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Erschienen in: The Journal of Supercomputing 10/2017

16.03.2017

A GPU-based genetic algorithm for the p-median problem

verfasst von: Bader F. AlBdaiwi, Hosam M. F. AboElFotoh

Erschienen in: The Journal of Supercomputing | Ausgabe 10/2017

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Abstract

The p-median problem is a well-known NP-hard problem. Many heuristics have been proposed in the literature for this problem. In this paper, we exploit a GPGPU parallel computing platform to present a new genetic algorithm implemented in CUDA and based on a pseudo-Boolean formulation of the p-median problem. We have tested the effectiveness of our algorithm using a Tesla K40 (2880 CUDA cores) on 290 different benchmark instances obtained from OR-Library, discrete location problems benchmark library, and benchmarks introduced in recent publications. The algorithm succeeded in finding optimal solutions for all instances except for two OR-library instances, namely pmed 30 and pmed 40, where better than 99.9% approximations were obtained.

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Fußnoten
1
We shall use distance and cost interchangeably.
 
Literatur
3.
Zurück zum Zitat NVIDIA (2015) CURAND Library. Programming guide. PG-05328-050_v7.5. NVIDIA NVIDIA (2015) CURAND Library. Programming guide. PG-05328-050_v7.5. NVIDIA
5.
Zurück zum Zitat AlBdaiwi BF, Goldengorin B, Sierksma G (2009) Equivalent instances of the simple plant location problem. Comput Math Appl 57(5):812–820MathSciNetCrossRefMATH AlBdaiwi BF, Goldengorin B, Sierksma G (2009) Equivalent instances of the simple plant location problem. Comput Math Appl 57(5):812–820MathSciNetCrossRefMATH
7.
Zurück zum Zitat Bargos FF, de Queiroz Lamas W, Bargos DC, Neto MB, Pardal PCPM (2016) Location problem method applied to sugar and ethanol mills location optimization. Renew Sustain Energy Rev 65:274–282CrossRef Bargos FF, de Queiroz Lamas W, Bargos DC, Neto MB, Pardal PCPM (2016) Location problem method applied to sugar and ethanol mills location optimization. Renew Sustain Energy Rev 65:274–282CrossRef
9.
Zurück zum Zitat Biesinger B, Hu B, Raidl G (2015) A hybrid genetic algorithm with solution archive for the discrete (r|p)-centroid problem. J Heuristics 21(3):391–431CrossRefMATH Biesinger B, Hu B, Raidl G (2015) A hybrid genetic algorithm with solution archive for the discrete (r|p)-centroid problem. J Heuristics 21(3):391–431CrossRefMATH
10.
Zurück zum Zitat Bozkaya B, Zhang J, Erkut E (2002) An efficient genetic algorithm for the p-median problem. Facil Locat Appl Theory 29: 179–205 Bozkaya B, Zhang J, Erkut E (2002) An efficient genetic algorithm for the p-median problem. Facil Locat Appl Theory 29: 179–205
11.
Zurück zum Zitat Daskin MS, Maass KL (2015) The p-median problem. In: Laporte G, Nickel S, da Gama FS (eds) Location science, chapter 2. Springer, Berlin, pp 21–45 Daskin MS, Maass KL (2015) The p-median problem. In: Laporte G, Nickel S, da Gama FS (eds) Location science, chapter 2. Springer, Berlin, pp 21–45
12.
Zurück zum Zitat Drezner Z, Brimberg J, Mladenović N, Salhi S (2015) New heuristic algorithms for solving the planar p-median problem. Comput Oper Res 62:296–304MathSciNetCrossRefMATH Drezner Z, Brimberg J, Mladenović N, Salhi S (2015) New heuristic algorithms for solving the planar p-median problem. Comput Oper Res 62:296–304MathSciNetCrossRefMATH
13.
Zurück zum Zitat El-Mihoub TA, Hopgood AA, Nolle L, Battersby A (2006) Hybrid genetic algorithms: a review. Eng Lett 13(2):124–137 El-Mihoub TA, Hopgood AA, Nolle L, Battersby A (2006) Hybrid genetic algorithms: a review. Eng Lett 13(2):124–137
14.
Zurück zum Zitat Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109CrossRef Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109CrossRef
15.
Zurück zum Zitat Goldengorin B, Kocheturov A, Pardalos PM (2014) A Pseudo-Boolean approach to the market graph analysis by means of the p-median model. In: Clusters, orders, and trees: methods and applications. Springer, pp 77–89 Goldengorin B, Kocheturov A, Pardalos PM (2014) A Pseudo-Boolean approach to the market graph analysis by means of the p-median model. In: Clusters, orders, and trees: methods and applications. Springer, pp 77–89
16.
Zurück zum Zitat Goldengorin B, Krushinsky D, Pardalos P (2013) Cell formation in industrial engineering, theory, algorithms and experiments. Springer, BerlinCrossRefMATH Goldengorin B, Krushinsky D, Pardalos P (2013) Cell formation in industrial engineering, theory, algorithms and experiments. Springer, BerlinCrossRefMATH
18.
Zurück zum Zitat Hammer PL (1968) Plant location-a pseudo-Boolean approach. Isr J Technol 6(5):330–332MATH Hammer PL (1968) Plant location-a pseudo-Boolean approach. Isr J Technol 6(5):330–332MATH
19.
Zurück zum Zitat HP Inc. (2015) QuickSpecs. HP Z820 workstation. c04111526-DA-14264-Worldwide-Version 48. HP Inc., USA HP Inc. (2015) QuickSpecs. HP Z820 workstation. c04111526-DA-14264-Worldwide-Version 48. HP Inc., USA
20.
Zurück zum Zitat Jaillet P, Song G, Yu G (1996) Airline network design and hub location problems. Locat Sci 4(3):195–212CrossRefMATH Jaillet P, Song G, Yu G (1996) Airline network design and hub location problems. Locat Sci 4(3):195–212CrossRefMATH
21.
Zurück zum Zitat Jaramillo JH, Bhadury J, Batta R (2002) On the use of genetic algorithms to solve location problems. Comput Oper Res 29(6):761–779MathSciNetCrossRefMATH Jaramillo JH, Bhadury J, Batta R (2002) On the use of genetic algorithms to solve location problems. Comput Oper Res 29(6):761–779MathSciNetCrossRefMATH
22.
23.
Zurück zum Zitat Kariv O, Hakimi S (1979) An algorithmic approach to network location problems. II: The p-medians. SIAM J Appl Math 37(3):539–560MathSciNetCrossRefMATH Kariv O, Hakimi S (1979) An algorithmic approach to network location problems. II: The p-medians. SIAM J Appl Math 37(3):539–560MathSciNetCrossRefMATH
24.
Zurück zum Zitat Kazakovtsev LA, Orlov V, Stupina AA, Kazakovtsev V (2015) Modified genetic algorithm with greedy heuristic for continuous and discrete p-median problems. Facta Univ Ser Math Inform 30(1):89–106 Kazakovtsev LA, Orlov V, Stupina AA, Kazakovtsev V (2015) Modified genetic algorithm with greedy heuristic for continuous and discrete p-median problems. Facta Univ Ser Math Inform 30(1):89–106
25.
26.
Zurück zum Zitat Lim G, Ma L (2013) GPU-based parallel vertex substitution algorithm for the p-median problem. Comput Ind Eng 64(1):381–388CrossRef Lim G, Ma L (2013) GPU-based parallel vertex substitution algorithm for the p-median problem. Comput Ind Eng 64(1):381–388CrossRef
27.
Zurück zum Zitat Ma L, Lim G (2011) GPU-based parallel computational algorithms for solving p-median problem. In: IIE Annual Conference. Proceedings. Institute of Industrial Engineers-Publisher, p 1 Ma L, Lim G (2011) GPU-based parallel computational algorithms for solving p-median problem. In: IIE Annual Conference. Proceedings. Institute of Industrial Engineers-Publisher, p 1
29.
Zurück zum Zitat Mitchell M (1998) An introduction to genetic algorithms. MIT Press, CambridgeMATH Mitchell M (1998) An introduction to genetic algorithms. MIT Press, CambridgeMATH
30.
Zurück zum Zitat Mladenović N, Brimberg J, Hansen P, Moreno-Pérez JA (2007) The p-median problem: a survey of metaheuristic approaches. Eur J Oper Res 179(3):927–939MathSciNetCrossRefMATH Mladenović N, Brimberg J, Hansen P, Moreno-Pérez JA (2007) The p-median problem: a survey of metaheuristic approaches. Eur J Oper Res 179(3):927–939MathSciNetCrossRefMATH
31.
Zurück zum Zitat NVIDIA (2013) Tesla K40 active accelerator. Board specification. BD-06949-001_v03. NVIDIA NVIDIA (2013) Tesla K40 active accelerator. Board specification. BD-06949-001_v03. NVIDIA
32.
Zurück zum Zitat Rebreyend P, Lemarchand L, Euler R (2015) A computational comparison of different algorithms for very large p-median problems. In: 15th European Conference on Evolutionary Computation in Combinatorial Optimization. Springer, pp 13–24 Rebreyend P, Lemarchand L, Euler R (2015) A computational comparison of different algorithms for very large p-median problems. In: 15th European Conference on Evolutionary Computation in Combinatorial Optimization. Springer, pp 13–24
34.
Zurück zum Zitat Ren Y, Awasthi A (2015) Investigating metaheuristics applications for capacitated location allocation problem on logistics networks. In: Chaos modeling and control systems design. Springer, pp 213–238 Ren Y, Awasthi A (2015) Investigating metaheuristics applications for capacitated location allocation problem on logistics networks. In: Chaos modeling and control systems design. Springer, pp 213–238
35.
Zurück zum Zitat Resende MGC, Werneck RF (2004) A hybrid heuristic for thep-median problem. J Heuristics 10(1):59–88CrossRefMATH Resende MGC, Werneck RF (2004) A hybrid heuristic for thep-median problem. J Heuristics 10(1):59–88CrossRefMATH
36.
Zurück zum Zitat Stanimirović Z (2012) A genetic algorithm approach for the capacitated single allocation p-hub median problem. Comput Inform 29(1):117–132MATH Stanimirović Z (2012) A genetic algorithm approach for the capacitated single allocation p-hub median problem. Comput Inform 29(1):117–132MATH
37.
Zurück zum Zitat Todosijević R, Urošević D, Mladenović N, Hanafi S (2015) A general variable neighborhood search for solving the uncapacitated r-allocation p-hub median problem. Optim Lett 23: 1–13 Todosijević R, Urošević D, Mladenović N, Hanafi S (2015) A general variable neighborhood search for solving the uncapacitated r-allocation p-hub median problem. Optim Lett 23: 1–13
Metadaten
Titel
A GPU-based genetic algorithm for the p-median problem
verfasst von
Bader F. AlBdaiwi
Hosam M. F. AboElFotoh
Publikationsdatum
16.03.2017
Verlag
Springer US
Erschienen in
The Journal of Supercomputing / Ausgabe 10/2017
Print ISSN: 0920-8542
Elektronische ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-017-2006-x

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