Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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Cost Relaxation Method to Escape from a Local Optimum of the Traveling Salesman Problem

외판원문제에서 국지해를 탈출하기 위한 비용완화법

  • Kwon, Sang-Ho (Department of Industrial Engineering, Hanyang University) ;
  • Kim, Sung-Min (Department of Industrial Engineering, Hanyang University) ;
  • Kang, Maing-Kyu (Department of Industrial Engineering, Hanyang University)
  • Published : 2004.06.30
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Abstract

This paper provides a simple but effective method, cost relaxation to escape from a local optimum of the traveling salesman problem. We would find a better solution if we repeat a local search heuristic at a different initial solution. To find a different initial solution, we use the cost relaxation method relaxing the cost of arcs. We used the Lin-Kernighan algorithm as a local search heuristic. In experimental result, we tested large instances, 30 random instances and 34 real world instances. In real-world instances, we found average 0.17% better above the optimum solution than the Concorde known as the chained Lin-Kernighan. In clustered random instances, we found average 0.9% better above the optimum solution than the Concorde.

Keywords

References

  1. Applegate, D., Bixby, R., Chvatal, V., and Cook, W. (1995), Finding Toursin the TSP,DIMACS Technical Report, 95-105
  2. Applegate, D., Bixby, R., Chvatal, Y., and Cook, W. (1999), Concorde, Computer Software, http://www.math.princeton.edu/tsp/ concorde.html.
  3. Applegate, D., Cook, W., and Rohe, A. (1999), Chained Lin- Kernighan for Large Traveling Salesman Problems, Technical Report No. 99887, Forschungsinstitut fur Diskrete Mathematik, University of Bonn, Germany
  4. Codenotti, B., Manzini, G., Margara, L., and Resta, G. (1996), Perturbation: An Efficient Technique for the Solution of Very Large Instances of the Euclidean TSP, INFORMS Journal on Computing, 8,125-133
  5. Held, M.and Karp, R. M. (1970), The Traveling Salesman Problem and Minimum Spanning Trees, Operations Research, 18, 1138-1162
  6. Helsgaun, K. (2000), An Effective Implementation of the LinKernighan Traveling Salesman Heuristics, European Journal of Operational Research, 126, 106-130
  7. Johnson, D. S. and McGeoch, L. A. (2002), Experimental Analysis of Heuristics for the STSP, The Traveling Salesman Problem and Its Variations, edited by Gutin G. and Punnen A., Kluwer Academic Publishers, Boston, MA, 369-444
  8. Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., and Shmoys, D. B. (1985), The Traveling Salesman Problem, John Wiley & Sons, NY
  9. Lin, S. (1965), Computer Solution of Traveling Salesman Problem, Bell System Tech. Journal, 44, 2245-2269
  10. Lin, S. and Kernighan, B. W. (1973), An Effective Heuristic Algorithm for the Traveling Salesman Problem, Operations Research, 21, 498-516
  11. Martin, O., Otto, S. W., and Felten, E. W. (1992), Large-step Markov Chains for the TSP Incorporating Local Search Heuristics, Operations Research Letters, 11, 219-224
  12. Martin, O. C. and Otto, S. W. (1996), Combining Simulated Annealing with Local Search Heuristics, Operations Research, 63, 57-75
  13. Reinelt, G.(1991),TSPLlB-A Traveling Salesman Library, Operati Research Society of America Journal on Computing, 3, 376-384
  14. Reinelt, G. (1994), The Traveling Salesman Problem, Springer Verlag, Berlin
  15. Zhang, W. (2002), Depth-First Branch and Bound Versus Local Search: A Case Study, 17th National Conf. on Artificial Intelligence (AAAI-2000), Austin, TX, 930-935