Nature-Inspired Intelligent Optimisation Using the Bees Algorithm

  • Duc Truong Pham
  • Marco Castellani
  • Hoai An Le Thi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8342)


The Bees Algorithm models the foraging behaviour of honey bees in order to solve optimisation problems. The algorithm performs a kind of exploitative neighbourhood search combined with random explorative search. This paper describes the Bees Algorithm, and compares its functioning and performance with those of other state-of-the-art nature-inspired intelligent optimisation methods. Two application cases are presented: the minimisation of a set of well-known benchmark functions, and the training of neural networks to reproduce the inverse kinematics of a robot manipulator. In both cases, the Bees Algorithm proved its effectiveness and speed. Compared with other state-of-the-art methods, the performance of the Bees Algorithm was very competitive.


intelligent optimisation swarm intelligence bees algorithm honey bees 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rechenberg, I.: Cybernetic Solution Path of an Experimental Problem. Ministry of Aviation, Royal Aircraft Establishment, Farnborough, Hants UK (1965)Google Scholar
  2. 2.
    Fogel, L., Owens, A., Walsh, M.: Artificial intelligence through simulated evolution. J. Wiley, New York (1966)MATHGoogle Scholar
  3. 3.
    Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  4. 4.
    Koza, J.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)MATHGoogle Scholar
  5. 5.
  6. 6.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm intelligence: from natural to artificial systems. Oxford University Press, New York (1999)MATHGoogle Scholar
  7. 7.
    Kennedy, J.: Swarm Intelligence. In: Zomaya, A. (ed.) Handbook of Nature-Inspired and Innovative Computing, pp. 187–219. Springer, USA (2006)CrossRefGoogle Scholar
  8. 8.
    Yang, X.: Nature-Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press (2010)Google Scholar
  9. 9.
    Gross, R., Dorigo, M.: Towards group transport by swarms of robots. International Journal Bio-Inspired Computation 1(1-2), 1–13 (2009)CrossRefGoogle Scholar
  10. 10.
    Jevtic, A., Andina, D.: Adaptive artificial ant colonies for edge detection in digital images. In: Proceedings IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society, Glendale, AZ, pp. 2813–2816 (2010)Google Scholar
  11. 11.
    Reynolds, C.: Flocks, herds and schools: A distributed behavioural model. Computer Graphics 21(4), 25–34 (1987)CrossRefGoogle Scholar
  12. 12.
  13. 13. (accessed June 2012)
  14. 14. (accessed June 2012)
  15. 15. (accessed June 2012)
  16. 16.
  17. 17. (accessed June 2012)
  18. 18.
    Pham, D.T., Castellani, M.: The Bees Algorithm – Modelling Foraging Behaviour to Solve Continuous Optimisation Problems. Proceedings of the Institution of Mechanical Engineers, Part C 223(12), 2919–2938 (2009)Google Scholar
  19. 19.
    Pham, D.T., Liu, X.: Neural Networks for Identification, Prediction and Control. Springler-Verlag Ltd., London (1995)CrossRefGoogle Scholar
  20. 20.
    Tereshko, V., Loengarov, A.: Collective Decision-Making in Honey Bee Foraging Dynamics. Journal of Computing and Information Systems 9(3), 1–7 (2005)Google Scholar
  21. 21.
    Seeley, T.: The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Harvard University Press, Cambridge (1996)Google Scholar
  22. 22.
    Tereshko, V., Lee, T.: How Information-Mapping Patterns Determine Foraging Behaviour of a Honey Bee Colony. Open Systems and Information Dynamics 9(2), 181–193 (2002)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Pham, D.T., Karaboga, D.: Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer, London (2000)CrossRefGoogle Scholar
  24. 24.
    Pham, D.T., Otri, S., Koc, E., Ghanbarzadeh, A., Rahim, S., Zaidi, M.: The Bees Algorithm, Technical Note, Manufacturing Engineering Centre, Cardiff University, Cardiff, UK (2005)Google Scholar
  25. 25.
    Pham, D.T., Ghanbarzadeh, A., Koc, E., Otri, S.: The Bees Algorithm, A Novel Tool for Complex Optimisation Problems. In: Proceedings 2nd Int Virtual Conf on Intelligent Production Machines and Systems (IPROMS 2006), pp. 454–459 (2006)Google Scholar
  26. 26.
    Pham, D.T., Ghanbarzadeh, A., Koc, E., Otri, S.: Application of the Bees Algorithm to the Training of Radial Basis Function Networks for Control Chart Pattern Recognition. In: Proceedings 5th CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (CIRP ICME 2006), Ischia, Italy, pp. 711–716 (2006)Google Scholar
  27. 27.
    Pham, D.T., Otri, S., Ghanbarzadeh, A., Koç, E.: Application of the Bees Algorithm to the training of learning vector quantisation networks for control chart pattern recognition. In: Proceedings Information and Communication Technologies (ICTTA 2006), Syria, pp. 1624–1629 (2006)Google Scholar
  28. 28.
    Pham, D.T., Soroka, A., Ghanbarzadeh, A., Koç, E., Otri, S., Packianather, M.: Optimising Neural Networks for Identification of Wood Defects Using the Bees Algorithm. In: Proceedings IEEE International Conference on Industrial Informatics, Singapore, pp. 1346–1351 (2006)Google Scholar
  29. 29.
    Pham, D.T., Sholedolu, M.: Using a Hybrid PSO-Bees Algorithm to train Neural Networks for Wood Defect Classification. In: Proceedings 4th International Virtual Conference on Intelligent Production Machines and Systems (IPROMS 2008), pp. 385–390 (2008)Google Scholar
  30. 30.
    Pham, D.T., Darwish, A.: Using the bees algorithm with Kalman filtering to train an artificial neural network for pattern classification. Journal of Systems and Control Engineering 224(7), 885–892 (2010)Google Scholar
  31. 31.
    Khanmirzaei, Z., Teshnehlab, M.: Prediction Using Recurrent Neural Network Based Fuzzy Inference system by the Modified Bees Algorithm. International Journal of Advancements in Computing Technology 2(2), 42–55 (2010)CrossRefGoogle Scholar
  32. 32.
    Pham, D.T., Zaidi, M., Mahmuddin, M., Ghanbarzadeh, A., Koc, E., Otri, S.: Using the bees algorithm to optimise a support vector machine for wood defect classification. In: IPROMS 2007 Innovative Production Machines and Systems Virtual Conference, pp. 454–461 (2007)Google Scholar
  33. 33.
    Pham, D.T., Otri, S., Afify, A., Massudi, M., Al-Jabbouli, H.: Data clustering using the bees algorithm. In: Proceedings 40th CIRP International Manufacturing Systems Seminar, Liverpool, UK (2007)Google Scholar
  34. 34.
    Pham, D.T., Suarez-Alvarez, M., Prostov, Y.: Random search with k-prototypes algorithm for clustering mixed datasets. Proceedings Royal Society 467, 2387–2403 (2011)CrossRefMATHMathSciNetGoogle Scholar
  35. 35.
    Pham, D.T., Castellani, M., Ghanbarzadeh, A.: Preliminary design using the Bees Algorithm. In: Proceedings Eigth LAMDAMAP International Conference on Laser Metrology, CMM and Machine Tool Performance, Cardiff, UK, pp. 420–429 (2007)Google Scholar
  36. 36.
    Pham, D.T., Soroka, A., Koç, E., Ghanbarzadeh, A., Otri, S.: Some applications of the Bees Algorithm in engineering design and manufacture. In: Proceedings International Conference on Manufacturing Automation (ICMA 2007), Singapore (2007)Google Scholar
  37. 37.
    Pham, D.T., Ghanbarzadeh, A., Otri, S., Koç, E.: Optimal design of mechanical components using the Bees Algorithm. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223(5), 1051–1056 (2009)Google Scholar
  38. 38.
    Xu, W., Zhou, Z., Pham, D.T., Liu, Q., Ji, C., Meng, W.: Quality of service in manufacturing networks: a service framework and its implementation. International Journal Advanced Manufacturing Technology (2012),
  39. 39.
    Tudu, B., Majumder, S., Mandal, K., Chakraborty, N.: Optimal unit sizing of stand-alone renewable hybrid energy system using bees algorithm. In: Proceedings of 2011 International Conference on Energy, Automation, and Signal (ICEAS), Bhubaneswar, Odisha, India, pp. 1–6 (2011)Google Scholar
  40. 40.
    Moradi, S., Razi, P., Fatahi, L.: On the application of bees algorithm to the problem of crack detection. Computers and Structures 89, 2169–2175 (2011)CrossRefGoogle Scholar
  41. 41.
    Pham, D.T., Darwish, A.: Optimising fuzzy membership functions using the Bees Algorithm with Kalman filtering. In: Proceedings 5th International Virtual Conference on Intelligent Production Machines and Systems (IPROMS 2009), pp. 328–333 (2009)Google Scholar
  42. 42.
    Pham, D.T., Kalyoncu, M.: Optimisation of a fuzzy logic controller for a flexible single-link robot arm using the Bees Algorithm. In: Proceedings 7th IEEE International Conference on Industrial Informatics, INDIN 2009, Cardiff, UK, pp. 475–480 (2009)Google Scholar
  43. 43.
    Pham, D.T., Darwish, A., Eldukhri, E.: Optimisation of a fuzzy logic controller using the Bees Algorithm. International Journal of Computer Aided Engineering and Technology 1, 250–264 (2009)CrossRefGoogle Scholar
  44. 44.
    Pham, D.T., Darwish, A., Eldukhri, E., Otri, S.: Using the Bees Algorithm to tune a fuzzy logic controller for a robot. In: Proceedings Third Virtual International Conference on Innovative Production Machines and Systems (IPROMS 2007), pp. 546–551 (2007)Google Scholar
  45. 45.
    Fahmy, A., Kalyoncu, M., Castellani, M.: Automatic design of control systems for robot manipulators using the bees algorithm. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226(4), 497–508 (2012)Google Scholar
  46. 46.
    Pham, D.T., Castellani, M., Fahmy, A.: Learning the Inverse Kinematics of a Robot Manipulator using the Bees Algorithm. In: Proceedings 6th IEEE International Conference on Industrial Informatics (INDIN 2008), pp. 493–498 (2008)Google Scholar
  47. 47.
    Jevtic, A., Gazi, P., Andina, D., Jamshidi, M.: Building a swarm of robotic bees. In: Proceedings 2010 World Automation Congress, WAC 2010, Kobe, Japan (2010)Google Scholar
  48. 48.
    Jevtic, A., Gutierrez-Martin, A.D.A., Jamshidi, M.: Distributed Bees Algorithm for Task Allocation in Swarm of Robots. IEEE Systems Journal 6(2), 296–304, 1–6 (2012)CrossRefGoogle Scholar
  49. 49.
    Xu, S., Yu, F., Luo, Z., Ji, Z., Pham, D.T., Qiu, R.: Honeybee Foraging to Optimize Fuel Economy of a Semi-Track Air-Cushion Vehicle. The Computer Journal 9, 54 (2011)Google Scholar
  50. 50.
    Guney, K., Onay, M.: Amplitude-only pattern nulling of linear antenna arrays with the use of bees algorithm. Progress In Electromagnetics Research 70, 21–36 (2007)CrossRefGoogle Scholar
  51. 51.
    Guney, K., Onay, M.: Bees algorithm for interference suppression of linear antenna arrays. Expert Systems with Applications 37, 3129–3135 (2010)CrossRefGoogle Scholar
  52. 52.
    Guney, K., Onay, M.: Synthesis of thinned linear antenna arrays using bees algorithm. Microwave and Optical Technology Letters 53, 795–799 (2011)CrossRefGoogle Scholar
  53. 53.
    Kavousi, A., Vahidi, B., Salehi, R., Bakhshizadeh, M., Farokhnia, N., Fathi, S.: Application of the Bee Algorithm for Selective Harmonic Elimination Strategy in Multilevel Inverters. IEEE Transactions on Power Electronics 27(4), 1689–1696 (2012)CrossRefGoogle Scholar
  54. 54.
    Pham, D.T., Pham, Q.T., Ghanbarzadeh, A., Castellani, M.: Dynamic Optimisation of Chemical Engineering Processes Using the Bees Algorithm. In: Proceedings of the 17th World Congress The International Federation of Automatic Control (IFAC), Seoul, Korea, pp. 6100–6105 (2008)Google Scholar
  55. 55.
    Castellani, M., Pham, Q.T., Pham, D.T.: Dynamic optimisation by a modified bees algorithm. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering (2012),
  56. 56.
    Pham, Q.T., Pham, D.T., Castellani, M.: A modified bees algorithm and a statistics-based method for tuning its parameters. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226, 287–301 (2012)Google Scholar
  57. 57.
    Alfi, A., Khosravi, A., Razavi, S.E.: Bee Algoritm–Based Nolinear Optimal Control Applied to a Continuous Stirred-Tank Chemical Reactor. Global Journal of Pure & Applied Science and Technology - GJPAST 1(2), 73–79 (2011)Google Scholar
  58. 58.
    Bahamish, H., Abdullah, R., Salam, R.: Protein Conformational Search Using Bees Algorithm. In: Second Asia International Conference on Modeling & Simulation (AICMS 2008), Kuala Lumpur, Malaysia, pp. 911–916 (2008)Google Scholar
  59. 59.
    Pham, D.T., Otri, S., Darwish, A.: Application of the Bees Algorithm to PCB assembly optimisation. In: Proceedings 3rd International Virtual Conference on Intelligent Production Machines and Systems (IPROMS 2007), pp. 511–516 (2007)Google Scholar
  60. 60.
    Pham, D.T., Afify, A., Koç, E.: Manufacturing cell formation using the Bees Algorithm. In: Proceedings 3rd International Virtual Conference on Intelligent Production Machines and Systems (IPROMS 2007), pp. 523–528 (2007)Google Scholar
  61. 61.
    Pham, D.T., Koç, E., Lee, J., Phrueksanant, J.: Using the Bees Algorithm to Schedule Jobs for a Machine. In: Proceedings 8th International Conference on Laser Metrology, CMM and Machine Tool Performance (LAMDAMAP), Cardiff, UK, pp. 430–439 (2007)Google Scholar
  62. 62.
    Lara, C., Flores, J., Calderon, F.: Solving a School Timetabling Problem Using a Bee Algorithm. In: Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence, Berlin Heidelberg, pp. 664–674 (2008)Google Scholar
  63. 63.
    Khang, N., Phuc, N., Nuong, T.: The Bees Algorithm for A Practical University Timetabling Problem in Vietnam. In: Proceedings of IEEE International Conference Computer Science and Automation Engineering (CSAE), Shanghai, China, pp. 42–47 (2011)Google Scholar
  64. 64.
    Alzaqebah, M., Abdullah, S.: The Bees Algorithm for Examination Timetabling Problems. International Journal of Soft Computing and Engineering (IJSCE) 1(5), 105–110 (2011)Google Scholar
  65. 65.
    Nguyen, K., Nguyen, P., Tran, N.: A hybrid algorithm of Harmony Search and Bees Algorithm for a University Course Timetabling Problem. IJCSI International Journal of Computer Science Issues 9(1), 12–17 (2012)MathSciNetGoogle Scholar
  66. 66.
    Baykasoğlu, A., Özbakır, L., Tapkan, P.: The bees algorithm for workload balancing in examination job assignment. European Journal Industrial Engineering 3(4), 424–435 (2009)CrossRefGoogle Scholar
  67. 67.
    Özbakır, L., Tapkan, P.: Bee colony intelligence in zone constrained two-sided assembly line balancing problem. Expert Systems with Applications 38, 11947–11957 (2011)CrossRefGoogle Scholar
  68. 68.
    Özbakır, L., Tapkan, P.: Bee colony intelligence in zone constrained two-sided assembly line balancing problem. Expert Systems with Applications 38, 11947–11957 (2011)CrossRefGoogle Scholar
  69. 69.
    Özbakir, L., Baykasoglu, A., Tapkan, P.: Bees algorithm for generalized assignment problem. Applied Mathematics and Computation 215, 3782–3795 (2010)CrossRefMATHMathSciNetGoogle Scholar
  70. 70.
    Saad, E., Awadalla, M., Darwish, R.: A Data Gathering Algorithm for a Mobile Sink in Large-Scale Sensor Networks. In: Proceedings of the Fourth International Conference on Wireless and Mobile Communications (ICWMC 2008), Athens, Greece, pp. 207–213 (2008)Google Scholar
  71. 71.
    Dhurandher, S., Misra, S., Pruthi, P., Singhal, S., Aggarwal, S., Woungang, I.: Using bee algorithm for peer-to-peer file searching in mobile ad hoc networks. Journal of Network and Computer Applications 34(5), 1498–1508 (2011)CrossRefGoogle Scholar
  72. 72.
    Derelia, T., Das, G.: A hybrid ‘bee(s) algorithm’ for solving container loading problems. Applied Soft Computing 11, 2854–2862 (2011)CrossRefGoogle Scholar
  73. 73.
    Pham, D.T., Ghanbarzadeh, A.: Multi-objective optimization using the Bees Algorithm. In: Pham, D.T., Eldukhri, E.E., Soroka, A.J. (eds.) Proceedings of the 3rd Virtual International Conference on Innovative Production Machines and Systems. Whittles, CRC Press, Dunbeath, Boca Raton (2007) ISBN 978-1904445-52-4Google Scholar
  74. 74.
    Lee, J., Darwish, A.: Multi-objective Environmental/Economic Dispatch Using the Bees Algorithm with Weighted Sum. In: Proceedings of the EU-Korea Conference on Science and Technology (EKC 2008), Heidelberg, pp. 267–274 (2008)Google Scholar
  75. 75.
    Pham, D.T., Lee, J.Y., Haj Darwish, A., Soroka, A.J.: Multi-objective Environmental/Economic Dispatch using the Bees Algorithm with Pareto optimality and Weighted Sum. In: Pham, D.T., Eldukhri, E.E., Soroka, A.J. (eds.) Proceedings of the 4th Virtual International Conference on Innovative Production Machines and Systems, pp. 422–430. Whittles, CRC Press, Dunbeath, Boca Raton (2008) ISBN 978-1-4398-0117-8 Google Scholar
  76. 76.
    Anantasate, S., Chokpanyasuwan, C., Bhasaputra, P.: Optimal Power Flow by using Bees Algorithm. In: International Conference on Electrical Engineering/Electronics Computer Telecommunications and Information Technology (ECTI-CON), Chiang Mai, Thailand, pp. 430–434 (2010)Google Scholar
  77. 77.
    Anantasate, S., Bhasaputra, P.: A Multi-objective Bees Algorithm for Multi-objective Optimal Power Flow Problem. In: Proceedings of 8th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Khon Kaen, Thailand, pp. 852–856 (2011)Google Scholar
  78. 78.
    Sayadi, F., Ismail, M., Misran, N., Jumari, K.: Multi-Objective Optimization Using the Bees Algorithm in Time-Varying Channel for MIMO MC-CDMA Systems. European Journal of Scientific Research 33(3), 411–428 (2009)Google Scholar
  79. 79.
    Chai-ead, N., Aungkulanon, P., Luangpaiboon, P.: Bees and Firefly Algorithms for Noisy Non-Linear Optimisation Problems. In: Proceedings of International MultiConference of Engineers and Computer Scientists 2011 (IMECS 2011), Hong Kong, China, pp. 1449–1454 (2011)Google Scholar
  80. 80.
    Pham, D.T., Koç, E.: Design of a two-dimensional recursive filter using the bees algorithm. International Journal Automation and Computing 7(3), 399–402 (2011)CrossRefGoogle Scholar
  81. 81.
    Tran, Q., Liatsis, P., Zhu, B., He, C.: An Approach for Multimodal Biometric Fusion Under the Missing Data Scenario. In: Proceedings of 2011 International Conference on Uncertainty Reasoning and Knowledge Engineering, Bali, Indonesia, pp. 185–188 (2011)Google Scholar
  82. 82.
    Baeck, T., Hoffmeister, F., Schwefel, H.: A survey of evolution strategies. In: Proceedings 4th International Conference on Genetic Algorithms, San Mateo, USA, pp. 2–9 (1991)Google Scholar
  83. 83.
    Goldberg, D.: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison Wesley, Reading (1989)Google Scholar
  84. 84.
    Storn, R., Price, K.: Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute (1995),
  85. 85.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings 1995 IEEE International Conference on Neural Networks, Perth, AU, pp. 1942–1948 (1995)Google Scholar
  86. 86.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Transactions Systems, Man & Cybernetics - Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  87. 87.
    Passino, K.: Biomimicry of Bacterial Foraging for Distributed Optimisation and Control. IEEE Control Syst. Magazine 22(3), 52–67 (2002)CrossRefMathSciNetGoogle Scholar
  88. 88.
    Roth, M., Wicker, S.: Termite: ad-hoc networking with stigmergy. In: Proceedings Global Telecommunication Conference GLOBECOM 2003, San Francisco, CA, pp. 2937–2941 (2003)Google Scholar
  89. 89.
    Mehrabian, A., Lucas, C.: A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics 1(4), 355–366 (2006)CrossRefGoogle Scholar
  90. 90.
    Yang, X., Deb, S.: Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation 1(4), 330–343 (2010)CrossRefMATHGoogle Scholar
  91. 91.
    Haddad, O., Afshar, A., Marino, M.A.: Honey-Bees Mating Optimization (HBMO) Algorithm: A New Heuristic Approach for Water Resources Optimization. Water Resources Management, 661–680 (2006)Google Scholar
  92. 92.
    Engelbrecht, A.: Fundamentals of Computational Swarm Intelligence. John Wiley & Sons, Chichester (2005)Google Scholar
  93. 93.
    Mengshoel, O., Goldberg, D.: The crowding approach to niching in genetic algorithms. Evolutionary Computation 16(3), 315–354 (2008)CrossRefGoogle Scholar
  94. 94.
    Juang, C.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(2), 997–1006 (2004)CrossRefGoogle Scholar
  95. 95.
    Shi, X., Lu, Y., Zhou, C., Lee, H., Lin, W., Liang, Y.: Hybrid evolutionary algorithms based on PSO and GA. In: Proceedings IEEE Congress Evolutionary Computation, Canberra, Australia, pp. 2393–2399 (2003)Google Scholar
  96. 96.
    Fogel, D.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, 2nd edn. IEEE Press, New York (2000)Google Scholar
  97. 97.
    Poli, R., Langdon, W., McPhee, N.: A Field Guide to Genetic Programming (2008), Published via, freely available at, ISBN 978-1-4092-0073-4
  98. 98.
    Bilchev, G., Parmee, I.: The ant colony metaphor for searching continuous design spaces. In: Fogarty, T.C. (ed.) AISB-WS 1995. LNCS, vol. 993, pp. 25–39. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  99. 99.
    Dréo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Generation Computer Systems 20, 841–856 (2004)CrossRefGoogle Scholar
  100. 100.
    Socha, K., Dorigo, M.: Ant colony optimisation for continuous domains. European Journal of Operational Research 185, 1155–1173 (2008)CrossRefMATHMathSciNetGoogle Scholar
  101. 101.
    Blackwell, T., Branke, J.: Multi-swarm optimization in dynamic environments. In: Raidl, G.R., Cagnoni, S., Branke, J., Corne, D.W., Drechsler, R., Jin, Y., Johnson, C.G., Machado, P., Marchiori, E., Rothlauf, F., Smith, G.D., Squillero, G. (eds.) EvoWorkshops 2004. LNCS, vol. 3005, pp. 489–500. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  102. 102.
    Adorio, E.: MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization (2005),
  103. 103.
    Wolpert, D., Macready, W.: No free lunch theorem for optimization. IEEE Transactions Evolutionary Computation 1(1), 67–82 (1997)CrossRefGoogle Scholar
  104. 104.
    Shi, Y., Eberhart, R.: Parameter Selection in Particle Swarm Optimization. In: Proceedings of the 1998 Annual Conference on Evolutionary Programming, San Diego, CA, pp. 591–600 (1998)Google Scholar
  105. 105.
    Lippmann, R.: An introduction to computing with neural nets. IEEE ASSP Magazine, 4–22 (1987)Google Scholar
  106. 106.
    Narendra, K., Parthasarathy, K.: Identification and Control of Dynamical Systems Using Neural Networks. IEEE Transactions on Neural Networks 1(1), 4–27 (1990)CrossRefGoogle Scholar
  107. 107.
    Thierens, D., Suykens, J., Vanderwalle, J., De Moor, B.: Genetic Weight Optimisation of a Feedforward Neural Network Controller. In: Artificial Neural Networks and Genetic Algorithms, pp. 658–663. Springler, Wien (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Duc Truong Pham
    • 1
  • Marco Castellani
    • 2
  • Hoai An Le Thi
    • 3
  1. 1.School of Mechanical EngineeringUniversity of BirminghamBirminghamUK
  2. 2.Department of BiologyUniversity of BergenBergenNorway
  3. 3.Laboratoty of Theoretical and Applied Computer ScienceUniversity of LorraineMetzFrance

Personalised recommendations