Subtour Preservation Crossover Operator for the Symmetric TSP

대칭 순회 판매원문제를 위한 Subtour 보존 교차 연산자

  • Soak, Sang-Moon (Information Systems Examination Team, Korean Intellectual Property Office) ;
  • Lee, Hong-Girl (Division of e-business, Kyungnam University) ;
  • Byun, Sung-Cheal (Information Systems Examination Team, Korean Intellectual Property Office)
  • Published : 2007.06.30

Abstract

Genetic algorithms (GAs) are very useful methods for global search and have been applied to various optimization problems. They have two kinds of important search mechanisms, crossover and mutation. Because the performance of GAs depends on these operators, a large number of operators have been developed for improving the performance of GAs. Especially, many researchers have been more interested in a crossover operator than a mutation operator. The reason is that a crossover operator is a main search operator in GAs and it has a more effect on the search performance. So, we also focus on a crossover operator. In this paper we first investigate the drawback of various crossovers, especially subtour-based crossovers and then introduce a new crossover operator to avoid such drawback and to increase efficiency. Also we compare it with several crossover operators for symmetric traveling salesman problem (STSP) for showing the performance of the proposed crossover. Finally, we introduce an efficient simple hybrid genetic algorithm using the proposed operator and then the quality and efficiency of the obtained results are discussed.

Keywords

References

  1. Baraglia, R., Hidalgo, J. I., and Perego, R. (2001), A hybrid heuristic for the traveling salesman problem, IEEE Trans. Evolutionary Computation, 5(6), 613-622 https://doi.org/10.1109/4235.974843
  2. Boese, K. D., Kang, A. B., and Muddu, S. (1994), A new adaptive multi-start technique for combinatorial global optimizations, Operations Research Letters, 16(2), 101-113 https://doi.org/10.1016/0167-6377(94)90065-5
  3. Bui, T. N. and Moon, B-R. (1994), A New Genetic Approach for the Traveling Salesman Problem, In IEEE Conf on Evolutionary Computation, 7-12
  4. Bui, T. N. and Moon, B-R. (1994), A new genetic approach for the traveling salesman problem, In IEEE Conf.e on Evolutionary Computation, 7-12
  5. Davis, L. (1985), Applying adaptive algorithms to domains. Proc. of the Int. Joint Conf. on Artificial Intelligence, 162-164
  6. Falco, I. D., Cioppa, A. D., and Tarantino, E. (2002), Mutationbased genetic algorithm: performance evolution, Applied Soft Computing, 1, 285-299 https://doi.org/10.1016/S1568-4946(02)00021-2
  7. Fox, B. R. and McMahon, M. B. (1991), Genetic Operators for Sequencing Problems. In Foundations of Genetic Algorithms, Kaufmann, 284-300
  8. Freisleben, B. and Merz, P. (1996), A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesmen Problems, IEEE Int. Conf. on Evolutionary Computation, 616-621
  9. Goldberg, D. (1989), Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, Reading, MA
  10. Goldberg, D. and Lingle, R. (1985), Alleles, loci and the traveling salesman problem, Proc. of the 1 st lnt Conf. on Genetic Algorithm, 154-159
  11. Grefenstette, Gopal, R., Rosmaita, B., and Gucht, D. (1985), Genetic Algorithms for the Traveling Salesman Problem, First Int. Conf. on GA and Their Applications, 160-168
  12. Jung, S. and Moon, B-R. (2002), Toward Minimal Restriction of Genetic Encoding and Crossovers for the 2D Euclidean TSP, IEEE Transactions on Evolutionary Computation, 6(6), 557-565 https://doi.org/10.1109/TEVC.2002.804321
  13. Karp, R. M. (1972), Reducibility among combinatorial problems. Complexity of Computer Computations, Advances in Computing Research, Plenum Press
  14. Katayama, K., Hirabayashi, H., and Narihisa, H. (1998), Performance Analysis of a New Genetic Crossover for the Traveling Salesman Problem. IEICE TRANS. FUNDAMENTALS, E81-A 5,738-750
  15. Kzubera, J. and Whitley, D. (1994), Advanced Correlation Analysis of Operators for the Traveling Salesman Problem, In parallel Problem Solving from Nature III, 68-77
  16. Maekawa, K., Mori, N., Tamaki, H., Kita, H., and Nishikawa, Y. (1996), A Genetic Solution for the Traveling Salesman Problem by Means of a Thermodynamical Selection Rule, Proc. of IEEE Int. Conf. on Evolutionary Computation, 529-534
  17. Mak K. T. and Morton, A. J. (1993), A modified Lin-Kernighan traveling-salesman heuristic, Operations Research Letters, 13, 127-132 https://doi.org/10.1016/0167-6377(93)90001-W
  18. Martin, O. C., Otto, S. W., and Felten, E. W. (1991), Large-step Markov chains for the traveling salesman problem, Complex Systems, 5, 299-326
  19. Mathias, K. and Whitley, D. (1992), Genetic operators, the fitness landscape and the traveling salesman problem. Proc. Parallel Problem Solving from Nature II, 219-228
  20. Michalewicz, Z. (1992), Genetic Algorithms-Data Structures = Evolution Programs
  21. Morikawa, K., Furuhashi, T., and Uchikawa, Y. (1992), Single Populated Genetic Algorithm and its Application to Jobshop Scheduling, Proc. of the 1992 Int. Conf. on Industrial Electronics, Control, Instrumentation, and Automation, 2,1014-1019
  22. Moscato, P. (1989), On Genetic Crossover Operators for Relative Order Preservation. Caltech Concurrent Computation Program, C3P Report 778
  23. Muhlenbein, H. (1992), Parallel Genetic Algorithm In Combinatorial Optimization, Computer Science and Operations Research, 441-456
  24. Murata, T. and Ishibuchi, H. (1996), Positive and Negative Combination Effects of Crossover and Mutation Operators in Sequencing Problems, IEEE Int. Conf. on Evolutionary Computation, 170-175
  25. Nguyen, H. D., Yoshihara, I., and Yasunaga, M. (2000), Modified Edge Recombination Operators of Genetic Algorithms for the Traveling Salesman Problem, 20th Annual Conf. of the IEEE on Industrial Electronics Society, 4, 2815-2820
  26. Oliver, I., Smith, D., and Holland, J. (1989), A Study of Permutation Crossover Operators on the Traveling Salesman Problem. Proc. of the 2nd Int. Conf. on GA, 224-230
  27. Poon, P. W. and Carter, J. N. (1995), Genetic Algorithm Crossover Operators For Ordering Application, Computers & Operations Research, 22(1),135-147 https://doi.org/10.1016/0305-0548(93)E0024-N
  28. Qu, L. and Sun, R. (1999), A synergetic approach to genetic algorithms for solving traveling salesman problem, International Journal of Information Sciences, 117, 267-283 https://doi.org/10.1016/S0020-0255(99)00026-2
  29. Seo, D-I. and Moon, B-R. (2002), Voronoi Quantized Crossover for Traveling Salesman Problem, Genetic and Evolutionary Computation Conference, 544-552
  30. Shang, Y. and Li, G. J. (1991), New Crossover Operators In Genetic Algorithms, Proc. of the 1991 IEEE Int. Conf. on Tools for Artificial Intelligence, 150-153
  31. Starkweather, T., McDaniel, S., Mathias, K., Whitley, D., and Whitley, C. (1991), A Comparison of Genetic Sequencing Operators, Proc. of the 4th Int. Conf. on Genetic Algorithm, 69-76
  32. Syswerda, G. (1991), Schedule Optimization Using Genetic Algorithms, In l. Davis, ed., handbook of Genetic Algorithms, New York, 332-349
  33. Tao, G. and Michalewicz, Z. (1998), Inver-over Operator for the TSP, Proc. of the 5th Int. Conf on Parallel Problem Sloving from Nature, Lecture Notes in Computer Science, 1498, Springer-Verlag, 803-812
  34. TSPLIB. http://www.iwr.uni-heidelberg.deli wr/comopt/soft/TSPLIB95/ TSPLIB.html
  35. Whitley, D., Starkweather, T., and Fuquay, D. (1989), Scheduling problems and traveling salesman: the genetic edge recombination and operator, Proc. 3rd Int. Conf. GA and their Applications,133-140
  36. Yamamura, M., Ono, I., and Kobayashi, S. (1992), Character-preserving genetic algorithms for traveling salesman problem. Journal of Japan Society for Artificial Intelligence, 6, 1049-1059
  37. Yamamura, M., Ono, I., and Kobayashi, S. (1996), Emergent Search on Double Circle TSPs using Subtour Exchange Crossover, Proc. of the 3rd IEEE Conf. on Evolutionary Computation,535-540
  38. Yang, L. and Stacey, D. A. (200 I), Solving the Traveling Salesman Problem U sing the Enhanced Genetic Algorithm, Lecture Notes in Computer Science, 2056, Springer-Verlag, 307-316
  39. Yang, R. (1997), Solving Large Traveling Salesman Problems with Small Populations, Genetic Algorithms in Engineering Systems: Innovations and Applications, 157-162.