Abstract
We proposed new genetic algorithms (GAs) to address well-known p-median problem in continuous space. Two GA approaches with different replacement procedures are developed to solve this problem. To make the approaches more efficient in finding near-optimal solution two hybrid algorithms are developed combining the new GAs and a traditional local search heuristic. The performance of the newly developed models is compared to that of the traditional alternating location-allocation heuristics by numerical simulation and it is found that the models are effective in finding optimum facility locations.
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References
Alp O, Erkut E, Drezner D (2003) An efficient genetic algorithm for the p-median problem. Ann Oper Res 122:21–42 doi:10.1023/A:1026130003508
Aytug H, Khouja M, Vergara FE (2003) Use of genetic algorithms to solve production and operations management problems: a review. Int J Prod Res 41(17):3955–4009 doi:10.1080/00207540310001626319
Brimberg J, Salhi S (2005) A continuous location-allocation problem with zone-dependent fixed cost. Ann Oper Res 136:99–115 doi:10.1007/s10479-005-2041-5
Chakraborty P, Deb K, Subramaniyam PS (1995) Optimal scheduling of urban transit systems using genetic algorithms. J Transp Eng 12(6):544–553 doi:10.1061/(ASCE)0733-947X(1995)121:6(544)
Chaudhry SS (2006) A genetic algorithm approach to solving the anti-covering location problem. Expert Systems: International Journal of Knowledge Engineering and Neural Networks 23(5):251–257 doi:10.1111/j.1468-0394.2006.00407.x
Chaudhry SS, Luo W (2005) Application of genetic algorithms in production and operations management: a review. Int J Prod Res 43(19):2005 doi:10.1080/00207540500143199
Chaudhry SS, Varano MW, Xu L (2000) System research, genetic algorithms, and information systems. Syst Res Behav Sci 17:149–162
Chaudhry SS, He S, Chaudhry PE (2003) Solving a class of facility location problems using genetic algorithm. Expert Systems: International Journal of Knowledge Engineering and Neural Networks 20:86–91 doi:10.1111/1468-0394.00229
Chen CL, Lin RH, Zhang J (2003) Genetic algorithms for MD-optimal follow-up designs. Comput Oper Res 30:233–252 doi:10.1016/S0305-0548(01)00093-4
Cooper L (1963) Location-allocation problem. Oper Res 11:331–343
Drezner Z, Klamroth K, Schöbel A, Wesolowsky G (2001) The Weber problem. In: Drezner Z, Hamacher HW (eds) Facility location: applications and theory. Springer, Berlin
Feng CM, Lin JJ (1999) Using a genetic algorithm to generate alternative sketch maps for urban planning. Comput Environ Urban Syst 23:91–108 doi:10.1016/S0198-9715(99)00004-6
Fung RY, Tang J, Wang D (2002) Extension of a hybrid genetic algorithm for nonlinear programming problems with equality and inequality constraints. Comput Oper Res 29:261–274 doi:10.1016/S0305-0548(00)00068-X
Goldberg DE (1989) Genetic Algorithms in search, Optimization & Machine Learning. Addison-Wesley, Wokingham
Goldengorin B, Ghosh D, Sierksma G (2004) Branch and peg algorithms for the simple plant location problem. Comput Oper Res 31:241–255 doi:10.1016/S0305-0548(02)00190-9
Gong D, Gen M, Xu W, Yamazaki G (1995) Hybrid evolutionary method for obstacle location-allocation. Comput Ind Eng 29(1–4):525–523 doi:10.1016/0360-8352(95)00128-N
Gong D, Gen M, Yamazaki G, Xu W (1997) Hybrid evolutionary method for capacitated location-allocation problem. Comput Ind Eng 33(3–4):577–580 doi:10.1016/S0360-8352(97)00197-6
Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13:462–475
Ho W, Ji P (2003) Component scheduling for chip shooter machines: a hybrid genetic algorithm approach. Comput Oper Res 30:2175–2189 doi:10.1016/S0305-0548(02)00129-6
Holland JH (1975) Adaptations in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI
Houck CR, Joines JA, Kay MG (1996) Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems. Comput Oper Res 23(6):587–596 doi:10.1016/0305-0548(95)00063-1
Jabalameli MS, Ghaderi A (2008) Hybrid algorithms for the uncapacitated continuous location-allocation problem. Int J Adv Manuf Technol 37:202–209 doi:10.1007/s00170-007-0944-9
Jaramillo JH, Bhadury J, Batta R (2002) On the use of genetic algorithms to solve location problems. Comput Oper Res 29(6):761–779
Kelly JD, Davis L (1991) Hybridizing the genetic algorithm and the K nearest neighbors classification algorithm. In Proceedings of the 4th international conference on genetic algorithms, pp. 370–383
Krzanowski RM, Raper J (1999) Hybrid genetic algorithm for transmitter location in wireless networks. Comput Environ Urban Syst 23:359–382 doi:10.1016/S0198-9715(99)00030-7
Lorena LAN, Senne ELF (2003) A column generation approach to capacitated p-median problems. URL: http://www.lac.inpe.br/~lorena/senne/col-gen-CPMP-final.pdf
Maniruzzaman KM, Okabe A, Asami Y (2001) GIS for cyclone disaster management in Bangladesh. Geogr Environ Model 5(2):123–131 doi:10.1080/13615930120086087
Michalewicz M (1992) Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin
Mladenovic N, Brimberg J, Hansen P, Moreno-Perez JA (2007) The p-median problem: a survey of metaheuristic approaches. Eur J Oper Res 179:927–939 doi:10.1016/j.ejor.2005.05.034
Moreno-Perez JA, Roda Garcia JL, Moreno-Vega JM (1994) A parallel genetic algorithm for the discrete p-median problem. Stud Locat Anal 7:131–141
Okabe A, Boots B, Sugihara K (1992) Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley & Sons Ltd., Chichester, England
Plastria F (1995) Continuous Location Problems. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer-Verlag, New York, pp 225–262
Reese J (2006) Solution methods for the p-median problem: an annotated bibliography. Networks 48(4):125–142
Rolland E, Gupta R (2004) New linkages between GIS and combinatorial optimization. URL: http://hsb.baylor.edu/ramsower/ais.ac.96/papers/rolland.htm - 15k
ReVelle C, Swain R (1970) Central Facilities Location. Geogr Anal 2:30–42
Revees CR (1997) Genetic algorithms for the operations researcher. Informs J Comput 9:231–250
Salhi S, Gamal MDH (2003) A genetic algorithm based approach for the uncapacitated continuous location-allocation problem. Ann Oper Res 123:203–222 doi:10.1023/A:1026131531250
Senne ELF, Lorena LAN (1999) A lagrangean/surrogate approach to p-median problems. URL: http://www.lac.inpe.br/~lorena/pmed99.pdf
Xu P (1999) Solving a joint inventory-location problem by a substitution algorithm. Undergraduate senior thesis, Northwestern University
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Neema, M.N., Maniruzzaman, K.M. & Ohgai, A. New Genetic Algorithms Based Approaches to Continuous p-Median Problem. Netw Spat Econ 11, 83–99 (2011). https://doi.org/10.1007/s11067-008-9084-5
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DOI: https://doi.org/10.1007/s11067-008-9084-5