Skip to main content

A Populated Iterated Greedy Algorithm with Inver-Over Operator for Traveling Salesman Problem

  • Conference paper
Swarm, Evolutionary, and Memetic Computing (SEMCCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8297))

Included in the following conference series:

Abstract

In this study, we propose a populated iterated greedy algorithm with an Inver-Over operator to solve the traveling salesman problem. The iterated greedy (IG) algorithm is mainly based on the central procedures of destruction and construction. The basic idea behind it is to remove some solution components from a current solution and reconstruct them in the partial solution to obtain the complete solution again. In this paper, we apply this idea in a populated manner (IGP) to the traveling salesman problem (TSP). Since the destruction and construction procedure is computationally expensive, we also propose an iteration jumping to an Inver-Over operator during the search process. We applied the proposed algorithm to the well-known 14 TSP instances from TSPLIB. The computational results show that the proposed algorithm is very competitive to the recent best performing algorithms from the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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 

  2. Albayrak, M.: Determination of route by means of Genetic Algorithms for printed circuit board driller machines. Master dissertation, p. 180, Selcuk University (2008)

    Google Scholar 

  3. Applegate, D., Cook, W., Rohe, A.: Chained Lin–Kernighan for large traveling salesman problems. INFORMS J. Comput. 15, 82–92 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Arora, S.: Polynomial-time approximation schemes for Euclidean TSP and other geometric problems. J. ACM 45, 753–782 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bentley, J.L.: Fast algorithm for geometric traveling salesman problems. ORSA J. Comput. 4, 387–441 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bentley, J.L.: Experiments on traveling salesman heuristics. In: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 91–99 (1990)

    Google Scholar 

  7. Bouamama, S., Blum, C., Boukerram, A.: A population-based iterated greedy algorithm for the minimum weight vertex cover problem. Appl. Soft. Comput. J. (2012), doi:10.1016/j.asoc.2012.02.013

    Google Scholar 

  8. 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 

  9. Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12, 568–581 (1964)

    Article  Google Scholar 

  10. Clerc, M.: Discrete particle swarm optimization, illustrated by the traveling salesman problem. In: Onwubolu, G.C., Babu, B.V. (eds.) New Optimization Techniques in Engineering. STUDFUZZ, vol. 141, pp. 219–239. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Créput, J.C., Koukam, A.: A Memetic neural network for the Euclidean traveling salesman problem. Neurocomputing 72, 1250–1264 (2009)

    Article  Google Scholar 

  12. Dorigo, M., Gambardella, L.M.: Ant colonies for the traveling salesman problem. BioSystems 43, 73–81 (1997)

    Article  Google Scholar 

  13. Fanjul-Peyro, L., Ruiz, R.: Iterated greedy local search methods for unrelated parallel machine scheduling. European Journal of Operational Research 207, 55–69 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Fiechter, C.-N.: A parallel Tabu search algorithm for large traveling salesman problems. Discrete Appl. Math. 51, 243–267 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Framinan, J.M., Leisten, R.: Total tardiness minimization in permutation flow shops: a simple approach based on a variable greedy algorithm. International Journal of Production Research 46(22), 6479–6498 (2008)

    Article  MATH  Google Scholar 

  16. Geem, Z.W., Tseng, C.-L., Park, Y.-J.: Harmony search for generalized orienteering problem: best touring in China. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 741–750. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Gendreau, M., Hertz, A., Laporte, G.: New insertion and post optimization procedures for the traveling salesman problem. Oper. Res. 40, 1086–1094 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  18. Gerardo Minella, G., Ruiz, R., Ciavotta, M.: Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems. Computers & Operations Research 38, 1521–1533 (2011)

    Article  MathSciNet  Google Scholar 

  19. Tao, G., 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 

  20. Gutin, G., Punnen, A.P.: The Traveling Salesman Problem and its Variations. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  21. Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operational Research 126(1), 106–130 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Jayalakshmi, G.A., Sathiamoorthy, S., Rajaram, R.: A hybrid genetic algorithm – a new approach to solve traveling salesman problem. International Journal of Computational Engineering Science 2(2), 339–355 (2001)

    Article  Google Scholar 

  23. 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 

  24. Kahraman, C., Engin, O., Kaya, I., Ozturk, R.E.: Multiprocessor task scheduling in multistage hybrid flow-shops: A parallel greedy algorithm approach. Applied Soft Computing 10, 1293–1300 (2010)

    Article  Google Scholar 

  25. Kuo-Ching Ying, K.-C., Lin, S.-W., Huang, C.-Y.: Sequencing single-machine tardiness problems with sequence dependent setup times using an iterated greedy heuristic. Expert Systems with Applications 36, 7087–7092 (2009)

    Article  Google Scholar 

  26. Leung, K.S., Jin, H.D., Xu, Z.B.: An expanding self-organizing neural network for the travelling salesman problem. Neurocomputing 62, 267–292 (2004)

    Article  Google Scholar 

  27. Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling salesman problem. Oper. Res. 21, 498–516 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  28. Louis, S.J., Li, G.: Case injected genetic algorithms for traveling salesman problems. Inform. Sci. 122, 201–225 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  29. Lozano, M., Molina, D., Garcia-Martinez, C.: Iterated greedy for the maximum diversity problem. European Journal of Operational Research 214, 31–38 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  30. Marinakis, Y., Marinaki, M., Dounias, G.: Honey bees mating optimization algorithm for the Euclidean traveling salesman problem. Inform. Sci. (2010), doi:10.1016/j.ins.2010.06.032

    Google Scholar 

  31. Merz, P., Freisleben, B.: Memetic algorithms for the traveling salesman problem. Complex Systems 13, 297–345 (2001)

    MATH  MathSciNet  Google Scholar 

  32. Misevicius, A.: Using iterated tabu search for the traveling salesman problem. Information Technology and Control 3(32), 29–40 (2004)

    Google Scholar 

  33. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  34. Nawaz, M., Enscore Jr., E.E., Ham, I.A.: Heuristic algorithm for the m-machine, n-node flow shop sequencing problem. OMEGA 11(1), 91–95 (1983)

    Article  Google Scholar 

  35. Qinma Kanga, Q., Heb, H., Song, H.: Task assignment in heterogeneous computing systems using an effective iterated greedy algorithm. The Journal of Systems and Software 84, 985–992 (2011)

    Article  Google Scholar 

  36. Onwubolu, G.C.: Optimizing CNC drilling machine operations: traveling salesman problem-differential evolution approach. In: Onwubolu, G.C., Babu, B.V. (eds.) New Optimization Techniques in Engineering. STUDFUZZ, vol. 141, pp. 537–565. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  37. Pan, Q.-K., Fatih, T.M., Liang, Y.-C.: A discrete differential evolution algorithm for the permutation flowshop scheduling problem. Computers & Industrial Engineering 55, 795–816 (2008)

    Article  Google Scholar 

  38. Pan, Q.-K., Wang, Y.-T., Li, J.-Q., Gao, K.-Z.: Memetic Algorithm based on improved Inver–Over operator and Lin–Kernighan local search for the euclidean traveling salesman problem. Computers and Mathematics with Applications 62, 2743–2754 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  39. Padberg, M.W., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33, 60–100 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  40. Reinelt, G.: TSPLIB—a traveling salesman problem library. ORSA J. Comput. 3, 376–384 (1991)

    Article  MATH  Google Scholar 

  41. Ribas, I., Ramon Companys, R., Tort-Martorell, X.: An iterated greedy algorithm for the flowshop scheduling problem with blocking. Omega 39, 293–301 (2011)

    Article  Google Scholar 

  42. Rosenkrantz, D.J., Stearns, R.E., Lewis, P.M.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6, 563–581 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  43. Ruiz, R., Stützle, T.: A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research 177(3), 2033–2049 (2007)

    Article  MATH  Google Scholar 

  44. Ruiz, R., Stützle, T.: An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives. European Journal of Operational Research 187, 1143–1159 (2008)

    Article  MATH  Google Scholar 

  45. Schleuter, M.G.: Asparagos96 and the traveling salesman problem. In: Proceedings of the 1997 IEEE International Conference on Evolutionary Computation, pp. 171–174. IEEE Press (1997)

    Google Scholar 

  46. Seo, D., Moon, B.: Voronoi quantized crossover for traveling salesman problem. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 544–552 (2002)

    Google Scholar 

  47. 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  MATH  MathSciNet  Google Scholar 

  48. Stützle, T., Hoos, H.: The MAX–MIN ant system and local search for the traveling salesman problem. In: Proceedings of the IEEE International Conference on Evolutionary Computation, Indianapolis, Indiana, USA, pp. 308–313 (1997)

    Google Scholar 

  49. Tao, G., 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 

  50. Tasgetiren, M., Fatih, P.Q.-K., Suganthan, P.N., Chen Angela, H.-L.: A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops. Information Sciences 181, 3459–3475 (2011)

    Article  MathSciNet  Google Scholar 

  51. Tasgetiren, M., Fatih, P.Q.-K., Liang, Y.-C.: A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times. Computers & Operations Research 36, 1900–1915 (2009)

    Article  MATH  Google Scholar 

  52. 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  MATH  MathSciNet  Google Scholar 

  53. Ying, K.-C., Cheng, H.-M.: Dynamic parallel machine scheduling with sequence-dependent setup times using an iterated greedy heuristic. Expert Systems with Applications 37, 2848–2852 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Tasgetiren, M.F., Buyukdagli, O., Kızılay, D., Karabulut, K. (2013). A Populated Iterated Greedy Algorithm with Inver-Over Operator for Traveling Salesman Problem. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Dash, S.S. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2013. Lecture Notes in Computer Science, vol 8297. Springer, Cham. https://doi.org/10.1007/978-3-319-03753-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03753-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03752-3

  • Online ISBN: 978-3-319-03753-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics