Skip to main content
SpringerLink
Log in

Meta-heuristic approach to proportional fairness

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

Proportional fairness is a concept from resource sharing tasks among n users, where each user receives at least 1/n of her or his total value of the infinitely divisible resource. Here we provide an approach to proportional fairness that allows its extension to discrete domains, as well as for the direct application of evolutionary computation to approximate proportional fair states. We employ the concept of relational optimization, where the optimization task becomes the finding of extreme elements of a binary relation, and define a proportional fairness relation correspondingly. By using a rank-ordered version of proportional fairness, the so-called ordered proportional fairness, we can improve the active finding of maximal proportional fair elements by evolutionary meta-heuristic algorithms. This is demonstrated by using modified versions of the strength pareto evolutionary algorithm (version 2, SPEA2) and multi-objective particle swarm optimization. In comparison between proportional and ordered proportional fairness, and by using relational SPEA2, the evolved maximum sets of ordered proportional fairness achieve 10 % more dominance cases against a set of random vectors than proportional fairness.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Note that two different points with the same product of components can never dominate each other.

References

  1. Bertsekas D, Gallager R (1992) Data networks. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  2. Kelly F (1997) Charging and rate control for elastic traffic. Eur Trans Telecommun 8:33–37

    Article  Google Scholar 

  3. Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybern Part B Cybern 38(5):1402–1412

    Article  Google Scholar 

  4. Dubins L, Spanier E (1961) How to cut a cake fairly? Am Math Mon 68(1):1–17

    Article  MathSciNet  MATH  Google Scholar 

  5. Ogryczak W (2009) Inequality measures and equitable locations. Ann Oper Res 167(1):61–86

    Article  MathSciNet  Google Scholar 

  6. Haldar S, Subramanian DK (1991) Fairness in processor scheduling in time sharing systems. SIGOPS Oper Syst Rev 25(1):4–18

    Article  Google Scholar 

  7. Hall RW, Tymoczko D (2012) Submajorization and the geometry of unordered collections. Am Math Mon 119(4):263–283

    Article  MathSciNet  Google Scholar 

  8. Baglietto M, Bolla R, Davoli F, Marchese M, Mongelli M (2003) Integration of pricing models between best-effort and guaranteed performance services in telecommunication networks. Control Eng Pract 11(10):1209–1226

    Article  Google Scholar 

  9. Bonald T, Massoulié L, Proutière A, Virtamo J (2006) A queueing analysis of max–min fairness, proportional fairness and balanced fairness. Queue Syst 53:65–84

    Article  MATH  Google Scholar 

  10. Tan B, Ying L, Srikant R (2010) Short-term fairness and long-term QoS in the internet. Perform Eval 67(5):406–414

    Article  Google Scholar 

  11. Harks T, Poschwatta T. (2008) Congestion control in utility fair networks. Comput Netw 52(15):2947–2960

    Article  MATH  Google Scholar 

  12. Zhou H, Fan P, Li J (2009) Cooperative proportional fairness scheduling for wireless transmissions. In: Proceedings of the international conference on wireless communications and mobile computing: connecting the world wirelessly 2009 (ser. IWCMC ‘09). ACM, pp 12–16

  13. Boche H, Schubert M (2009) Nash bargaining and proportional fairness for wireless systems. IEEE/ACM Trans Netw 17(5):1453–1466

    Article  Google Scholar 

  14. Uchida M, Kurose J (2011) An information-theoretic characterization of weighted α-proportional fairness in network resource allocation. Inf Sci 181(18):4009–4023

    Article  MATH  Google Scholar 

  15. Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco

    MATH  Google Scholar 

  16. Suzumura K (2009) Rational choice, collective decisions, and social welfare. Cambridge University Press, Cambridge

    Google Scholar 

  17. Ogryczak W, Śliwiński T, Wierzbicki A (2003) Fair resource allocation schemes and network dimensioning problems. J Telecommun Inf Technol 3:34–42

    Google Scholar 

  18. Ogryczak W, Wierzbicki A, Milewski M (2008) A multi-criteria approach to fair and efficient bandwidth allocation. Omega 36:451–463

    Article  Google Scholar 

  19. Kleinberg J, Rabani Y, Tardos E (2001) Fairness in routing and load balancing. J Comput Syst Sci 63(1):2–21

    Article  MathSciNet  MATH  Google Scholar 

  20. Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux J, Papailou P, Fogarty T (eds) EUROGEN 2001, evolutionary methods for design, optimization and control with applications to industrial problems, Athens, Greece, pp 95–100

  21. Reyes-Sierra M, Coello CAC (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308

    MathSciNet  Google Scholar 

  22. Knowles J, Corne D (2007) Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Evolutionary multi-criterion optimization, ser. LNCS 4403. Springer, Matsushima, pp 757–771

  23. Köppen M, Yoshida K, Tsuru M (2011) Unsorting the proportional fairness relation. In: Proceedings of the third international conference on intelligent networking and collaborative systems (INCoS 2011), Fukuoka, Japan, pp 47–52

  24. Köppen M, Yoshida K, Tsuru M, Oie Y (2009) Fairness-based global optimization of user-centric networks. In: Fifth international joint conference on INC, IMS and IDC, 2009. NCM ’09. IEEE, pp 441–443

  25. Köppen M, Verschae R, Yoshida K, Tsuru M (2010) Comparison of evolutionary multi-objective optimization algorithms for the utilization of fairness in network control. In: Proceedings of the 2010 IEEE international conference on systems, man, and cybernetics (SMC 2010), Istanbul, Turkey, pp 2647–2655

  26. Sun J, Modiano E, Zheng L (2006) Wireless channel allocation using an auction algorithm. IEEE J Sel Areas Commun 24(5):1085–1096

    Article  Google Scholar 

  27. Jaffe J (1981) Bottleneck flow control. IEEE Trans Commun 29(7):954–962

    Google Scholar 

  28. Köppen M, Yoshida K, Ohnishi K (2011) Meta-heuristic optimization reloaded. In: Proceedings of the third world congress on nature and biologically inspired computing (NaBIC2011). IEEE CS Press, Salamanca, pp 562–568

Download references

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 24650030.

Author information

Authors and Affiliations

  1. Network Design and Research Center (NDRC), Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka, 820-8502, Japan

    Mario Köppen, Kaori Yoshida, Kei Ohnishi & Masato Tsuru

Authors
  1. Mario Köppen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaori Yoshida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kei Ohnishi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Masato Tsuru
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Köppen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Köppen, M., Yoshida, K., Ohnishi, K. et al. Meta-heuristic approach to proportional fairness. Evol. Intel. 5, 231–244 (2012). https://doi.org/10.1007/s12065-012-0084-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-012-0084-5

Keywords

Search

Navigation