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Median line location problem with positive and negative weights and Euclidean norm

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Abstract

Let n existing facilities be given in the plane. The classical version of the median line location problem asks to find a line L in the plane, so that the sum of the weighted distances from L to all existing facilities is minimized. We consider the semi-obnoxious case, where every point has either a positive or a negative weight. In this paper, we discuss some properties of semi-obnoxious median line location problem with Euclidean norm and propose a particle swarm optimization algorithm for this problem.

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References

  1. Abido MA (2002) Optimal power flow using particle swarm optimization. Int J Elect Power Energy Syst 24(7):563–571

    Article  Google Scholar 

  2. Beasley JE (1990) OR-Library: distributing test problems by electronic mail. J Operat Res Soc 41:1069–1072

    Google Scholar 

  3. Berman O, Wang Q (2008) Locating a semi-obnoxious facility with expropriation. Comput Operat Res 35:392–403

    Article  MATH  MathSciNet  Google Scholar 

  4. Blanquero R, Carrizosa E, Schobel A, Scholz D (2011) A global optimization procedure for the location of a median line in the three-dimensional space. Eur J Operat Res 215:14–20

    Article  MATH  MathSciNet  Google Scholar 

  5. Brimberg J, Juel H, Schobel A (2003) Properties of three-dimensional median line location models. Ann Operat Res 122:71–85

    Article  MATH  MathSciNet  Google Scholar 

  6. Burkard RE, Çela E, Dollani H (2000) 2-Median in trees with pos/neg weights. Discrete Appl Math 105:51–71

    Article  MATH  MathSciNet  Google Scholar 

  7. Burkard RE, Krarup J (1998) A linear algorithm for the pos/neg-weighted 1-median problem on a cactus. Computing 60:193–215

    Article  MATH  MathSciNet  Google Scholar 

  8. Carrizosa E, Plastria F (1999) Location of semi-obnoxious facilities. Stud Locat Stud 12:1–27

    MATH  MathSciNet  Google Scholar 

  9. Chen DZ, Wang H (2009) Locating an Obnoxious line among planar objects. Dong Y , Du D-Z , Ibarra O (eds) ISAAC 2009, LNCS 5878, pp. 740–749

  10. Clerc M (2004) Discrete particle swarm optimization, illustrated by the traveling salesman problem. In: Onwubolu GC, Babu BV (eds) New optimization techniques in engineering. Springer, Heidelberg, pp 219–239

  11. Drezner Z, Wesolowsky GO (1989) Location of an obnoxious route. J Operat Res Soc 40(11):1011–1018

    MATH  Google Scholar 

  12. Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, Nagoya, Japan, pp 39–43

  13. Fathali J, Kakhki HT, Burkard RE (2006) An ant colony algorithm for the pos/neg weighted p-median problem. Cent Eur J Operat Res, 14:229–246

    Article  MATH  MathSciNet  Google Scholar 

  14. Kennedy J, Eberhart R, Shi Y (2001) Swarm intelligence, Morgan Kaufmann Publishers, San Francisco

    Google Scholar 

  15. Lee DT, Ching YT (1985) The power of geometric duality revisited. Inf Process Lett 21:117–122

    Article  MATH  MathSciNet  Google Scholar 

  16. MacKinnon R, Barber GM (1972) A new approach to network generation and map representation: the linear case of the location-allocation problem. Geogr Anal 4:156–168

    Article  Google Scholar 

  17. Megiddo N, Tamir A (1983) Finding least-distance lines, SIAM J Algeb Disc Methods, 4:207–211

    Article  MATH  MathSciNet  Google Scholar 

  18. Mendes R, Cortez P, Rocha M, Neves J, Particle swarms for feedforward neural network training. In: Proceedings of the international joint conference on neural networks (IJCNN 2002), pp 1895–1899

  19. Morris JG, Norback JP (1980) A simple approach to linear facility location. Transport Sci 14:1–8

    Article  Google Scholar 

  20. Morris JG, Norback JP (1983) Linear facility location-solving extensions on the basic problems. Eur J Oper Res 12:90–94

    Article  MATH  MathSciNet  Google Scholar 

  21. Ohsawa Y, Tamura K (2003) Efficient location for a semi-obnoxious facility. Ann Operat Res 123:173–188

    Article  MATH  MathSciNet  Google Scholar 

  22. Parsopoulos KE, Papageorgiou EI, Groumpos PP, Vrahatis MN, (2003) A first study of fuzzy cognitive maps learning using particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC 2003), Canbella, Australia, pp 1440–1447

  23. Poli R, Kennedy J, Blackwell T, (2007) Particle swarm optimization an overview. Swarm Intell 1:33–57

    Article  Google Scholar 

  24. Schobel A (1999) Locating lines and hyperplanes: theory and algorithms. Kluwer, Dordrecht

    Book  Google Scholar 

  25. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of IEEE international conference on evolutionary computation, Anchorage, AK, pp 69–73

  26. Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Proceedings of congress on evolutionary computation, Washington, DC, pp 1945–1949

  27. Tandon V, El-Mounayri H, Kishawy H (2002). NC end milling optimization using evolutionary computation. Int J Mach Tools Manuf 42:595–605

    Article  Google Scholar 

  28. Venayagamoorthy GK, Doctor S (2004) Navigation of mobile sensors using PSO and embedded PSO in a fuzzy logic controller. In: Proceedings of the 39th IEEE IAS annual meeting on industry applications, Seattle, USA, pp 1200–1206

  29. Van den Bergh F, Engelbrecht AP, (2000) Cooperative learning in neural network using particle swarm optimizers. S Afr Comput J 26:84–90

    Google Scholar 

  30. Wesolowsky GO (1975) Location of the median line for weighted points. Environ Plann A7:163–170

    Article  Google Scholar 

  31. Yapicioglu H, Smith AE, Dozier G (2007) Solving the semi-desirable facility location problem using bi-objective particle swarm. Eur J Operat Res 177:733–749

    Article  MATH  Google Scholar 

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Acknowledgments

The authors would like to express their sincere gratitude to the anonymous referees for their careful reading of the manuscript and their constructive comments which resulted in the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahrood University of Technology, University Blvd., Shahrood, Iran

    Mehdi Golpayegani & Jafar Fathali

  2. Department of Engineering, Shahrood University of Technology, University Blvd., Shahrood, Iran

    Eiman Khosravian

Authors
  1. Mehdi Golpayegani
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  2. Jafar Fathali
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  3. Eiman Khosravian
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Correspondence to Jafar Fathali.

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Golpayegani, M., Fathali, J. & Khosravian, E. Median line location problem with positive and negative weights and Euclidean norm. Neural Comput & Applic 24, 613–619 (2014). https://doi.org/10.1007/s00521-012-1262-1

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  • DOI: https://doi.org/10.1007/s00521-012-1262-1

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