Genetic Algorithm Using-Floating Point Representation for Steiner Tree

스타이너 트리를 구하기 위한 부동소수점 표현을 이용한 유전자 알고리즘

  • 김채주 (부경대학교 대학원 컴퓨터공학과) ;
  • 성길영 (경상대학교 정보통신공학과, 해양산업연구) ;
  • 우종호 (부경대학교 전자컴퓨터정보통신공학부)
  • Published : 2004.08.01

Abstract

The genetic algorithms have been used to take a near optimal solution because The generation of the optimal Steiner tree from a given network is NP-hard problem,. The chromosomes in genetic algorithm are represented with the floating point representation instead of the existing binary string for solving this problem. A spanning tree was obtained from a given network using Prim's algorithm. Then, the new Steiner point was computed using genetic algorithm with the chromosomes in the floating point representation, and it was added to the tree for approaching the result. After repeating these evolving steps, the near optimal Steiner tree was obtained. Using this method, the tree is quickly and exactly approached to the near optimal Steiner tree compared with the existing genetic algorithms using binary string.

References

  1. G.R.Raidl and B.A.Julstrom, 'Edge-Sets: An Effective Evolutionary Coding of Spanning Trees', Technishe Univ., Technical Report, 2002
  2. Pawel Winter and Martin Zachariasen, 'Euclidean Steiner Minimum Trees: An Improved Exact Algorithm', Networks, Vol.30, pp.149-166, 1997 https://doi.org/10.1002/(SICI)1097-0037(199710)30:3<149::AID-NET1>3.0.CO;2-L
  3. Pawel Winter, 'An algorithm for the Steiner problem in the Euclidean plan', Networks, Vol.15, pp.323-345, 1985 https://doi.org/10.1002/net.3230150305
  4. Cockayne and D.E.Hewgill, 'Improved Computation of Plane Steiner Topology, Agorithmica, Vol.7, pp.219-229, 1992 https://doi.org/10.1007/BF01758759
  5. David J. Thuente and Pulin Sampat, 'Mathematical Programming in A Hybrid Genetic Algorithm for Steiner point Problems', Proc.of the ACM symposium, 1995
  6. Jorge Barreiros, 'An Hierarchic Genetic Algorithm for Comuting (near)Optimal Euclidean Steiner Trees', GECC02003, pp.56-65, 2003
  7. Zbigniew Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Third Extended Edition, Springer-Verlag, 1995
  8. Jianhua Jiang, 'Rigorous Analysis and Design of Diffractive Optical Elements', A Dissertation, Univ. Alabama, pp.74-89, 2000
  9. Richard Courant and Herbert Robbins, What is Mathematics?, Second Edition, Oxford University Press, 1996
  10. Joseph Jones, Frederick C and Harris.Jr, 'A Genetic Algorithm for the Steiner Minimal Tree Problem', ISCA's Int. Conf. on Intelligent Systems, 1996