Neural Computing and Applications

, Volume 27, Issue 7, pp 1853–1866 | Cite as

A novel discrete bat algorithm for solving the travelling salesman problem

Original Article
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Abstract

The travelling salesman problem (TSP) is one of the well-known NP-hard combinatorial optimization and extensively studied problems in discrete optimization. The bat algorithm is a new nature-inspired metaheuristic optimization algorithm introduced by Yang in 2010, especially based on echolocation behavior of microbats when searching their prey. Firstly, this algorithm is used to solve various continuous optimization problems. In this paper we extend a discrete bat-inspired algorithm to solve the famous TSP. Although many algorithms have been used to solve TSP, the main objective of this research is to investigate this discrete version to achieve significant improvements, not only compared to traditional algorithms but also to another metaheuristics. Moreover, this study is based on a benchmark dataset of symmetric TSP from TSPLIB library.

Keywords

Travelling salesman problem NP-hard combinatorial optimization problem Nature-inspired metaheuristic Discrete bat-inspired algorithm 
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References

  1. 1.
    Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann ArborMATHGoogle Scholar
  2. 2.
    Schwefel H-P (1981) Numerical optimization of computer models. Wiley, LondonMATHGoogle Scholar
  3. 3.
    Kirkpatrick S (1984) Optimization by simulated annealing: quantitative studies. J Stat Phys 34(5–6):975–986MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kennedy J (2010) Particle swarm optimization. Encyclopedia of machine learning. Springer, Berlin, pp 760–766Google Scholar
  5. 5.
    Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: Proceedings of the first European conference on artificial life. Paris, France, pp 134–142Google Scholar
  6. 6.
    Wolsey LA, Nemhauser GL (2014) Integer and combinatorial optimization. Wiley, LondonMATHGoogle Scholar
  7. 7.
    Papadimitriou CH, Steiglitz K (1998) Combinatorial optimization: algorithms and complexity. Courier Dover Publications, MineolaMATHGoogle Scholar
  8. 8.
    Wong W (1995) Matrix representation and gradient flows for NP-hard problems. J Optim Theory Appl 87(1):197–220MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Dorigo M, Birattari M (2010) Ant colony optimization. Encyclopedia of machine learning. Springer, Berlin, pp 36–39Google Scholar
  10. 10.
    Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33–57CrossRefGoogle Scholar
  11. 11.
    Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013) Chaos-enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simul 18(2):327–340MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Lučić P, Teodorović D (2003) Computing with bees: attacking complex transportation engineering problems. Int J Artif Intell Tools 12(03):375–394CrossRefGoogle Scholar
  13. 13.
    Yang X-S (2009) Firefly algorithms for multimodal optimization. Stochastic algorithms: foundations and applications. Springer, Berlin, pp 169–178CrossRefGoogle Scholar
  14. 14.
    Yang X-S, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343MATHGoogle Scholar
  15. 15.
    Yang X-S (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74CrossRefGoogle Scholar
  16. 16.
    Yang X-S, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483CrossRefGoogle Scholar
  17. 17.
    Arora S (1998) Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J ACM (JACM) 45(5):753–782MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Bland RG, Shallcross DF (1989) Large travelling salesman problems arising from experiments in X-ray crystallography: a preliminary report on computation. Oper Res Lett 8(3):125–128MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Lenstra JK, Kan AR (1975) Some simple applications of the travelling salesman problem. Oper Res Q 717–733Google Scholar
  20. 20.
    Grötschel M, Jünger M, Reinelt G (1991) Optimal control of plotting and drilling machines: a case study. Math Methods Oper Res 35(1):61–84CrossRefMATHGoogle Scholar
  21. 21.
    Ratliff HD, Rosenthal AS (1983) Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem. Oper Res 31(3):507–521CrossRefMATHGoogle Scholar
  22. 22.
    Zachariasen M, Dam M (1996) Tabu search on the geometric traveling salesman problem. Meta-heuristics. Springer, Berlin, pp 571–587CrossRefGoogle Scholar
  23. 23.
    Chen Y, Zhang P (2006) Optimized annealing of traveling salesman problem from the nth-nearest-neighbor distribution. Phys A 371(2):627–632CrossRefGoogle Scholar
  24. 24.
    Potvin J-Y (1996) Genetic algorithms for the traveling salesman problem. Ann Oper Res 63(3):337–370CrossRefMATHGoogle Scholar
  25. 25.
    Qu L, Sun R (1999) A synergetic approach to genetic algorithms for solving traveling salesman problem. Inf Sci 117(3):267–283CrossRefGoogle Scholar
  26. 26.
    Marinakis Y, Migdalas A, Pardalos PM (2005) Expanding neighborhood GRASP for the traveling salesman problem. Comput Optim Appl 32(3):231–257MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. Evol Comput IEEE Trans 1(1):53–66CrossRefGoogle Scholar
  28. 28.
    Dorigo M, Gambardella LM (1997) Ant colonies for the travelling salesman problem. BioSystems 43(2):73–81CrossRefGoogle Scholar
  29. 29.
    Liu A, Deng G, Shan S (2006) Mean-contribution ant system: an improved version of ant colony optimization for traveling salesman problem. Simulated evolution and learning. Springer, Berlin, pp 489–496CrossRefGoogle Scholar
  30. 30.
    Manfrin M, Birattari M, Stützle T, Dorigo M (2006) Parallel ant colony optimization for the traveling salesman problem. Ant colony optimization and swarm intelligence. Springer, Berlin, pp 224–234CrossRefGoogle Scholar
  31. 31.
    Clerc M (2004) Discrete particle swarm optimization, illustrated by the traveling salesman problem. New optimization techniques in engineering. Springer, Berlin, pp 219–239CrossRefGoogle Scholar
  32. 32.
    Li X, Tian P, Hua J, Zhong N (2006) A hybrid discrete particle swarm optimization for the traveling salesman problem. Simulated evolution and learning. Springer, Berlin, pp 181–188CrossRefGoogle Scholar
  33. 33.
    Shi XH, Liang YC, Lee HP, Lu C, Wang Q (2007) Particle swarm optimization-based algorithms for TSP and generalized TSP. Inf Process Lett 103(5):169–176MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Ouaarab A, Ahiod B, Yang X-S (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24(7–8):1659–1669CrossRefGoogle Scholar
  35. 35.
    Reinelt G (1991) TSPLIB—a traveling salesman problem library. ORSA J Comput 3(4):376–384MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Kenndy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. pp 1942–1948Google Scholar
  38. 38.
    Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. Control Syst IEEE 22(3):52–67. doi: 10.1109/MCS.2002.1004010 MathSciNetCrossRefGoogle Scholar
  39. 39.
    Krishnanand K, Ghose D (2009) Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions. Swarm Intell 3(2):87–124CrossRefGoogle Scholar
  40. 40.
    Chu S-C, Tsai P-W, Pan J-S (2006) Cat swarm optimization. PRICAI 2006: trends in artificial intelligence. Springer, Berlin, pp 854–858CrossRefGoogle Scholar
  41. 41.
    Gandomi AH, Alavi AH (2012) Krill Herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Gheraibia Y, Moussaoui A (2013) Penguins search optimization algorithm (PeSOA). Recent trends in applied artificial intelligence. Springer, Berlin, pp 222–231CrossRefGoogle Scholar
  43. 43.
    Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. Advances in swarm intelligence. Springer, Berlin, pp 86–94Google Scholar
  44. 44.
    Bansal JC, Sharma H, Jadon SS, Clerc M (2014) Spider monkey optimization algorithm for numerical optimization. Memetic Comput 6(1):31–47CrossRefGoogle Scholar
  45. 45.
    Gandomi AH, Yang X-S, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255CrossRefGoogle Scholar
  46. 46.
    Khan K, Nikov A, Sahai A (2011) A fuzzy bat clustering method for ergonomic screening of office workplaces. In: Dicheva D, Markov Z, Stefanova E (eds) Third international conference on software, services and semantic technologies S3T 2011, vol 101., Advances in intelligent and soft computingSpringer, Berlin Heidelberg, pp 59–66. doi: 10.1007/978-3-642-23163-6_9 CrossRefGoogle Scholar
  47. 47.
    Tamiru AL, Hashim FM (2013) Application of bat algorithm and fuzzy systems to model energy changes in a gas turbine. In: Yang X-S (ed) Artificial intelligence, evolutionary computing and metaheuristics, vol 427., Studies in computational intelligenceSpringer, Berlin Heidelberg, pp 685–719. doi: 10.1007/978-3-642-29694-9_26 CrossRefGoogle Scholar
  48. 48.
    Yılmaz S, Küçüksille EU (2015) A new modification approach on bat algorithm for solving optimization problems. Appl Soft Comput 28:259–275CrossRefGoogle Scholar
  49. 49.
    Nguyen T-T, Pan J-S, Dao T-K, Kuo M-Y, Horng M-F (2014) Hybrid bat algorithm with artificial bee colony. In: Pan J-S, Snasel V, Corchado ES, Abraham A, Wang S-L (eds) Intelligent data analysis and its applications, vol II-298., Advances in intelligent systems and computingSpringer, Berlin, pp 45–55. doi: 10.1007/978-3-319-07773-4_5 Google Scholar
  50. 50.
    Pan T-S, Dao T-K, Nguyen T-T, Chu S-C (2015) Hybrid particle swarm optimization with bat algorithm. In: Sun H, Yang C-Y, Lin C-W, Pan J-S, Snasel V, Abraham A (eds) Genetic and evolutionary computing, vol 329., Advances in intelligent systems and computingSpringer, Berlin, pp 37–47. doi: 10.1007/978-3-319-12286-1_5 Google Scholar
  51. 51.
    Cai X, Wang L, Kang Q, Wu Q (2014) Bat algorithm with Gaussian walk. Int J Bio-Inspired Comput 6(3):166–174CrossRefGoogle Scholar
  52. 52.
    Gandomi AH, Yang X-S (2014) Chaotic bat algorithm. J Comput Sci 5(2):224–232MathSciNetCrossRefGoogle Scholar
  53. 53.
    Mirjalili S, Mirjalili S, Yang X-S (2014) Binary bat algorithm. Neural Comput Appl 25(3–4):663–681. doi: 10.1007/s00521-013-1525-5 CrossRefGoogle Scholar
  54. 54.
    Yang X-S, He X (2013) Bat algorithm: literature review and applications. Int J Bio-Inspired Comput 5(3):141–149CrossRefGoogle Scholar
  55. 55.
    Nakamura RY, Pereira LA, Costa K, Rodrigues D, Papa JP, Yang X-S (2012) BBA: A binary bat algorithm for feature selection. In: Graphics, patterns and images (SIBGRAPI), 2012 25th SIBGRAPI Conference on IEEE, pp 291–297Google Scholar
  56. 56.
    Xie J, Zhou Y, Tang Z (2013) Differential Lévy-Flights bat algorithm for minimization makespan in permutation flow shops. In: Huang D-S, Jo K-H, Zhou Y-Q, Han K (eds) Intelligent computing theories and technology, vol 7996., Lecture Notes in Computer ScienceSpringer, Berlin Heidelberg, pp 179–188. doi: 10.1007/978-3-642-39482-9_21 CrossRefGoogle Scholar
  57. 57.
    Sabba S, Chikhi S (2014) A discrete binary version of bat algorithm for multidimensional knapsack problem. Int J Bio-Inspired Comput 6(2):140–152CrossRefGoogle Scholar
  58. 58.
    Büyüksaatçı S (2015) Bat algorithm application for the single row facility layout problem. In: Yang X-S (ed) Recent advances in swarm intelligence and evolutionary computation, vol 585., Studies in computational intelligenceSpringer, Berlin, pp 101–120. doi: 10.1007/978-3-319-13826-8_6 Google Scholar
  59. 59.
    Fister I, Rauter S, Yang X-S, Ljubič K (2015) Planning the sports training sessions with the bat algorithm. Neurocomputing 149:993–1002CrossRefGoogle Scholar
  60. 60.
    Yang X-S (2011) Bat algorithm for multi-objective optimisation. Int J Bio-Inspired Comput 3(5):267–274CrossRefGoogle Scholar
  61. 61.
    Pappalardo E, Pardalos P, Stracquadanio G (2013) Mathematical optimization. Optimization approaches for solving string selection problems., Springer Briefs in OptimizationSpringer, New York, pp 13–25CrossRefGoogle Scholar
  62. 62.
    Du D-Z, Pardalos PM (1999) Handbook of combinatorial optimization: supplement, vol 1. Springer, BerlinCrossRefMATHGoogle Scholar
  63. 63.
    Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation. 1997 IEEE International Conference on, IEEE, pp 4104–4108Google Scholar
  64. 64.
    Larrañaga P, Kuijpers CMH, Murga RH, Inza I, Dizdarevic S (1999) Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif Intell Rev 13(2):129–170. doi: 10.1023/A:1006529012972 CrossRefGoogle Scholar
  65. 65.
    Li L, Zhang Y (2007) An improved genetic algorithm for the traveling salesman problem. Advanced intelligent computing theories and applications. With aspects of contemporary intelligent computing techniques. Springer, Berlin, pp 208–216CrossRefGoogle Scholar
  66. 66.
    Chen S-M, Chien C-Y (2011) Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst Appl 38(12):14439–14450CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2015

Authors and Affiliations

  1. 1.LAROSERI Laboratory, Department of Computer Science, Faculty of ScienceChouaïb Doukkali UniversityEl JadidaMorocco

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