A New DNA Encoding Method for Traveling Salesman Problem

  • Aili Han
  • Daming Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4115)


We have devised a new DNA encoding method to represent weight and apply it to solve the traveling salesman problem, an instance of optimization problems on weighted graphs. For any weighted graphG=(V,E), v i V, 1≤in, where exists weight w ij on edgev i v j , we use two DNA strands with different lengths to encode each of the edges. The longerDNA strand consists of three parts: one for the departure vertex, another for the weight, and the last for the arrival vertex. The shorter DNA strand is the reverse complementation of the center part of the longer one. The proposed weight encoding method is an improvement on the previous weight encoding methods, and it can more easily find the optimal solutions than the former ones. This work extends the capability of DNA computing to solving numerical optimization problems, which is contrasted with other DNA computing methods focusing on decision problems.


Short Path Travel Salesman Problem Travel Salesman Problem Encode Method Reverse Complementation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adleman, L.M.: Molecular Computation of Solutions to Combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Lipton, R.J.: DNA Solution of Hard Computational Problems. Science 268, 542–545 (1995)CrossRefGoogle Scholar
  3. 3.
    Ouyang, Q., Kaplan, P.D., Liu, S., et al.: DNA Solution of the Maximal Clique Problem. Science 278, 446–449 (1997)CrossRefGoogle Scholar
  4. 4.
    Head, T., Rozenberg, G., Bladergroen, R.S., et al.: Computing with DNA by Operating on Plasmids. Biosystems 57, 87–93 (2000)CrossRefGoogle Scholar
  5. 5.
    Sakamoto, K., Gouzu, H., Komiya, K., et al.: Molecular Computation by DNA Hairpin Formation. Science 288, 1223–1226 (2000)CrossRefGoogle Scholar
  6. 6.
    Narayanan, A., Zorbalas, S., et al.: DNA Algorithms for Computing Shortest Paths. In: Proceedings of the Genetic Programming, pp. 718–723. Morgan Kaufmann, San Francisco (1998)Google Scholar
  7. 7.
    Shin, S.Y., Zhang, B.T., Jun, S.S., et al.: Solving Traveling Salesman Problems Using Molecular Programming. In: Proceedings of the Congress on Evolutionary Computation, pp. 994–1000. IEEE Press, Los Alamitos (1999)Google Scholar
  8. 8.
    Yamamura, M., Hiroto, Y., Matoba, T.: Solutions of Shortest Path Problems by Concentration Control. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 231–240. Springer, Heidelberg (2002)Google Scholar
  9. 9.
    Lee, J.Y., Shin, S.Y., Park, T.H., et al.: Solving Traveling Salesman Problems with DNA Molecules Encoding Numerical Values. BioSystems 78, 39–47 (2004)CrossRefGoogle Scholar
  10. 10.
    Yin, Z.: DNA Computing in Graph and Combination Optimization, pp. 57–72. Science Press (2004) (in Chinese)Google Scholar
  11. 11.
    Xu, J., Dong, Y., et al.: Sticker DNA Computer Model-Part I: Theory. Chinese Science Bulletin 49, 772–780 (2004)MATHMathSciNetGoogle Scholar
  12. 12.
    Zhang, Z., Zhao, J., He, L.: Molecular Biology Development of DNA Computer. Journal of Genetics 30, 886–892 (2003) (in Chinese)Google Scholar
  13. 13.
    Wang, L., Lin, Y., Li, Z.: DNA Computation for a Category of Special Integer Planning Problem. Computer Research and Development 42, 1431–1437 (2005) (in Chinese)CrossRefGoogle Scholar
  14. 14.
    Chen, Z., Li, X., Wang, L., et al.: A Surface-Based DNA Algorithm for the Perfect Matching Problem. Computer Research and Development 42, 1241–1246 (2005) (in Chinese)CrossRefGoogle Scholar
  15. 15.
    Braich, R.S., Chelyapov, N., Johnson, C., et al.: Solution of a 20-variable 3-SAT Problem on a DNA Computer. Science 296, 499–502 (2002)CrossRefGoogle Scholar
  16. 16.
    Lancia, G.: Integer Programming Models for Computional Biology Problems. Journal of Computer Science and Technology 19, 60–77 (2004)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Han, A., Yang, Z., et al.: Complexity Analysis for HEWN Algorithm. Journal of Software 13, 2337–2342 (2002) (in Chinese)Google Scholar
  18. 18.
    Han, A.: Complexity Research for B Algorithm. In: Proceedings of the Tenth Joint International Computer Conference, pp. 188–192. International Academic Publishers (2004)Google Scholar
  19. 19.
    Han, A.: A Study on the Solution of 9-room Diagram by State Space Method. Journal of Shandong University (Engineering Science) 34, 51–54 (2004) (in Chinese)Google Scholar
  20. 20.
    Han, A., Pan, J.: A Network Layout Algorithm Based on the Principle of Regular Hexagons Covering a Plane. In: Proceedings of the 8th International Conference for Young Computer Scientist, pp. 223–227. International Academic Publishers (2005)Google Scholar
  21. 21.
    Liu, Q., Wang, L., Frutos, A.G., et al.: DNA Computing on Surfaces. Nature 403, 175–179 (2000)CrossRefGoogle Scholar
  22. 22.
    Ibrahim, Z., Tsuboi, Y., Muhammad, M.S., et al.: DNA Implementation of K-shortest Paths Computation. In: IEEE Congress on Evolutionary Computation. IEEE CEC 2005 Proceedings, vol. 1, pp. 707–713 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Aili Han
    • 1
    • 2
  • Daming Zhu
    • 2
  1. 1.Department of Computer Science and TechnologyShandong UniversityWeihaiChina
  2. 2.School of Computer Science and TechnologyShandong UniversityJinanChina

Personalised recommendations