:1(35)
   Web of Science ®Google Scholar
• Zheng, Y., & Ling, H. (2013). Emergency transportation planning in disaster relief supply chain management: A cooperative fuzzy optimization approach. Soft Computing, 17(7), 1301–1314. https://doi.org/10.1007/s00500-012-0968-4
   Web of Science ®Google Scholar