Enumeration of Pareto Optima for a Bicriteria Evacuation Scheduling Problem

Kaouthar Deghdak, Vincent T'kindt, Jean-Louis Bouquard

Abstract

In this paper, we consider a large-scale evacuation problem after an important disaster. We model the evacuation of a region from a set of collection points to a set of capacitated shelters with the help of buses, thus leading to scheduling the evacuation operations by buses (Bus Evacuation Problem, BEP). The goal is twofold; first, minimizing the total evacuation time needed to bring the resident out of the endangered region, and secondly, minimizing the total exposure to danger. The resulting problem is a bicriteria problem. We propose a time-indexed formulation, as well as several approaches for finding both upper and lower bounds for BEP used within a branch and bound algorithm. In computational experiments, we analyse and evaluate the efficiency of the proposed solution algorithms.

References

  1. Berghman, L., Leus, R., and Spieksma, F. (2010). Optimal solutions for a dock assignment problem with trailer transportation. FBE Research Report KBI 1010, pages 1-28.
  2. Bish, D. R. (2011). Planning for a bus-based evacuation. OR Spectrum, 33(3):629-654.
  3. Bretschneider, S. (2012). Mathematical Models for Evacuation Planning in Urban Areas. Springer- Heidelberg New York Dordrecht London.
  4. Chalmet, L., Francis, R., and Saunders, P. (1982). Network models for building evacuation. Fire Technology, 18(1):90-113.
  5. Chiu, Y.-C., Zheng, H., Villalobos, J., and Gautam, B. (2007). Modeling no-notice mass evacuation using a dynamic traffic flow optimization model. IIE Transactions, 39(1):83-94.
  6. Choi, W., Hamacher, H., and Tufekci, S. (1988). Modeling of building evacuation problems by network flows with side constraints. European Journal of Operational Research, 35(1):98 - 110.
  7. Daganzo, C. F. (1994). The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B, 28(4):269.
  8. Della Croce, F., Grosso, A., and Salassa, F. (2014). A matheuristic approach for the two-machine total completion time flow shop problem. Annals of Operations Research, 213(1):67-78.
  9. Goerigk, M., Deghdak, K., and T'Kindt, V. (2013a). A two-stage robustness approach to evacuation planning with buses. Technical report, Technische Universität Kaiserslautern.
  10. Goerigk, M. and Gruen, B. (2014). A robust bus evacuation model with delayed scenario information. OR Spectrum, pages 1-26.
  11. Goerigk, M., Gruen, B., and Hessler, P. (2013b). Branch and bound algorithms for the bus evacuation problem. Computers & Operations Research, 40(12):3010- 3020.
  12. Hamacher, H. W. and Tjandra, S. A. (2001). Mathematical modeling of evacuation problems: A state of the art. In In Pedestrian and Evacuation Dynamics (Schreckinberg, M. and Sharma, S. D. eds), volume 1964, pages 227-266. Springer.
  13. Han, L. D., F.Yuan, Chin, S.-M., and Hwang, H. (2006). Proposed framework for simultaneous optimization of evacuation traffic destination and route assignment. Transportation Research Record: Journal of the Transportation Research Board, 1964(1):50 - 58.
  14. Jaszkiewicz, A. (2004). Evaluation of multiple objective metaheuristics. In Metaheuristics for Multiobjective Optimisation, volume 535, pages 65-89. Springer Berlin Heidelberg.
  15. Kim, S., B.George, and Shekhar, S. (2007). Gis 7807: Proceedings of the 15th annual acm international symposium on advances in geographic information systems. New York, NY, USA. ACM.
  16. Lim, G., S.Zangeneh, Baharnemati, M., and Assavapokee, T. (2009). A simple binary search algorithm for short notice evacuation scheduling and routing.
  17. Liu, Y., Lai, X., and Chang, G. (2006). Two-level integrated optimization system for planning of emergency evacuation. Journal of Transportation Engineering, 132(10):800-807.
  18. Lu, Q., George, B., and Shekhar, S. (2005). Capacity constrained routing algorithms for evacuation planning: A summary of results. In Bauzer Medeiros, C., Egenhofer, M., and Bertino, E., editors, Advances in Spatial and Temporal Databases, volume 3633 of Lecture Notes in Computer Science, pages 291-307. Springer Berlin Heidelberg.
  19. Mamada, S., Uno, T., Makino, K., and Fujishige, S. (2005). A tree partitioning problem arising from an evacuation problem in tree dynamic networks. J Oper Res Soc Jpn, 48(3):196-206.
  20. Ng, M. and Waller, S. T. (2010). Reliable evacuation planning via demand inflation and supply deflation. Transportation Research Part E: Logistics and Transportation Review, 46(6):1086 - 1094.
  21. Peeta, S. and Ziliaskopoulos, A. K. (2001). Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics, 1(3- 4):233.
  22. Pisinger, D. (1995). Algorithms for knapsack problems.
  23. Sattayhatewa, P. and Ran, B. (2000). Developing A Dynamic Traffic Management Model For Nuclear Power Plant Evacuation. Transportation Research Board, 79th Annual Meeting.
  24. Sheffi, Y., Mahmassani, H. S., and Powell, W. (1982). A transportation network evacuation model. Transportation Research Part A, 16(1):209-218.
  25. T'kindt, V. and Billaut, J.-C. (2006). Multicriteria scheduling: theory, models and algorithms. Springer-Verlag Berlin Heidelberg, 2nd edition.
  26. Yamada, T. (1996). A network flow approach to a city emergency evacuation planning. International Journal of Systems Science, 27(10):931-936.
  27. Yazici, M. and Ozbay, K. (2007). Impact of probabilistic road capacity constraints on the spatial distribution of hurricane evacuation shelter capacities. Transport Res Rec: J Transport Res Board, 2022(1):55-62.
  28. Ziliaskopoulos, A. K. (2000). A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Science, 34(1):37-49.
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Paper Citation


in Harvard Style

Deghdak K., T'kindt V. and Bouquard J. (2015). Enumeration of Pareto Optima for a Bicriteria Evacuation Scheduling Problem . In Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-075-8, pages 162-171. DOI: 10.5220/0005221201620171


in Bibtex Style

@conference{icores15,
author={Kaouthar Deghdak and Vincent T'kindt and Jean-Louis Bouquard},
title={Enumeration of Pareto Optima for a Bicriteria Evacuation Scheduling Problem},
booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2015},
pages={162-171},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005221201620171},
isbn={978-989-758-075-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Enumeration of Pareto Optima for a Bicriteria Evacuation Scheduling Problem
SN - 978-989-758-075-8
AU - Deghdak K.
AU - T'kindt V.
AU - Bouquard J.
PY - 2015
SP - 162
EP - 171
DO - 10.5220/0005221201620171