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Journal of Computer Science and Technology

, Volume 27, Issue 5, pp 937–949 | Cite as

A Puzzle-Based Genetic Algorithm with Block Mining and Recombination Heuristic for the Traveling Salesman Problem

  • Pei-Chann ChangEmail author
  • Wei-Hsiu Huang
  • Zhen-Zhen Zhang
Regular Paper

Abstract

In this research, we introduce a new heuristic approach using the concept of ant colony optimization (ACO) to extract patterns from the chromosomes generated by previous generations for solving the generalized traveling salesman problem. The proposed heuristic is composed of two phases. In the first phase the ACO technique is adopted to establish an archive consisting of a set of non-overlapping blocks and of a set of remaining cities (nodes) to be visited. The second phase is a block recombination phase where the set of blocks and the rest of cities are combined to form an artificial chromosome. The generated artificial chromosomes (ACs) will then be injected into a standard genetic algorithm (SGA) to speed up the convergence. The proposed method is called “Puzzle-Based Genetic Algorithm” or “p-ACGA”. We demonstrate that p-ACGA performs very well on all TSPLIB problems, which have been solved to optimality by other researchers. The proposed approach can prevent the early convergence of the genetic algorithm (GA) and lead the algorithm to explore and exploit the search space by taking advantage of the artificial chromosomes.

Keywords

artificial chromosome blocks mining block recombination traveling salesman problem 

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References

  1. [1]
    Papadimitriou C H, Steglitz K. Combinatorial Optimization: Algorithms and Complexity. India: Dover Publications, 1998.Google Scholar
  2. [2]
    Garey M R, Graham R L, Johnson D S. Some NP-complete geometric problems. In Proc. the 8th Annual ACM Symposium on Theory of Computing, May 1976, pp.10–22.Google Scholar
  3. [3]
    Ozcan E, Erenturk M. A brief review of memetic algorithms for solving Euclidean 2D traveling salesman problem. In Proc. the 13th Turkish Symposium on Artificial Intelligence and Neural Networks, June 2004, pp.99–108.Google Scholar
  4. [4]
    Sankoff D, Zheng C, Muñoz A, Yang Z, Adam Z, Warren R, Choi V, Zhu Q. Issues in the reconstruction of gene order evolution. Journal of Computer Science and Technology, 2010, 25(1): 10–25.CrossRefGoogle Scholar
  5. [5]
    Black T, Fogel D B, Michalewicz Z. Handbook on Evolutionary Computation. USA: Oxford University Press, 1997.Google Scholar
  6. [6]
    Laporte G. The vehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 1992, 59(3): 345–358.zbMATHCrossRefGoogle Scholar
  7. [7]
    Onwubolu G C, Clerc M. Optimal path for automated drilling operations by a new heuristic approach using particle swarm optimization. International Journal of Production Research, 2004, 42 (3): 473–491.zbMATHCrossRefGoogle Scholar
  8. [8]
    Affenzeller M, Wanger S. A self-adaptive model for selective pressure handling within the theory of genetic algorithms. In Proc. the 9th EUROCAST, February 2003, pp.384–393.Google Scholar
  9. [9]
    Budinich M. A self-organizing neural network for the traveling salesman problem that is competitive with simulated annealing. Neural Computation, 1996, 8(2): 416–424.CrossRefGoogle Scholar
  10. [10]
    Liu G, He Y, Fang Y, Oiu Y. A novel adaptive search strategy of intensification and diversification in tabu search. In Proc. International Conference on Neural Networks and Signal Processing, December 2003, pp.428–431.Google Scholar
  11. [11]
    Bianchi L, Knowles J, Bowler N. Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms. European Journal of Operational Research, 2005, 162(1): 206–219.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Chu S C, Roddick J F, Pan J S. Ant colony system with communication strategies. Information Sciences, 2004, 167 (1-4): 63–76.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Leung K S, Jin H D, Xu Z B. An expanding self-organizing neural network for the traveling salesman problem. Neurocomputing, 2004, 62: 267–292.CrossRefGoogle Scholar
  14. [14]
    Kirkpatrick S, Gelatt Jr. C D, Vecchi M P. Optimization by simulated annealing. Science, 1983, 220(4598): 671–680.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Grefenstette J, Gopal R, Rosimaita B, Gucht D V. Genetic algorithms for the traveling salesman problem. In Proc. Int. Conf. Genetics Algorithms and Their Applications, October 1985, pp.160–168.Google Scholar
  16. [16]
    Braun H. On solving traveling salesman problems by genetic algorithm. In Lecture Notes in Computer Science 496, Schwefel H P, Männer R (eds.), Springer-Verlag, pp.129–133.Google Scholar
  17. [17]
    Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs (3rd edition). Berlin, Germany: Springer-Verlag, 1996.Google Scholar
  18. [18]
    Fan J, Li D. An overview of data mining and knowledge discovery. Journal of Computer Science and Technology, 1998, 13(4): 348–368.MathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    Moscato P, Norman M G. A memetic approach for the traveling salesman problem implementation of a computational ecology for combinatorial optimization on message-passing systems. In Proc. International Conference on Parallel Computing and Transputer Application, Sept. 1992, pp.177–186.Google Scholar
  20. [20]
    Oliver I M, Smith D J, Holland J R C. A study of permutation crossovers on the TSP. In Proc. the 2nd International Conference on Genetic Algorithm and Their Applications, July 1987, pp.224–230.Google Scholar
  21. [21]
    Whitely L D, Starkweather T, Fuquay D'A. Scheduling problems and traveling salesman: The genetic edge recombination operator. In Proc. the 3rd International Conference on Genetic Algorithms, June 1988, pp.133–140.Google Scholar
  22. [22]
    Mühlenbein H, Gorges-Schleuter M, Krämer O. Evolution algorithms in combinatorial optimization. Parallel Computing, 1988, 7(1): pp.65–85.zbMATHCrossRefGoogle Scholar
  23. [23]
    Nagata Y, Kobayashi S. Edge assembly crossover: A high-power genetic algorithm for the travelling salesman problem. In Proc. the 7th International Conference on Genetic Algorithms, July 1997, pp.450–457.Google Scholar
  24. [24]
    Tao G, Michalewicz Z. Inver-over operator for the TSP. In Proc. the 5th Int. Conf. Parallel Problem Solving from Nature, September 1998, pp.803–812.Google Scholar
  25. [25]
    Johnson D S, McGeoch L A. The traveling salesman problem: A case study in local optimization. In Local Search in Combinatorial Optimization, Aarts E, Lenstra J K (eds.), John Wiley and Sons, Ltd., 1997, pp.215–310.Google Scholar
  26. [26]
    Zou P, Zhou Z,Wan Y Y, Chen G L, Gu J. New meta-heuristic for combinatorial optimization problems: Intersection based scaling. Journal of Computer Science and Technology, 2004, 19(6): 740–751.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Merz P. A comparison of memetic recombination operators for the traveling salesman problem. In Proc. the Genetic and Evolutionary Computation Conference, July 2002, pp.472–479.Google Scholar
  28. [28]
    Baraglia R, Hidalgo J I, Perego R. A hybrid heuristic for the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 2001, 5(6): 613–622.CrossRefGoogle Scholar
  29. [29]
    Tsai H K, Yang J M, Tsai Y F, Kao C Y. Some issues of designing genetic algorithms for traveling salesman problems. Soft Computing, 2004, 8(10): 689–697.zbMATHCrossRefGoogle Scholar
  30. [30]
    Goldberg D E, Korb B, Deb K. Messy genetic algorithms: Motivation, analysis, and first results. Complex Syst., 1989, 3(5): 493–530.MathSciNetzbMATHGoogle Scholar
  31. [31]
    Goldberg D E, Deb K, Kargupta H, Hank G. Rapid accurate optimization of difficult problems using fast messy genetic algorithms. In Proc. the 5th Int. Conf. Genetic Algorithms, June 1993, pp.56–64.Google Scholar
  32. [32]
    Kujazew D, Golberg D E. OMEGA-ordering messy GA: Solving permutation problems with the fast messy genetic algorithm and random keys. In Proc. Genetic Evolutionary Computation Conf., July 2000, pp.181–188.Google Scholar
  33. [33]
    Zaritsky A, Sipper M. The preservation of favored building blocks in the struggle for fitness: The Puzzle Algorithm. IEEE Transactions on Evolutionary Computation, 2004, 8(5): 443–455.CrossRefGoogle Scholar
  34. [34]
    Chang P C, Chen S H, Fan C Y. Mining gene structures to inject artificial chromosomes for genetic algorithm in single machine scheduling problems. Applied Soft Computing, 2008, 8(1): 767–777.CrossRefGoogle Scholar
  35. [35]
    Chang P C, Chen S H, Fan C Y, Chan C L. Genetic algorithm with artificial chromosomes for multi-objective flow shop scheduling problems. Applied Mathematics and Computation, 2008, 205(2): 550–561.zbMATHCrossRefGoogle Scholar
  36. [36]
    Chang P C, Chen S H, Fan C Y, Mani V. Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems. Annals of Operations Research, 2010, 180(1): 197–211.MathSciNetzbMATHCrossRefGoogle Scholar
  37. [37]
    Kantardzic M. Data Mining: Concepts, Models, Methods, and Algorithms. Totowa, USA, Wiley-IEEE Press, 2003.zbMATHGoogle Scholar
  38. [38]
    Sangkavichitr C, Chongstitvatana P. Fragment as a small evidence of the building blocks existence. In Exploitation of Linkage Learning in Evolutionary Algorithms, Chen Y P (ed.), Adaptation, Learning, and Optimization, Springer-Verlag Berlin Heidelberg, 2010, pp.5–44.Google Scholar
  39. [39]
    Dorigo M, Gambardella L M. Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 53–66.CrossRefGoogle Scholar
  40. [40]
    Narendra P M, Fukunaga K. A branch and bound algorithm for feature subset selection. IEEE Transactions on Computers, 1977, C-26(9): 917–922.CrossRefGoogle Scholar
  41. [41]
    Skellam J G. Studies in statistical ecology: I. Spatial pattern. Biometrica, 1952, 39(3/4): 346–362.zbMATHGoogle Scholar
  42. [42]
    Pasti R, de Castro L N. A Neuro-immune network for solving the traveling salesman problem. In Proc. International Joint Conference on Neural Networks, July 2006, 6: 3760–3766.CrossRefGoogle Scholar
  43. [43]
    Somhom S, Modares A, Enkawa T. A self-organizing model for the travelling salesman problem. Journal of the Operational Research Society, 1997, 48: 919–928.zbMATHGoogle Scholar
  44. [44]
    Smith J, Fogarty T C. Recombination strategy adaptation via evolution of gene linkage. In Proc. the IEEE Conference on Evolutionary Computation, USA, May 1996, pp.826–831.Google Scholar
  45. [45]
    Hahsler M, Hornik K. TSP - Infrastructure for the traveling salesperson problem. Journal of Statistical Software, 2007, 23(2): 1–21.MathSciNetGoogle Scholar
  46. [46]
    Yao X. An empirical study of genetic operators in genetic algorithms. Microprocessing and Microprogramming, 1993, 38(1-5): 707–714.CrossRefGoogle Scholar
  47. [47]
    Dai H W, Yang Y, Li C, Shi J, Gao S, Tang Z. Quantum interference crossover-based clonal selection algorithm and its application to travelling salesman problem. IEICE Trans. Inf. & Syst., 2009, E92.D(1): 78–85.CrossRefGoogle Scholar
  48. [48]
    Chang P C, Huang W H, Ting C J. Developing a varietal GA with ESMA strategy for solving the pick and place problem in printed circuit board assembly line. Journal of Intelligent Manufacturing, 2010, DOI:  10.1007/s10845-010-0461-9.

Copyright information

© Springer Science+Business Media New York & Science Press, China 2012

Authors and Affiliations

  • Pei-Chann Chang
    • 1
    Email author
  • Wei-Hsiu Huang
    • 1
  • Zhen-Zhen Zhang
    • 2
  1. 1.Department of Information ManagementYuan Ze UniversityTaiwanChina
  2. 2.Department of Computer ScienceXiamen UniversityXiamenChina

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