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Adaptive cooperative particle swarm optimizer

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Abstract

An Adaptive Cooperative Particle Swarm Optimizer (ACPSO) is introduced in this paper, which facilitates cooperation technique through the usage of the Learning Automata (LA) algorithm. The cooperative strategy of ACPSO optimizes the problem collaboratively and evaluates it in different contexts. In the ACPSO algorithm, a set of learning automata associated with dimensions of the problem are trying to find the correlated variables of the search space and optimize the problem intelligently. This collective behavior of ACPSO will fulfill the task of adaptive selection of swarm members. Simulations were conducted on four types of benchmark suites which contain three state-of-the-art numerical optimization benchmark functions in addition to one new set of active coordinate rotated test functions. The results demonstrate the learning ability of ACPSO in finding correlated variables of the search space and also describe how efficiently it can optimize the coordinate rotated multimodal problems, composition functions and high-dimensional multimodal problems.

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References

  1. Kennedy J (2006) Swarm intelligence. In: Handbook of nature-inspired and innovative computing, pp 187–219

    Chapter  Google Scholar 

  2. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings IEEE international conference on neural networks, 1995. vol 4, pp 1942–1948

    Google Scholar 

  3. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, MHS’95, pp 39–43

    Chapter  Google Scholar 

  4. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: IEEE swarm intelligence symposium, 2007, SIS 2007, pp 120–127

    Chapter  Google Scholar 

  5. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–72

    Article  Google Scholar 

  6. Potter M, De Jong K (1994) A cooperative coevolutionary approach to function optimization. In: Parallel problem solving from nature—PPSN III, pp 249–257

    Chapter  Google Scholar 

  7. van den Bergh F, Engelbrecht AP (2000) Cooperative learning in neural networks using particle swarm optimizers. South Afr Comput J 26:84–90

    Google Scholar 

  8. van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239

    Article  Google Scholar 

  9. Narendra KS, Thathachar M (1974) Learning automata: a survey. IEEE Trans Syst Man Cybern 4:323–334

    Article  MathSciNet  MATH  Google Scholar 

  10. Narendra KS, Thathachar MAL (1989) Learning automata: an introduction. Prentice Hall, New York

    Google Scholar 

  11. Ünsal C (1997) Intelligent navigation of autonomous vehicles in an automated highway system: Learning methods and interacting vehicles approach, Virginia Polytechnic Institute and State University

  12. Beigy H, Meybodi MR (2010) Cellular learning automata with multiple learning automata in each cell and its applications. IEEE Trans Syst Man Cybern, Part B, Cybern 40(1):54–65

    Article  Google Scholar 

  13. Esnaashari M, Meybodi MR (2010) Dynamic point coverage problem in wireless sensor networks: a cellular learning automata approach. J Ad Hoc Sens Wirel Netw 10(2–3):193–234

    Google Scholar 

  14. Hashemi AB, Meybodi MR (2011) A note on the learning automata based algorithms for adaptive parameter selection in PSO. Appl Soft Comput 11(1):689–705

    Article  Google Scholar 

  15. Hashemi A, Meybodi M (2009) Cellular PSO: a PSO for dynamic environments. In: Advances in computation and intelligence, pp 422–433

    Chapter  Google Scholar 

  16. Thathachar M, Sastry PS (2002) Varieties of learning automata: an overview. IEEE Trans Syst Man Cybern, Part B, Cybern 32(6):711–722

    Article  Google Scholar 

  17. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Nanyang Technol. Univ., Singapore, IIT Kanpur, Kanpur, India, #2005005, May 2005

  18. Liang J, Qin A, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  19. Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182

    MATH  Google Scholar 

  20. He S, Wu Q, Saunders J (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evol Comput 13(5):973–990

    Article  Google Scholar 

  21. He S, Wu Q, Saunders J (2006) A novel group search optimizer inspired by animal behavioural ecology. In: IEEE Congress on evolutionary computation. CEC 2006, pp 1272–1278

    Google Scholar 

  22. Bellman R (1956) Dynamic programming and Lagrange multipliers. Proc Natl Acad Sci USA 42(10):767

    Article  MATH  Google Scholar 

  23. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. An overview. Swarm Intell 1(1):33–57

    Article  Google Scholar 

  24. Lim A, Lin J, Xiao F (2007) Particle swarm optimization and hill climbing for the bandwidth minimization problem. Appl Intell 26(3):175–182

    Article  MATH  Google Scholar 

  25. Khan SA, Engelbrecht AP (2012) A fuzzy particle swarm optimization algorithm for computer communication network topology design. Appl Intell 36(1):161–177

    Article  Google Scholar 

  26. Chu CP, Chang YC, Tsai CC (2011) PC 2 PSO: personalized e-course composition based on particle swarm optimization. Appl Intell 34(1):141–154

    Article  Google Scholar 

  27. Wang K, Zheng YJ (2012) A new particle swarm optimization algorithm for fuzzy optimization of armored vehicle scheme design. Appl Intell 37(4):520–526

    Article  Google Scholar 

  28. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: The 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence, 1998, pp 69–73

    Google Scholar 

  29. Zhan ZH, Zhang J, Li Y, Chung HSH (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern, Part B, Cybern 39(6):1362–1381

    Article  Google Scholar 

  30. Zhu Z, Zhou J, Ji Z, Shi YH (2011) DNA sequence compression using adaptive particle swarm optimization-based memetic algorithm. IEEE Trans Evol Comput 15(5):643–658

    Article  Google Scholar 

  31. Ji, Z, Liao H, Wang Y, Wu QH (2007) A novel intelligent particle optimizer for global optimization of multimodal functions. In: IEEE congress on evolutionary computation. CEC 2007, pp 3272–3275.

    Google Scholar 

  32. Zhan Z-H, Zhang J, Li Y, Shi Y-H (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evol Comput 15(6):832–847

    Article  Google Scholar 

  33. Zhang Q, Leung Y-W (1999) An orthogonal genetic algorithm for multimedia multicast routing. IEEE Trans Evol Comput 3(1):53–62

    Article  Google Scholar 

  34. Norouzzadeh MS, Ahmadzadeh MR, Palhang M (2012) LADPSO: using fuzzy logic to conduct PSO algorithm. Appl Intell 37(2):290–304

    Article  Google Scholar 

  35. Blackwell T, Branke J (2006) Multiswarms, exclusion, and anti-convergence in dynamic environments. IEEE Trans Evol Comput 10(4):459–472

    Article  Google Scholar 

  36. Niu B, Zhu Y, He X, Wu H (2007) MCPSO: a multi-swarm cooperative particle swarm optimizer. Appl Math Comput 185(2):1050–1062

    Article  MATH  Google Scholar 

  37. Zhang J, Ding X (2011) A multi-swarm self-adaptive and cooperative particle swarm optimization. Engineering applications of artificial intelligence

  38. Ali YMB (2012) Psychological model of particle swarm optimization based multiple emotions. Appll Intell 36(3):649–663

    Article  Google Scholar 

  39. Ong YS, Keane AJ, Nair PB (2002) Surrogate-assisted coevolutionary search. In: Proceedings of the 9th international conference on neural information processing, ICONIP’02, vol 3, pp 1140–1145

    Google Scholar 

  40. Bäck T, Schwefel HP (1993) An overview of evolutionary algorithms for parameter optimization. Evol Comput 1(1):1–23

    Article  Google Scholar 

  41. Sofge D, De Jong K, Schultz A (2002) A blended population approach to cooperative coevolution for decomposition of complex problems. In: Proceedings of the 2002 Congress on evolutionary computation. CEC’02, vol 1, pp 413–418

    Google Scholar 

  42. Han MF, Liao SH, Chang JY, Lin CT (2012) Dynamic group-based differential evolution using a self-adaptive strategy for global optimization problems. Appl Intell. doi:10.1007/s10489-012-0393-5

    Google Scholar 

  43. Shi Y, Teng H, Li Z (2005) Cooperative co-evolutionary differential evolution for function optimization. In: Advances in natural computation, p 428

    Google Scholar 

  44. Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999

    Article  MathSciNet  Google Scholar 

  45. Cuevas E, Sención F, Zaldivar D, Pérez-Cisneros M, Sossa H (2012) A multi-threshold segmentation approach based on Artificial Bee Colony optimization. Appl Intell 37(3):321–336

    Article  Google Scholar 

  46. El-Abd M (2010) A cooperative approach to the artificial bee colony algorithm. In: 2010 IEEE congress on evolutionary computation (CEC), pp 1–5

    Chapter  Google Scholar 

  47. Esnaashari M, Meybodi MR (2011) A cellular learning automata-based deployment strategy for mobile wireless sensor networks. J Parallel Distrib Comput 71:988–1001

    Article  MATH  Google Scholar 

  48. Akbari Torkestani J, Meybodi MR (2011) A cellular learning automata-based algorithm for solving the vertex coloring problem. Expert Syst Appl 38:9237–9247

    Article  Google Scholar 

  49. Misir M, Wauters T, Verbeeck K, Vanden Berghe G (2012) A hyper-heuristic with learning automata for the traveling tournament problem. In: Metaheuristics: intelligent decision making

    Google Scholar 

  50. Noroozi V, Hashemi A, Meybodi M (2011) CellularDE: a cellular based differential evolution for dynamic optimization problems. In: Adaptive and natural computing algorithms, pp 340–349

    Chapter  Google Scholar 

  51. Vafashoar R, Meybodi MR, Momeni Azandaryani AH (2011) CLA-DE: a hybrid model based on cellular learning automata for numerical optimization. Appl Intell

  52. Cheshmehgaz HR, Haron H, Maybodi MR (2011) Cellular-based population to enhance genetic algorithm for assignment problems. Am J Intell Syst 1(1):1–5

    Google Scholar 

  53. Wallenta C, Kim J, Bentley PJ, Hailes S (2010) Detecting interest cache poisoning in sensor networks using an artificial immune algorithm. Appl Intell 32(1):1–26

    Article  Google Scholar 

  54. Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications, pp 169–178

    Chapter  Google Scholar 

  55. Farahani SM, Abshouri AA, Nasiri B, Meybodi M (2012) Some hybrid models to improve firefly algorithm performance. Int J Artif Intell 8(S12):97–117

    Google Scholar 

  56. Rezvanian A, Meybodi MR (2010) LACAIS: learning automata based cooperative artificial immune system for function optimization. In: 3rd international conference on contemporary computing (IC3 2010), CCIS, 2010, Noida, India. Contemporary computing, vol 94 pp 64–75

    Google Scholar 

  57. Meybodi M, Beigy H (2002) A note on learning automata-based schemes for adaptation of BP parameters. Neurocomputing 48(1):957–974

    Article  MATH  Google Scholar 

  58. Rastegar R, Meybodi MR, Badie K (2004) A new discrete binary particle swarm optimization based on learning automata. In: Proceedings international conference on machine learning and applications, 2004, pp 456–462

    Chapter  Google Scholar 

  59. Jafarpour B, Meybodi M, Shiry S (2007) A hybrid method for optimization (discrete PSO+ CLA). In: International conference on intelligent and advanced systems. ICIAS 2007, pp 55–60. 2007

    Google Scholar 

  60. Sheybani M, Meybodi MR (2007) PSO-LA: a new model for optimization. In: Proceedings of 12th annual CSI computer conference of Iran, pp 1162–1169

    Google Scholar 

  61. Soleimanzadeh R, Farahani BJ, Fathy M (2010) PSO based deployment algorithms in hybrid sensor networks. Int J Comput Sci Netw Secur 10(7):167–171

    Google Scholar 

  62. Hamidi M, Meybodi MR (2008) New learning automata based particle swarm optimization algorithms. In: Iran data mining conference (IDMC), pp 1–15

    Google Scholar 

  63. Hasanzadeh M, Meybodi MR, Shiry S (2011) Improving learning automata based particle swarm: an optimization algorithm. In: 12th IEEE international symposium on computational intelligence and informatics, Budapest

    Google Scholar 

  64. Hasanzadeh M, Meybodi MR, Ebadzadeh MM (2012) A robust heuristic algorithm for cooperative particle swarm optimizer: a learning automata approach. In: 20th Iranian conference on electrical engineering (ICEE), pp 656–661

    Chapter  Google Scholar 

  65. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66

    Article  MathSciNet  Google Scholar 

  66. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

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Acknowledgements

The work is supported by Iran Telecommunication Research Center (ITRC) grant.

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Authors and Affiliations

  1. Computer Engineering and Information Technology Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Mohammad Hasanzadeh, Mohammad Reza Meybodi & Mohammad Mehdi Ebadzadeh

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  1. Mohammad Hasanzadeh
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  2. Mohammad Reza Meybodi
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  3. Mohammad Mehdi Ebadzadeh
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Correspondence to Mohammad Hasanzadeh.

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Hasanzadeh, M., Meybodi, M.R. & Ebadzadeh, M.M. Adaptive cooperative particle swarm optimizer. Appl Intell 39, 397–420 (2013). https://doi.org/10.1007/s10489-012-0420-6

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