A Modified Inver-over Operator for the Traveling Salesman Problem (original) (raw)

Abstract

The Inver-over operator holds a good result for small size Traveling Salesman Problem (TSP) while has worse capability for the large scale TSP. In this study, a Modified Inver-over operator is proposed to solve the TSP. In the Modified Inver-over operator, the direction of the tour is considered when applying the inversion and the city c is decided whether it is kept same after the inversion according to adaptively increasing probability, meanwhile, the _α_-nearest candidate set is used when selecting city c ′. We evaluate the proposed operator based on standard TSP test problems selected from TSPLIB and show that the proposed operator performs better than the Basic Inver-over operator and other operator in terms of solution quality and computational effort.

Preview

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Gutin, G., Punnen, A.P.: The Traveling Salesman Problem and Its Variations. Kluwer Academic Publishers, Dordrecht (2002)
    MATH Google Scholar
  2. Helsgaun, K.: An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. Eur. J. Oper. Res. 126, 106–130 (2000)
    Article MathSciNet MATH Google Scholar
  3. Arora, S.: Polynomial-time Approximation Schemes for Euclidean TSP and Other Geometric Problems. J. ACM 45, 753–782 (1998)
    Article MATH Google Scholar
  4. Jeong, C.S., Kim, M.H.: Fast Parallel Simulated Annealing for Traveling Salesman Problem on SIMD Machines with Linear Interconnections. Parallel Comput. 17, 221–228 (1991)
    Article MathSciNet Google Scholar
  5. Chen, Y., Zhang, P.: Optimized Annealing of Traveling Salesman Problem from the Nth-nearest-neighbor Distribution. Physica A 371, 627–632 (2006)
    Article Google Scholar
  6. Fiechter, C.-N.: A Parallel Tabu Search Algorithm for Large Traveling Salesman Problems. Discrete Appl. Math. 51, 226–243 (1994)
    Article MathSciNet MATH Google Scholar
  7. Guo, T., Michalewicz, Z.: Inver-over Operator for the Tsp. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 803–812. Springer, Heidelberg (1998)
    Chapter Google Scholar
  8. Louis, S.J., Li, G.: Case Injected Genetic Algorithms for Traveling Salesman Problems. Inform. Sci. 122, 201–225 (2000)
    Article MathSciNet MATH Google Scholar
  9. Albayrak, M., Allahverdi, N.: Development A New Mutation Operator to Solve the Traveling Salesman Problem by aid of Genetic Algorithms. Expert Syst. Appl. 38, 1313–1320 (2011)
    Article Google Scholar
  10. Mladenović, N., Hansen, P.: Variable Neighborhood Search. Comput. Oper. Res. 24, 1097–1100 (1997)
    Article MathSciNet MATH Google Scholar
  11. Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for Large Traveling Salesman Problems. Informs J. Comput. 15, 82–92 (2003)
    Article MathSciNet MATH Google Scholar
  12. Tsai, C.F., Tsai, C.W., Tseng, C.C.: A New Hybrid Heuristic Approach for Solving Large Traveling Salesman Problem. Inform. Sci. 166, 67–81 (2004)
    Article MathSciNet MATH Google Scholar
  13. Shi, X.H., Liang, Y.C., Lee, H.P., Lu, C., Wang, Q.X.: Particle Swarm Optimization-based Algorithms for TSP and Generalized TSP. Inform. Process. Lett. 103, 169–176 (2007)
    Article MathSciNet MATH Google Scholar
  14. Créput, J.C., Koukam, A.: A Memetic Neural Network for the Euclidean Traveling Salesman Problem. Neurocomputing 72, 1250–1264 (2009)
    Article Google Scholar
  15. Reinelt, G.: TSPLIB—A Traveling Salesman Problem Library. ORSA J. Comput. 3, 376–384 (1991)
    Article MATH Google Scholar

Download references

Author information

Authors and Affiliations

  1. College of Computer Science, Liaocheng University, Liaocheng, P.R. China
    Yuting Wang, Jian Sun, Junqing Li & Kaizhou Gao

Authors

  1. Yuting Wang
  2. Jian Sun
  3. Junqing Li
  4. Kaizhou Gao

Editor information

Editors and Affiliations

  1. School of Electronics and Information Engineering, Tongji University, 4800 Caoan Road, 201804, Shanghai, China
    De-Shuang Huang
  2. School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 5, Dongfeng Road, Jinshui District, 450002, Zhengzhou, Henan, China
    Yong Gan
  3. Indian Institute of Technology Kanpur, 208016, Kanpur, India
    Phalguni Gupta
  4. Department of Biotechnology, Indian Institute of Technology Madras, 600 036, Chennai, Tamilnadu, India
    M. Michael Gromiha

Rights and permissions

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Y., Sun, J., Li, J., Gao, K. (2012). A Modified Inver-over Operator for the Traveling Salesman Problem. In: Huang, DS., Gan, Y., Gupta, P., Gromiha, M.M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2011. Lecture Notes in Computer Science(), vol 6839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25944-9\_3

Download citation

Keywords

Publish with us