한국컴퓨터정보학회논문지 (Journal of the Korea Society of Computer and Information)

  • 제17권10호
  • /
  • Pages.155-165
  • /
  • 2012
  • /
  • 1598-849X(pISSN)
  • /
  • 2383-9945(eISSN)
한국컴퓨터정보학회 (Korean Society of Computer Information)
권호 표지
DOI QR코드

DOI QR Code

외판원 문제의 확장된 k-opt 알고리즘

The Extended k-opt Algorithm for Traveling Salesman Problem

  • 이상운 (강릉원주대학교 멀티미디어공학과)
  • Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
  • 투고 : 2012.06.19
  • 심사 : 2012.09.10
  • 발행 : 2012.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 지금까지 해결하지 못한 NP-Hard 문제들 중의 하나인 외판원 문제를 해결할 수 있는 알고리즘을 제안한다. 제안된 알고리즘은 간선교환 방법을 적용한 발견적 알고리즘이다. 초기해를 구하는 전형적인 방법은 첫 번째 노드부터 가장 인접한 노드를 방문하여 외판원의 경로를 결정하는 방법이다. 본 논문에서는 각 노드의 최소 간선을 선택하여 선택된 간선들 중 최소값을 가진 노드부터 출발하는 Min-Min 방법과 최대값을 가진 노드부터 출발하는 Min-Max 방법을 적용하고 두 방법 중 최소 경로길이를 가진 방법을 초기해로 결정하였다. 초기해로부터 최적해를 구하는 과정은 기존의 2-간선 교환 방법 (2-opt)을 기본적으로 적용하고, 추가로 확장된 3-opt와 4-opt를 제안하였다. 이와 같은 방법을 7개의 실제 데이터들에 적용한 결과 지금까지 알려진 최적해를 빠르고 정확히 구하는데 성공하였다.

This paper suggests traveling salesman problem algorithm that have been unsolved problem with NP-Hard. The proposed algorithm is a heuristic with edge-swap method. The classical method finds the initial solution starts with first node and visits to mostly adjacent nodes then decides the traveling path. This paper selects minimum weight edge for each nodes, then perform Min-Min method that start from minimum weight edge among the selected edges and Min-Max method that starts from maximum weight edges among it. Then we decide tie initial solution to minimum path length between Min-Min and Min-Max method. To get the final optimal solution, we apply previous two-opt to initial solution. Also, we suggest extended 3-opt and 4-opt additionally. For the 7 actual experimental data, this algorithm can be get the optimal solutions of state-of-the-art with fast and correct.

키워드

참고문헌

  1. Wikipedia, "Travelling Salesman Problem," http://en.wikipedia.org/wiki/Travelling_Salesm an_Problem, Wikimedia Foundation Inc., 2012.
  2. A. Likas and V. T. Paschos, "A Note on a New Greedy-solution Representation and a New Greedy Parallelizable Heuristic for the Traveling Salesman Problem," Chaos, Solitons and Fractals, Vol. 13, pp. 71-78, 2002. https://doi.org/10.1016/S0960-0779(00)00227-7
  3. A. Schrijver, "On the History of Combinatorial Optimization (till 1960)," in Handbook of Discrete Optimization'' (K. Aardal, G.L. Nemhauser, R. Weismantel, eds.), Elsevier, Amsterdam, pp. 1-68, 2005,
  4. J. Denzinger, D. Fuchs, M. Fuchs, and M. Kronenburg, "The Teamwork Method for Knowledge -Based Distributed Search: The travelling salesman problem," University of Kaiserslautern, 2008.
  5. J. Pleines, "ZIP-Methode: ein Kombinatorischer Ansatz zur Optimalen Lősung Allgemeiner Traveling- Salesman-Problem (TSP)," Konnen bekannte Losungen nicht nur auf Gesamtgrphen sondern auf Teilgraphen angewandt werden, so bringt die ZIP-Methode den entscheidenden Quantensprung der rechentechnischen Vereinfachung, 2006.
  6. S. Vempala, "18.433 Combinatorial Optimization: NP -completeness," http://ocw.mit.edu/NR/rdonlyres/ Mathematics/18-433Fall2003/778D00DB-F21C -486C-ABD8-F5E7F5C929C3/O/I20.pdf, 2003.
  7. E. Charniak and M. Herlihy, "CSC 751 Computational Complexity: Local Search Heuristics," Department od Computer Science, Brown University, 2008.
  8. L. Stougie, "2P350: Optimaliseringsmethoden, "http://www.win.tue.nl/-leen/OW/2P350/We ek8/week8.pdf, College Wordt ggeven op vinjdagmiddag, 2001.
  9. W. Cook, "The Traveling Salesman Problem," The School of Industrial and Systems Engineering, Gatorgia Tech, 2008.
  10. A. Battese, "Millennium Problems," Clay Mathematics Institute, http://www.claymath.org/millennium/, 2008.
  11. J. Kratica and S. Radojevi, "One Improvement to Nearest Neighbor Method for Solving Traveling Salesman Problem," LIRA 95 Proceedings, pp. 77-82, Novi Sad, 1996.
  12. D. S. Johnson and L. A. McGeoch, "The Traveling Salesman Problem: A Case Study in Local Optimization," Department of Mathematics and Computer Science, Amherst College, 1995.
  13. H. D. Beale, "Neural Network Design," PWS Publishing Company, 1996.
  14. B. Chandra, H. Karloff, and C. Tovey, "New Results on the Old k-Opt Algorithm for the TSP," SIAM Journal on Computing, Vol. 28, No. 6, pp. 1998-2029, 1999. https://doi.org/10.1137/S0097539793251244
  15. K. Helsagaun, "General k-Opt Submoves for the Lin-Kernighan TSP Heuristic," Math. Prog. Comp., Vol. 1, pp. 119-163, 2009. https://doi.org/10.1007/s12532-009-0004-6
  16. P. S. Tsilingiris, "A Multi-stage Decision-Support Methodology for The Optimization-based Linear-network Design," Degree of Diploma in Naval Architecture and Marine Engineering at the School of Naval Architecture and Marine Engineering of the National Technical University of Athens, 2005.

피인용 문헌

  1. 외판원 문제의 다항시간 알고리즘 vol.18, pp.12, 2012, https://doi.org/10.9708/jksci.2013.18.12.075
  2. DNN과 k-opt를 적용한 대규모 외판원 문제의 최적 해법 vol.15, pp.4, 2012, https://doi.org/10.7236/jiibc.2015.15.4.249
  3. 안정된 결혼문제에 대한 최적화 알고리즘 vol.18, pp.4, 2018, https://doi.org/10.7236/jiibc.2018.18.4.149