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Multi-criteria location planning for public facilities in tsunami-prone coastal areas. (English) Zbl 1163.90598
Summary: We present a model for multi-objective decision analysis with respect to the location of public facilities as schools in areas near to coasts, taking risks of inundation by tsunamis into account. A mathematical programming formulation with three objective functions is given. The first objective function is a weighted mean of a minisum and a maximum coverage criterion. The second objective function expresses risk by possible tsunami events; for quantifying this risk, a statistical model for tsunami occurrences by Kaistrenko and Pinegina is applied. The third criterion represents costs. For the solution of the multi-objective optimization problem, we propose a heuristic approach based on the NSGA-II algorithm and compare it with a decomposition technique where the region under consideration is partitioned into smaller sub-regions, and the problem is solved for each separate subregion either exactly or heuristically. Both approaches are tested on two real-life instances from southern Sri Lanka.

##### MSC:
 90B80 Discrete location and assignment 90C29 Multi-objective and goal programming 90C27 Combinatorial optimization 90B50 Management decision making, including multiple objectives
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##### References:
 [1] Altay N and Green WG (2007). OR/MS research in disaster operations management. Eur J Oper Res 175: 475–493 · Zbl 1137.90574 · doi:10.1016/j.ejor.2005.05.016 [2] Chalmet LG, Lemonidis L and Elzinga DJ (1986). An algorithm for the bi-criterion integer programming problem. Eur J Oper Res 25: 292–300 · Zbl 0592.90085 · doi:10.1016/0377-2217(86)90093-7 [3] Collette Y and Siarry P (2005). Three new metrics to measure the convergence of metaheuristics towards the Pareto frontier and the aesthetic of a set solutions in biobjective optimization. Comput Oper Res 32(4): 773–792 · Zbl 1071.90041 · doi:10.1016/j.cor.2003.08.017 [4] Czyzak P and Jaszkiewicz A (1996). A multiobjective metaheuristic approach to the localization of a chain of petrol stations by the capital budgeting model. Control Cybernet 25(1): 177–187 · Zbl 0847.90085 [5] Dalal J, Mohapatra PKJ and Mitra GC (2007). Locating cyclone shelters: a case. Disaster Prevent Manage 16(2): 235–244 · doi:10.1108/09653560710739559 [6] Deb K (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput 6(2): 182–197 · Zbl 05451853 · doi:10.1109/4235.996017 [7] Drezner Z (1995). On the conditional p-median problem. Comput Oper Res 22(5): 525–530 · Zbl 0830.90070 · doi:10.1016/0305-0548(94)00033-5 [8] Drezner T (2004). Location of casualty collection points. Environ Plann C Govern Policy 22: 899–912 · doi:10.1068/c13r [9] Drezner T, Drezner Z and Salhi S (2006). A multi-objective heuristic approach for the casualty collection points location. J Oper Res Soc 57(6): 727–734 · Zbl 1151.90585 · doi:10.1057/palgrave.jors.2602047 [10] Drezner T (2007) Casualty collection points: number and population covered. In: Proceedings of the southwest Decision Sciences Institute 38th annual meeting, pp 426–433 [11] Ehrgott M and Gandibleux X (2004). Approximative solution methods for multiobjective combinatorial optimization. Top 12(1): 1–63 · Zbl 1148.90300 · doi:10.1007/BF02578918 [12] Fiorucci P, Gaetani F, Minciardi R and Trasforini E (2005). Natural risk assessment and decision planning for disaster mitigation. Adv Geosci 2: 161–165 · doi:10.5194/adgeo-2-161-2005 [13] Gutjahr WJ (2005) Two metaheuristics for multiobjective stochastic combinatorial optimization. In: Proc. SAGA 2005 (Stochastic Algorithms: foundations and applications). Springer LNCS, vol 3777, pp 116–125 · Zbl 1159.68641 [14] House of Hope: 5000 Euro for the children at Tangalle, http://en.houseofhope.de/de;projects-sri-lanka;d:459.htm , February 12, 2007. [15] Institute for Integrative Conflict Transformation and Peace Building, http://www.iicp.at/ , February 12, 2007. [16] Jaszkiewicz A (2004) Evaluation of multiple objective metaheuristics. In: Gandibleux X et al. (eds) Metaheuristics for multiobjective optimization. Springer, Berlin, pp 66–89 · Zbl 1140.90488 [17] Kaistrenko V, Pinegina T: A Tsunami hazard parameter for Zhupanovo, Kamchatka, calculated using Historical and Paleotsunami Data. In: ITS 2001 Proceedings, Session 1, Number 1 – 11, pp 349–354 [18] Kongsomsaksakul S, Yang C and Chen A (2005). Shelter location-allocation model for flood evacuation planning. J Eastern Asia Soc Transp Stud 6: 4237–4252 [19] Marianov V, ReVelle C (1995) Siting emergency services. In: Drezner Z (ed) Facility location: a survey of applications and methods, pp 199–244 [20] Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s thesis, Department of Aeronautics and Astronautics, MIT, Cambridge [21] Stirn W (1996) Katastrophenhilfe in Entwicklungslaendern: Effizienzpotentiale der Deutschen Auslandshilfe. Lit Verlag, Hamburg [22] Ulungu EL, Teghem J, Fortemps P and Tuyttens D (1999). MOSA method: a tool for solving multiobjective combinatorial optimization problems. J Multi-Criteria Decis Anlays 8: 221–236 · Zbl 0935.90034 · doi:10.1002/(SICI)1099-1360(199907)8:4<221::AID-MCDA247>3.0.CO;2-O [23] Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. thesis, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio [24] Vincke P (1992). Multicriteria decision-aid. Wiley, Chichester · Zbl 0842.90003 [25] Yi W and Ă–zdamar L (2007). A dynamic logistics coordination model for evacuation and support in disaster response activities. Eur J Oper Res 179: 1177–1193 · Zbl 1163.90377 · doi:10.1016/j.ejor.2005.03.077 [26] Zitzler E and Thiele L (1999). Multiple objective evolutionary algorithms: a comparative case study and the strength of the pareto approach. IEEE Trans Evolut Comput 3(4): 257–271 · Zbl 05452215 · doi:10.1109/4235.797969 [27] Zitzler E, Thiele L, Laumanns M, Fonseca CM and da Fonseca VG (2003). Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evolut Comput 7(2): 117–132 · Zbl 05452216 · doi:10.1109/TEVC.2003.810758
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