Skip to main content
SpringerLink
Log in

Multi-objective k-Center Sum Clustering Problem

  • Conference paper
Emerging ICT for Bridging the Future - Proceedings of the 49th Annual Convention of the Computer Society of India (CSI) Volume 1

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 337))

Abstract

Given a set P of n objects in two dimensional plane and a positive integer k ( ≤ n), we have considered the problem of partitioning P into k clusters of circular shape so as to minimize the following two objectives: (i) the sum of radii of these k circular clusters and (ii) the number of points of P covered by more than one circular cluster. The NSGA-II based multi-objective genetic algorithm (MOGA) has been proposed to solve this problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Xu, R., II Wunsch, D.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)

    Article  Google Scholar 

  2. Xu, R., Wunsch, D.: Clustering. Wiley-IEEE Press (2009)

    Google Scholar 

  3. Hochbaum, D.S., Shmoys, D.B.: A best possible approximation algorithm for the k-center problem. Math. Oper. Res. 10, 180–184 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dyer, M.E., Frieze, A.M.: A Simple Heuristic for the P-centre Problem. Oper. Res. Lett. 3(6), 285–288 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hansen, P., Jaumard, B.: Minimum sum of diameters clustering. Journal of Classification 4(2), 215–226

    Google Scholar 

  6. Behsaz, B., Salavatipour, M.R.: On Minimum Sum of Radii and Diameters Clustering. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 71–82. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Charikar, M., Panigrahy, R.: Clustering to Minimize the Sum of Cluster Diameters. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, STOC 2001, pp. 1–10. ACM, New York (2001)

    Chapter  Google Scholar 

  8. Hamacher, H.W., Drezner, Z.: Facility location: applications and theory. Springer (2002)

    Google Scholar 

  9. Ranjan, P., Mahapatra, S.: Studies on Variations of Enclosing Problem using Rectangular Objects. PhD thesis, University of Kalyani (2012)

    Google Scholar 

  10. Churchand, R.L., ReVelle, C.S.: Theoretical and Computational Links between the p-Median, Location Set-covering, and the Maximal Covering Location Problem. Geographical Analysis 8(4), 406–415 (1976)

    Article  Google Scholar 

  11. Alt, H., Arkin, E.M., Brönnimann, H., Erickson, J., Fekete, S.P., Knauer, C., Lenchner, J., Mitchell, J.S.B., Whittlesey, K.: Minimum-cost Coverage of Point Sets by Disks. In: Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, SCG 2006, pp. 449–458. ACM, New York (2006)

    Chapter  Google Scholar 

  12. Sharir, M., Welzl, E.: Rectilinear and Polygonal p-Piercing and p-Center Problems.. In: Symposium on Computational Geometry, pp. 122–132 (1996)

    Google Scholar 

  13. Mukherjee, M., Chakraborty, K.: A polynomial-time optimization algorithm for a rectilinear partitioning problem with applications in VLSI design automation. Inf. Process. Lett. 83(1), 41–48 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mukherjee, J., Ranjan, P., Mahapatra, S., Karmakar, A., Das, S.: Minimum-width rectangular annulus. Theor. Comput. Sci. 508, 74–80 (2013)

    Article  MATH  Google Scholar 

  15. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  16. Atta, S., Mahapatra, P.R.S.: Genetic Algorithm Based Approaches to Install Different Types of Facilities. In: Satapathy, S.C., Avadahani, P.S., Udgata, S.K., Lakshminarayana, S. (eds.) ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of CSI - Volume I. AISC, vol. 248, pp. 195–203. Springer, Heidelberg (2014), http://dx.doi.org/10.1007/978-3-319-03107-1_23

    Chapter  Google Scholar 

  17. Ranjan, P., Mahapatra, S., Goswami, P.P., Das, S.: Covering Points by Isothetic Unit Squares. In: Proceeding of the 19th Canadian Conference on Computational Geometry (CCCG 2007), pp. 169–172 (2007)

    Google Scholar 

  18. Ranjan, P., Mahapatra, S., Goswami, P.P., Das, S.: Maximal Covering by Two Isothetic Unit Squares. In: Proceeding of the 20th Canadian Conference on Computational Geometry (CCCG 2008), pp. 103–106 (2008)

    Google Scholar 

  19. Mahapatra, P.R.S., Karmakar, A., Das, S., Goswami, P.P.: k-enclosing axis-parallel square. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part III. LNCS, vol. 6784, pp. 84–93. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Atta, S., Ranjan, P., Mahapatra, S.: Genetic Algorithm based Approach for Serving Maximum Number of Customers Using Limited Resources, 10th edn., pp. 492–497. Elsevier (2013)

    Google Scholar 

  21. Megiddo, N., Supowit, K.J.: On the Complexity of Some Common Geometric Location Problems.. SIAM J. Comput. 13(1), 182–196 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  22. Deb, K.: Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, Chichester (2001)

    MATH  Google Scholar 

  23. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  24. Agrawal, R.B., Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space (1994)

    Google Scholar 

  25. Beyer, H.-G., Deb, K.: On Self-adaptive Features in Real-parameter Evolutionary Algorithms. Trans. Evol. Comp 5(3), 250–270 (2001)

    Article  Google Scholar 

  26. Raghuwanshi, M.M., Kakde, O.G.: Survey on multiobjective evolutionary and real coded genetic algorithms. In: Proceedings of the 8th Asia Pacific Symposium on Intelligent and Evolutionary Systems, pp. 150–161 (2004)

    Google Scholar 

  27. Bandyopadhyay, S., Maulik, U.: Nonparametric genetic clustering: comparison of validity indices. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 31(1), 120–125 (2001)

    Article  Google Scholar 

  28. Bandyopadhyay, S., Maulik, U.: Genetic clustering for automatic evolution of clusters and application to image classification.. Pattern Recognition 35(6), 1197–1208 (2002)

    Article  MATH  Google Scholar 

  29. Bandyopadhyay, S., Pal, S.K.: Classification and learning using genetic algorithms: applications in bioinformatics and web intelligence. Springer (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Kalyani, Nadia, W.B., India

    Soumen Atta & Priya Ranjan Sinha Mahapatra

Authors
  1. Soumen Atta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Priya Ranjan Sinha Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soumen Atta .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Anil Neerukonda Institute of Technology and Sciences, Vishakapatnam, India

    Suresh Chandra Satapathy

  2. School of Information Technology, Jawaharlal Nehru Technological University Hyderabad, Hyderabad, India

    A. Govardhan

  3. Department of CSE, CMR Technical Campus, Hyderabad, India

    K. Srujan Raju

  4. Department of Computer Science & Engineering, Faculty of Engg., Tech. & Management, University of Kalyani, Kalyani, West Bengal, India

    J. K. Mandal

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Atta, S., Mahapatra, P.R.S. (2015). Multi-objective k-Center Sum Clustering Problem. In: Satapathy, S., Govardhan, A., Raju, K., Mandal, J. (eds) Emerging ICT for Bridging the Future - Proceedings of the 49th Annual Convention of the Computer Society of India (CSI) Volume 1. Advances in Intelligent Systems and Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-13728-5_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13728-5_47

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13727-8

  • Online ISBN: 978-3-319-13728-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation