한국정보과학회논문지:소프트웨어및응용 (Journal of KIISE:Software and Applications)

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
권호 표지

최적 통신 걸침 나무 문제를 해결하기 위한 진화 알고리즘

Evolutionary Algorithm for solving Optimum Communication Spanning Tree Problem

  • 석상문 (광주과학기술원 기전공학과) ;
  • 장석철 (광주과학기술원 기전공학과) ;
  • 변성철 (광주과학기술원 기전공학과) ;
  • 안병하 (광주과학기술원 기전공학과)
  • 발행 : 2005.04.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 최적 통신 걸침 나무 문제(Optimum Communication Spanning Tree Problem OCST)를 다룬다. 일반적으로, OCST문제는 WP-hard 문제로 알려져 있으며 최근에 Papadimitriou 와 Yannakakis에 의해서 MAX SNP-hard로 밝혀졌다. 그럼에도 불구하고 OCST 문제를 해결하기 위한 기존의 주된 접근법은 polynomial time 알고리즘들 이었다. 본 논문에서는 OCST 문제를 해결하기 위한 진화 알고리즘을 소개한다. 특히, 진화 알고리즘을 어떤 문제에 적용할 때 가장 우선적으로 고려되어야 하는 사항은 해를 어떻게 표현할 것인가 하는 표현법(representation)에 관한 것이다. 따라서 본 논문에서는 기존에 차수 제약 걸침 나무 문제를 해결하기 위해 제안한 표현법의 단점을 개선하는 새로운 표현법을 제안하고 이 표현법을 이용해서 트리(tree)를 만들어 내는 decoding 방법 또한 소개한다. 그리고 제안하는 해 표현법에 맞는 유전 연산자를 찾기 위해 네트워크의 정보 및 부모세대가 지닌 유전 정보를 이용하는 3가지 방법을 실험하였다. 결론적으로, 다양한 실험을 통해서 제안하는 방법이 기존의 방법에 비해 우수한 결과를 보여 준다는 것을 확인할 수 있었다.

This paper deals with optimum communication spanning tree(OCST) problem. Generally, OCST problem is known as NP-hard problem and recently, it is reveled as MAX SNP hard by Papadimitriou and Yannakakis. Nevertheless, many researchers have used polynomial approximation algorithm for solving this problem. This paper uses evolutionary algorithm. Especially, when an evolutionary algorithm is applied to tree network problem such as the OCST problem, representation and genetic operator should be considered simultaneously because they affect greatly the performance of algorithm. So, we introduce a new representation method to improve the weakness of previous representation which is proposed for solving the degree constrained minimum spanning tree problem. And we also propose a new decoding method to generate a reliable tree using the proposed representation. And then, for finding a suitable genetic operator which works well on the proposed representation, we tested three kinds of genetic operators using the information of network or the genetic information of parents. Consequently, we could confirm that the proposed method gives better results than the previous methods.

키워드

참고문헌

  1. Hu, T.C., 'Optimum communication spanning trees,' SLAM J. Computing, Vol.3, No.3, pp. 188-195, 1974 https://doi.org/10.1137/0203015
  2. Garey, M.R. and Johnson, D.S., 'Computers and Intractability: A Guide to the Theory of NPCompleteness,' San Francisco, Freeman, 1979
  3. Papadimitriou, C. H and Yannakakis, M., 'Optimization, approximation, and complexity classes, Journal of Computer and System Science,' Vol.43, pp. 425-440, 1991 https://doi.org/10.1016/0022-0000(91)90023-X
  4. Arora, S. Lund, C. Motwani, R. Sundan, M. and Szegedy, M., 'ProofVarification and the Hardness of Approximation Problems,' Colloquium on Computational Complexity Report TR98-008, University of Trier
  5. Peleg, D. and Reshcf, E., 'Deterministic Polylog Approximation for Minimum Communication Spanning Trees,' ICALP'98, LNCS Vol.1443, pp. 670-681, 1998
  6. Wu, B.Y. Chao, K.M. and Tang, C.Y., 'Approximation algorithms for Some Optimum Communication Spanning Tree Problem,' ISAAC'98, LNCS Vol.1533, pp. 407-416, 1998
  7. Wu, B.Y. Chao, K.M. and Tang, C.Y., 'A Polynomial Time Approximation Scheme for Optimal Product-Requirement Communication Spanning Trees,' Journal of Algorithms, Vol.36, pp. 182-204, 2000 https://doi.org/10.1006/jagm.2000.1088
  8. Gaube, T. and Rothlauf, F. 'The Link and Node Biased Encoding Revisited: Bias and Adjustment of Parameters,' EvoWorkshop 2001, LNCS Vol. 2037, pp.1-10, 2001 https://doi.org/10.1007/3-540-45365-2_1
  9. Rothlauf, F. Goldberg, D.E. and Heinzl, A., 'Network Random Keys - A Tree Network Representation Scheme for Genetic and Evolutionary Algorithms,' Evolutionary Computation, Vol.10 (1), pp. 75-97, 2002 https://doi.org/10.1162/106365602317301781
  10. Yu Li, 'An Effective Implementation of a Direct Spanning Tree Representation in GAs,' Evoworkshop 2001, LNCS Vol.2037, pp. 11-19, 2001 https://doi.org/10.1007/3-540-45365-2_2
  11. Yu Li and Bouchebaba, Y., 'A New Genetic Algorithm for the Optimal Communication Spanning Tree Problem,' Proceedings of Artificial Evolution: Fifth European Conference, pp. 162-173, 1999
  12. Gen, M. Cheng, R., Genetic Algorithms and Engineering Design, John Wiley & Sons, 1997
  13. Abuali, F.N. Wainwright, R.L. and Schoenefeld, D.A., 'Determinant Factorization: A New Encoding Scheme for Spanning Trees Applied to the Probabilistic Minimum Spanning Tree Problem,' in Proceedings of the Sixth International Conference on Genetic Algorithms. Larry J. Eshelman, Ed, pp. 470-477, 1995
  14. Bean, J. C., 'Genetic algorithms and random keys for sequencing and optimization,' ORSA Journal on Computing, Vol.6, No.2, pp. 154-160, 1994 https://doi.org/10.1287/ijoc.6.2.154
  15. Soak, S.M. Crone, D. and Ahn, B.H., 'A New Encoding for the Degree Constrained Minimum Spanning Tree Problem.' KES2004, LNAI Vol. 3213, pp. 952-958. 2004 https://doi.org/10.1007/b100909
  16. 석상문, 안병하, '차수 제약 걸침 나무 문제를 해결하기 위한 트리 표현법',한국정보과학회 추계 학술 대회, 2003
  17. Rothlauf, F. Gerstacker, J. and Heinzl, A.,'On the Optimal Communication Spanning Tree Problem,' Working Papers in Information Systems, University of Mannheim, 2003