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Mathematical Problems in Engineering
Volume 2017, Article ID 3046830, 20 pages
https://doi.org/10.1155/2017/3046830
Review Article

Bee-Inspired Algorithms Applied to Vehicle Routing Problems: A Survey and a Proposal

Natural Computing and Machine Learning Laboratory (LCoN), Graduate Program in Electrical Engineering and Computing, Mackenzie Presbyterian University, R. da Consolação 930, Higienópolis, 01302-000 São Paulo, SP, Brazil

Correspondence should be addressed to Leandro N. de Castro; rb.eiznekcam@senunl

Received 25 January 2017; Revised 29 July 2017; Accepted 22 August 2017; Published 8 October 2017

Academic Editor: Jorge Magalhaes-Mendes

Copyright © 2017 Thiago A. S. Masutti and Leandro N. de Castro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Luke, Essentials of Metaheuristics, Lulu, 2nd edition, 2013.
  2. Z. Michalewicz and D. Fogel, How to Solve It: Modern Heuristics, Springer Science & Business Media, 2013.
  3. A. G. Cunha, R. Takahashi, and C. H. Antunes, Evolutionary Computing and Metaheuristics Manual, Imprensa da Universidade de Coimbra, Coimbra, Portugal, 2012.
  4. C. B. da Cunha, “Practical aspects of the application of vehicle routing models to real world problems,” Transportes, vol. 8, no. 2, pp. 1–23, 2000. View at Google Scholar
  5. E. Lawler, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, John Wiley & Sons, Incorporated, 1985.
  6. G. Laporte, “The traveling salesman problem: an overview of exact and approximate algorithms,” European Journal of Operational Research, vol. 59, no. 2, pp. 231–247, 1992. View at Publisher · View at Google Scholar · View at Scopus
  7. G. Reinelt, “TSPLIB: A traveling salesman problem library,” ORSA Journal on Computing, vol. 3, no. 4, pp. 376–384, 1991. View at Publisher · View at Google Scholar
  8. P. Toth and D. Vigo, The Vehicle Routing Problem, Society for Industrial and Applied Mathematics (SIAM), 2001.
  9. G. Gutin and A. Punnen, The Traveling Salesman Problem And Its Variations, Springer Science & Business Media, 2002.
  10. G. Laporte, “Fifty years of vehicle routing,” Transportation Science, vol. 43, no. 4, pp. 408–416, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Laporte, M. Gendreau, J. Potvin, and F. Semet, “Classical and modern heuristics for the vehicle routing problem,” International Transactions in Operational Research, vol. 7, no. 4-5, pp. 285–300, 2000. View at Publisher · View at Google Scholar
  12. P. Toth and D. Vigo, Vehicle Routing, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2014. View at Publisher · View at Google Scholar
  13. L. N. de Castro, Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications and Applications, CRC Press, 2006.
  14. X.-S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, 2010.
  15. H. Zang, S. Zhang, and K. Hapeshi, “A review of nature-inspired algorithms,” Journal of Bionic Engineering, vol. 7, pp. S232–S237, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. L. N. de Castro, “Fundamentals of natural computing: an overview,” Physics of Life Reviews, vol. 4, no. 1, pp. 1–36, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems. [S.l.], Oxford University Press, 1999.
  18. C. Blum and D. Merkle, Swarm Intelligence: Introduction and Applications, Natural Computing Series, Springer, 2008. View at Publisher · View at Google Scholar
  19. M. Dorigo, M. Birattari, and T. Stützle, “Ant colony optimization,” IEEE Computational Intelligence Magazine, vol. 1, no. 4, pp. 28–39, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Eberhart and Y. Shi, “Particle Swarm Optimization: Developments, Applications and Resources,” in Proceedings of the Congress on Evolutionary Computation, IEEE 2001, pp. 81–86, 2001.
  21. R. D. Maia, L. N. de Castro, and W. M. Caminhas, “Collective decision-making by bee colonies as model for optimization - the OptBees algorithm,” Applied Mathematical Sciences, vol. 7, no. 85-88, pp. 4327–4351, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Karaboga and B. Akay, “A survey: algorithms simulating bee swarm intelligence,” Artificial Intelligence Review, vol. 31, no. 1–4, pp. 61–85, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. S. Bitam, M. Batouche, and E.-G. Talbi, “A survey on bee colony algorithms,” in Proceedings of the IEEE International Symposium on Parallel and Distributed Processing, Workshops and Phd Forum (IPDPSW '10), pp. 1–8, IEEE, New York, NY, USA, April 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. J. A. Ruiz-Vanoye, O. Díaz-Parra, F. Cocón et al., “Meta-heuristics algorithms based on the grouping of animals by social behavior for the traveling salesman problem,” International Journal of Combinatorial Optimization Problems and Informatics, vol. 3, no. 3, pp. 104–123, 2012. View at Google Scholar
  25. B. K. Verma and D. Kumar, “A review on artificial bee colony algorithm,” International Journal of Engineering & Technology, vol. 2, no. 3, pp. 175–186, 2013. View at Publisher · View at Google Scholar
  26. D. Karaboga, B. Gorkemli, C. Ozturk, and N. Karaboga, “A comprehensive survey: artificial bee colony (ABC) algorithm and applications,” Artificial Intelligence Review, vol. 42, pp. 21–57, 2014. View at Publisher · View at Google Scholar · View at Scopus
  27. D. Agarwal, A. Gupta, and P. K. Singh, “A systematic review on artificial bee colony optimization technique,” International Journal of Control Theory and Applications, vol. 9, no. 11, pp. 5487–5500, 2016. View at Google Scholar · View at Scopus
  28. M. M. Millonas, “Swarms, Phase Transitions, and Collective Intelligence,” in LANGTON, C. G. Artificial Life III: Proceedings of the Workshop on Artificial Life, pp. 417–445, LANGTON, C. G. Artificial Life III: Proceedings of the Workshop on Artificial Life, 1994. View at Google Scholar
  29. D. S. Johnson and A. McGeoch, “The traveling salesman problem: A case study in local optimization,” Local search in Combinatorial Optimization, vol. 1, pp. 215–310, 1997. View at Google Scholar
  30. R. D. Angel, W. L. Caudle, R. Noonan, and A. Whinston, “Computer-assisted school bus scheduling,” Management Science, vol. 18, no. 6, pp. 279–288, 1972. View at Publisher · View at Google Scholar
  31. T. Bektas, “The multiple traveling salesman problem: an overview of formulations and solution procedures,” Omega, vol. 34, no. 3, pp. 209–219, 2006. View at Publisher · View at Google Scholar · View at Scopus
  32. D. Karaboga, “An idea based on honey bee swarm for numerical optimization,” Tech. Rep. tr06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005, vol. 200. View at Google Scholar
  33. B. Basturk and D. Karaboga, “On the performance of artificial bee colony (ABC) algorithm,” Applied Soft Computing Journal, vol. 8, no. 1, pp. 687–697, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Banharnsakun, T. Achalakul, and B. Sirinaovakul, “ABC-GSX: A hybrid method for solving the traveling salesman problem,” in Proceedings of the 2010 2nd World Congress on Nature and Biologically Inspired Computing, NaBIC 2010, pp. 7–12, jpn, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Nakrani and C. Tovey, “On honey bees and dynamic server allocation in internet hosting centers,” Adaptive Behavior, vol. 12, no. 3-4, pp. 223–240, 2004. View at Publisher · View at Google Scholar · View at Scopus
  36. L. P. Wong, M. Y. H. Low, and C. S. Chong, “A bee colony optimization algorithm for traveling salesman problem,” in Proceedings of the Second Asia International Conference on Modelling & Simulation, pp. 818–823, 2008.
  37. X. Lu and Y. Zhou, “A novel global convergence algorithm: bee collecting pollen algorithm,” in Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science, D. S. Huang, D. C. Wunsch, D. S. Levine, and Jo. K. H., Eds., vol. 5227, Springer, Berlin, Heidelberg, 2008. View at Google Scholar
  38. P. Lučić and D. Teodorović, “Bee System: Modeling Combinatorial Optimization Transportation Engineering Problems by Swarm Intelligence,” in Preprints of the TRISTAN IV Triennial Symposium on Transportation Analysis, pp. 441–445, 2001. View at Google Scholar
  39. P. Lučić and D. Teodorović, “Transportation modeling: An artificial life approach,” Proceedings of the International Conference on Tools with Artificial Intelligence, pp. 216–223, 2002. View at Publisher · View at Google Scholar · View at Scopus
  40. D. Teodorovic, P. Lucic, G. Markovic, and M. Dell'Orco, “Bee colony optimization: principles and applications,” in In Neural Network Applications in Electrical Engineering, pp. 151–156, NEUREL, 2006. View at Google Scholar
  41. H. Abbass, “MHBO: Marriage in honey bees optimization-A haplometrosis polygynous swarming approach,” in Proceedings of the, 2001 IEEE Congress on Evolutionary Computation, vol. 1, pp. 207–214, 2001.
  42. C. Yang, J. Chen, and X. Tu, “Algorithm of marriage in honey bees optimization based on the nelder-mead method,” in Proceedings of the International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2007). Advances in Intelligent Systems Research, 2007. View at Publisher · View at Google Scholar
  43. C. Yang, X. Tu, and J. Chen, “Algorithm of marriage in honey bees optimization based on the wolf pack search,” in Proceedings of the 2007 International Conference on Intelligent Pervasive Computing, IPC 2007, pp. 462–467, kor, October 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. Y. Marinakis, M. Marinaki, and G. Dounias, “Honey bees mating optimization algorithm for the vehicle routing problem,” Studies in Computational Intelligence, vol. 129, pp. 139–148, 2008. View at Publisher · View at Google Scholar · View at Scopus
  45. D. Karaboga and B. Gorkemli, “A combinatorial Artificial Bee Colony algorithm for traveling salesman problem,” in Proceedings of the International Symposium on Innovations in Intelligent Systems and Applications (INISTA '11), pp. 50–53, Istanbul, Turky, June 2011. View at Publisher · View at Google Scholar · View at Scopus
  46. V. Singh, R. Tiwari, D. Singh, and A. Shukla, “RGBCA-genetic bee colony algorithm for travelling salesman problem,” in Proceedings of the 2011 World Congress on Information and Communication Technologies, WICT 2011, pp. 1002–1008, ind, December 2011. View at Publisher · View at Google Scholar · View at Scopus
  47. X. Zhang, Q. Bai, and X. Yun, “A new hybrid artificial bee colony algorithm for the traveling salesman problem,” in Proceedings of the 2011 IEEE 3rd International Conference on Communication Software and Networks, ICCSN 2011, pp. 155–159, chn, May 2011. View at Publisher · View at Google Scholar · View at Scopus
  48. W. Y. Szeto, Y. Wu, and S. C. Ho, “An artificial bee colony algorithm for the capacitated vehicle routing problem,” European Journal of Operational Research, vol. 215, no. 1, pp. 126–135, 2011. View at Publisher · View at Google Scholar · View at Scopus
  49. E. Özceylan, M. S. Kiran, and Y. Atasagun, “A new hybrid heuristic approach for solving green traveling salesman problem,” in Proceedings of the 41st International Conference on Computers and Industrial Engineering, pp. 23–26, 2011. View at Scopus
  50. P. Ji and Y. Wu, “An improved artificial bee colony algorithm for the capacitated vehicle routing problem with time-dependent travel times,” in Proceedings of the Tenth International Symposium On Operations Research And Its Applications (ISORA 2011, pp. 75–82, 2011.
  51. W. Li, W. Li, Y. Yang, H. Liao, J. Li, and X. Zheng, “Artificial bee colony algorithm for traveling salesman problem,” Advanced Materials Research, vol. 314-316, pp. 2191–2196, 2011. View at Publisher · View at Google Scholar · View at Scopus
  52. I. Brajevic, “Artificial bee colony algorithm for the capacitated vehicle routing problem,” in Proceedings of the European Computing Conference, ECC '11, pp. 239–244, 2011. View at Scopus
  53. Y.-J. Shi, F.-W. Meng, and G.-J. Shen, “A modified artificial bee colony algorithm for vehicle routing problems with time windows,” Information Technology Journal, vol. 11, no. 10, pp. 1490–1495, 2012. View at Publisher · View at Google Scholar · View at Scopus
  54. S. Iqbal and M. S. Rahman, “Vehicle routing problems with soft time windows,” in Proceedings of the 2012 7th International Conference on Electrical and Computer Engineering, ICECE 2012, pp. 634–638, 2012. View at Publisher · View at Google Scholar · View at Scopus
  55. K. Karabulut and M. F. Tasgetiren, “A discrete artificial bee colony algorithm for the traveling salesman problem with time windows,” in Proceedings of the 2012 IEEE Congress on Evolutionary Computation, CEC 2012, aus, June 2012. View at Publisher · View at Google Scholar · View at Scopus
  56. A. S. Bhagade and P. V. Puranik, “Artificial Bee Colony (ABC) Algorithm For Vehicle Routing Optimization Problem,” International Journal of Soft Computing and Engineering, vol. 2, pp. 329–333, 2012. View at Google Scholar
  57. N. Pathak and S. P. Tiwari, “Traveling Salesman Problem Using Bee Colony with SPV,” International Journal of Soft Computing and Engineering, vol. 2, no. 3, pp. 410–414, 2012. View at Google Scholar
  58. L. Li, Y. Cheng, L. Tan, and B. Niu, “A discrete artificial bee colony algorithm for TSP problem,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6840, pp. 566–573, 2012. View at Publisher · View at Google Scholar · View at Scopus
  59. W. Bin, C. Hong, and Z.-Y. Cui, “Artificial bee colony algorithm for two-dimensional loading capacitated vehicle routing problem,” in Proceedings of the 2013 20th International Conference on Management Science and Engineering, ICMSE 2013, pp. 406–412, chn, July 2013. View at Publisher · View at Google Scholar · View at Scopus
  60. M. S. Kiran, H. Işcan, and M. Gündüz, “The analysis of discrete artificial bee colony algorithm with neighborhood operator on traveling salesman problem,” Neural Computing and Applications, vol. 23, no. 1, pp. 9–21, 2013. View at Publisher · View at Google Scholar · View at Scopus
  61. S. Sabet, F. Farokhi, and M. Shokouhifar, “A hybrid mutation-based artificial bee colony for traveling salesman problem,” Lecture Notes on Information Theory, vol. 1, no. 3, pp. 99–103, 2013. View at Publisher · View at Google Scholar
  62. B. Yao, P. Hu, M. Zhang, and S. Wang, “Artificial bee colony algorithm with scanning strategy for the periodic vehicle routing problem,” Simulation, vol. 89, no. 6, pp. 762–770, 2013. View at Publisher · View at Google Scholar · View at Scopus
  63. C.-Y. Liu, “An improved adaptive genetic algorithm for the multi-depot vehicle routing problem with time window,” Journal of Networks, vol. 8, no. 5, pp. 1035–1042, 2013. View at Publisher · View at Google Scholar · View at Scopus
  64. W. Yang and Z. Pei, “Hybrid ABC/PSO to solve travelling salesman problem,” International Journal of Computing Science and Mathematics, vol. 4, no. 3, pp. 214–221, 2013. View at Publisher · View at Google Scholar · View at Scopus
  65. S. Pandey and S. Kumar, “Enhanced artificial bee colony algorithm and its application to travelling salesman problem,” HCTL Open International Journal of Technology Innovations and Research, vol. 2, pp. 137–146, 2013. View at Google Scholar
  66. A. Rekaby, A. A. Youssif, and A. Sharaf Eldin, “Introducing adaptive artificial bee colony algorithm and using it in solving traveling salesman problem,” in Proceedings of the Science and Information Conference (SAI '13), pp. 502–506, 2013. View at Scopus
  67. Y. Yuan and Y. Zhu, “A hybrid artificial bee colony optimization algorithm,” in Proceedings of the 2014 10th International Conference on Natural Computation, ICNC 2014, pp. 492–496, chn, August 2014. View at Publisher · View at Google Scholar · View at Scopus
  68. S. Zhang, C. K. M. Lee, K. L. Choy, W. Ho, and W. H. Ip, “Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem,” Transportation Research Part D: Transport and Environment, vol. 31, pp. 85–99, 2014. View at Publisher · View at Google Scholar · View at Scopus
  69. O. E. Nahum, Y. Hadas, and U. Spiegel, “Multi-objective vehicle routing problems with time windows: A vector evaluated artificial bee colony approach,” International Journal of Computer and Information Technology, vol. 3, pp. 41–47, 2014. View at Google Scholar
  70. H. E. Kocer and M. R. Akca, “An improved artificial bee colony algorithm with local search for traveling salesman problem,” Cybernetics and Systems, vol. 45, no. 8, pp. 635–649, 2014. View at Publisher · View at Google Scholar · View at Scopus
  71. Y.-T. Chung, “A Hybrid Artificial Bee Colony Algorithm to Solve the Capacitated Vehicle Routing Problem in Logistics Management, Master's Dissertation,” in Department of Industrial Management, p. 81, National Taiwan University of Science and Technology, 2014. View at Google Scholar
  72. R. Nagaya and A. Inoie, “Hybrid ABC algorithm for the capacitated vehicle routing problem,” in Proceedings of the 8th International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS), 383, p. 382, 2014. View at Publisher · View at Google Scholar
  73. S. Z. Zhang and C. K. M. Lee, “An Improved Artificial Bee Colony Algorithm for the Capacitated Vehicle Routing Problem,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, SMC 2015, pp. 2124–2128, hkg, October 2015. View at Publisher · View at Google Scholar · View at Scopus
  74. M. Gündüz, M. S. Kiran, and E. Özceylan, “A hierarchic approach based on swarm intelligence to solve the traveling salesman problem,” Turkish Journal of Electrical Engineering and Computer Sciences, vol. 23, no. 1, pp. 103–117, 2015. View at Publisher · View at Google Scholar · View at Scopus
  75. M. Alzaqebah, S. Abdullah, and S. Jawarneh, “Modified artificial bee colony for the vehicle routing problems with time windows,” SpringerPlus, vol. 5, no. 1, article no. 1298, 2016. View at Publisher · View at Google Scholar · View at Scopus
  76. L. P. Wong, M. Y. Hean Low, and C. S. Chong, “An efficient bee colony optimization algorithm for traveling salesman problem using frequency-based pruning,” in Proceedings of the 7th IEEE International Conference on Industrial Informatics (INDIN '09), pp. 775–782, IEEE, Wales, UK, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  77. L. P. Wong, M. Y. H. Low, and C. S. Chong, “A bee colony optimization algorithm with the fragmentation state transition rule for traveling salesman problem,” in Proceedings of the 2009 Conference on Innovative Production Machines and Systems (IPROMS 2009), pp. 399–404, 2009.
  78. L.-P. Wong, M. Y. Hean Low, and C. S. Chong, “A generic bee colony optimization framework for combinatorial optimization problems,” in Proceedings of the Asia Modelling Symposium 2010: 4th International Conference on Mathematical Modelling and Computer Simulation, AMS2010, pp. 144–151, 2010. View at Publisher · View at Google Scholar · View at Scopus
  79. L.-P. Wong, M. Y. H. Low, and C. S. Chong, “Bee colony optimization with local search for traveling salesman problem,” International Journal on Artificial Intelligence Tools, vol. 19, no. 3, pp. 305–334, 2010. View at Publisher · View at Google Scholar · View at Scopus
  80. S. Häckel and P. Dippold, “The Bee Colony-inspired Algorithm (BCiA): A two-stage approach for solving the vehicle routing problem with time windows,” in Proceedings of the 11th Annual Genetic and Evolutionary Computation Conference, GECCO-2009, pp. 25–32, can, July 2009. View at Publisher · View at Google Scholar · View at Scopus
  81. A. S. Girsang, C.-W. Tsai, and C.-S. Yang, “A fast bee colony optimization for traveling salesman problem,” in Proceedings of the 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012, pp. 7–12, 2012. View at Publisher · View at Google Scholar · View at Scopus
  82. P. Lučić and D. Teodorović, “Computing with bees: Attacking complex transportation engineering problems,” International Journal on Artificial Intelligence Tools, vol. 12, no. 03, pp. 375–394, 2003. View at Publisher · View at Google Scholar
  83. P. Lučić and D. Teodorović, “Vehicle routing problem with uncertain demand at nodes: the bee system and fuzzy logic approach,” in Fuzzy Sets Based Heuristics for Optimization, vol. 126 of Studies in Fuzziness and Soft Computing, pp. 67–82, Springer Berlin Heidelberg, Berlin, Heidelberg, 2003. View at Publisher · View at Google Scholar
  84. M. Nikolić, D. Teodorović, and M. Šelmić, “Solving the vehicle routing problem with time windows by bee colony optimization metaheuristic,” in In Proceedings of the 1st Logistics International Conference, pp. 44–48, 2013.
  85. S. Jawarneh and S. Abdullah, “Sequential insertion heuristic with adaptive bee colony optimisation algorithm for vehicle routing problem with time windows,” PLoS ONE, vol. 10, no. 7, 2015. View at Google Scholar · View at Scopus
  86. Y. Marinakis, M. Marinaki, and G. Dounias, “Honey bees mating optimization algorithm for the Euclidean traveling salesman problem,” Information Sciences, vol. 181, no. 20, pp. 4684–4698, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  87. Y. Celik and E. Ulker, “A marriage in honey bee optimisation approach to the asymmetric travelling salesman problem,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 6, pp. 4123–4132, 2012. View at Google Scholar · View at Scopus
  88. Q. Ruan, Z. Zhang, L. Miao, and H. Shen, “A hybrid approach for the vehicle routing problem with three-dimensional loading constraints,” Computers & Operations Research, vol. 40, no. 6, pp. 1579–1589, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  89. A. Singh and D. Narayan, “Augmentation of travelling salesman problem using bee colony optimization,” International Journal of Innovative Technology and Exploring Engineering, 2012. View at Google Scholar
  90. R. D. Maia, L. N. De Castro, and W. M. Caminhas, “Bee colonies as model for multimodal continuous optimization: The OptBees algorithm,” in Proceedings of the 2012 IEEE Congress on Evolutionary Computation, CEC 2012, aus, June 2012. View at Publisher · View at Google Scholar · View at Scopus
  91. D. P. F. Cruz, R. D. Maia, A. Szabo, and L. N. de Castro, “A bee-inspired algorithm for optimal data clustering,” in Proceedings of the 2013 IEEE Congress on Evolutionary Computation, CEC 2013, pp. 3140–3147, mex, June 2013. View at Publisher · View at Google Scholar · View at Scopus
  92. D. P. F. Cruz, R. D. Maia, L. A. da Silva, and L. N. de Castro, “BeeRBF: A bee-inspired data clustering approach to design RBF neural network classifiers,” Neurocomputing, vol. 172, Article ID 15835, pp. 427–437, 2016. View at Publisher · View at Google Scholar · View at Scopus
  93. T. A. S. Masutti and L. N. De Castro, “TSPoptBees: A bee-inspired algorithm to solve the traveling salesman problem,” in Proceedings of the 5th IIAI International Congress on Advanced Applied Informatics, IIAI-AAI 2016, pp. 593–598, jpn, July 2016. View at Publisher · View at Google Scholar · View at Scopus
  94. L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold, 1991.
  95. P. Larrañaga, C. M. H. Kuijpers, R. H. Murga, I. Inza, and S. Dizdarevic, “Genetic algorithms for the travelling salesman problem: A review of representations and operators,” Artificial Intelligence Review, vol. 13, no. 2, pp. 129–170, 1999. View at Publisher · View at Google Scholar · View at Scopus
  96. T. A. S. Masutti and L. N. de Castro, “Parameter analysis of a bee-inspired algorithm to solve the traveling salesman problem,” in Proceedings of the 15th IASTED International Conference on Intelligent Systems and Control, ISC 2016, pp. 245–252, 2016. View at Scopus
  97. Y. Marinakis, A. Migdalas, and P. M. Pardalos, “Expanding neighborhood GRASP for the traveling salesman problem,” Computational Optimization and Applications, vol. 32, no. 3, pp. 231–257, 2005. View at Publisher · View at Google Scholar · View at Scopus