Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach
Tóm tắt
This paper considers evacuation via surface transportation networks in an uncertain environment. We focus on demand uncertainty which can lead to significant infeasibility cost during evacuation, where loss of life or property may appear. We develop a robust linear programming model based on a robust optimization approach where hard constraints are guaranteed within an appropriate uncertainty set. The robust counterpart solutions have been shown tractable. We show that the robustness in evacuation is important and a robust solution outperforms a nominal deterministic solution in both quality and feasibility.
Tài liệu tham khảo
Ahuja RK, Magnanti TL, Orlin JB (2003) Network flows: Theory, algorithms and applications. Pretince Hall, New Jersey
Atamturk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55:662–673
Bazaraa MS, Jarvis JJ, Sherali HD (2005) Linear programming and network flows. Wiley, New Jersey
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805
Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424
Ben-Tal A, Nemirovski A (2002) Robust optimization—methodology and applications. Math Program 92:453–480
Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math Program 99:351–376
Ben-Tal A, Golany B, Nemirovski A (2005) Retailer-supplier flexible commitments contracts: a robust optimization approach. Manuf Serv Oper Manag 7:248–271
Ben-Tal A, Ghaoui LE, Nemirovski A (2007) Robust optimization. Available via http://www2.isye.gatech.edu/~nemirovs/RBIntroTOC.pdf. Accessd 1 Dec 2008
Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98:49–71
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53
Bertsimas D, Perakis G (2005) Robust and adaptive optimization: a tractable approach to optimization under uncertainty. NSF/CMMI/OR 0556106
Bertsimas D, Brown DB, Caramanis C (2007) Theory and applications of robust optimization. Available via http://users.ece.utexas.edu/~cmcaram/pubs/RobustOptimizationSV.pdf. Accessd 1 Dec 2008
Chiu YC, Zheng H, Villalobos J, Gautam B (2007) Modeling no-notice mass evacuation using a dynamic traffic flow optimization model. IIE Trans 39:83–94
Daganzo CF (1994) The cell transmission model part I: a simple dynamic representation of highway traffic. Transp Res Part B 28:269–287
Daganzo CF (1995) The cell transmission model part II: network traffic. Transp Res Part B 29:79–93
Erera AL, Morales JC, Savelsbergh M (2007) Robust optimization for empty repositioning problems, to appear in Oper Res
Ghaoui LE, Oustry F, AitRami M (1997) A cone complementarity linearization algorithm for static output-feedback and related problems. IIE Trans Autom Control 42:1171–1176
Ghaoui LE, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper Res 51:543–556
Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. J Transp Res Board 2029:58–71
Li Y, Waller ST, Ziliaskopoulos T (2003) A decomposition scheme for system optimal dynamic traffic assignment models. Netw Spat Econ 3:441–455
Mahmassani HS (2001) Dynamic network traffic assignment and simulation methodology for advanced System management applications. Netw Spat Econ 1:267–292
Mudchanatongsuk S, Ordonez F, Liu J (2008) Robust solutions for network design under transportation cost and demand uncertainty. J Oper Res Soc 59:652–662
Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281
Ordonez F, Zhao J (2007) Robust capacity expansion of network flows. Netw 50:136–145
Pearce V (2008) ITS to the rescue. Avaiable via http://www.its.dot.gov/eto/eto_rescue.htm. Accessed 1 Dec 2008
Peeta S, Zhou C (1999) Robustness of the off-line a priori stochastic dynamic traffic assignment solution for on-line operations. Transp Res Part C 7:281–303
Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Netw Spat Econ 1:233–265
Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157
Tuydes H (2005) Network traffic management under disaster conditions. Ph.D Dissertation, Northwestern University, Evanston, IL
Ukkusuri SV, Waller ST (2008) Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions. Netw Spat Econ 8:383–406
Waller ST, Ziliaskopoulos AK (2006) A chance-constrained based stochastic dynamic traffic assignment model: analysis, formulation and solution algorithms. Transp Res Part C 14:418–427
Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34:37–49