Reinforced cuckoo search algorithm-based multimodal optimization

Abstract

This work proposes a Reinforced Cuckoo Search Algorithm (RCSA) for multimodal optimization, which comprises three different strategies: modified selection strategy, Patron-Prophet concept, and self-adaptive strategy. The modified selection strategy has been proposed for efficient selection of next generation individuals instead of choosing a random set of individuals, which is predominantly followed in a standard Cuckoo Search (CS). The Patron-Prophet concept is based on a donor-acceptor concept where a donor donates information and the acceptor makes use of it. In the RCSA, the deviated information of abandoned solutions from selected solutions will be calculated and subsequently used by the newly generated solutions. A self-adaptive step size has been introduced to achieve multimodality in the RCSA. Experimental results using benchmark problems show that the RCSA performs well in terms of multimodality when compared with other existing algorithms found in the literature. This proposed RCSA is also implemented in three different engineering design problems for performance evaluation.

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References

  1. 1.

    Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press

  2. 2.

    Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Article  Google Scholar 

  3. 3.

    Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 26(1):29–41

    Article  Google Scholar 

  4. 4.

    Kennedy J (2011) Particle swarm optimization. In Encyclopedia of machine learning, pp. 760–766. Springer US

  5. 5.

    Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department 200

  6. 6.

    Yang X-S, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput & Applic 24(1):169–174

    Article  Google Scholar 

  7. 7.

    Mallick A, Roy S, Chaudhuri SS, Roy S (2014) Study of parametric optimization of the Cuckoo Search algorithm. In: Control, Instrumentation, Energy and Communication (CIEC), 2014 International Conference on, pp. 767–772. IEEE

  8. 8.

    Civicioglu P, Besdok E (2014) Comparative analysis of the cuckoo search algorithm. Cuckoo Search and Firefly Algorithm. Springer International Publishing, pp. 85–113

  9. 9.

    Wang G-G et al (2016) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Comput 20(1):273–285

    Article  Google Scholar 

  10. 10.

    Ouaarab A, Ahiod B, Yang X-S (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput & Applic 24(7–8):1659–1669

    Article  Google Scholar 

  11. 11.

    Majumder A, Laha D (2016) A new cuckoo search algorithm for 2-machine robotic cell scheduling problem with sequence-dependent setup times. Swarm and Evolutionary Computation 28:131–143

    Article  Google Scholar 

  12. 12.

    Gherboudj A, Layeb A, Chikhi S (2014) Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm. International Journal of Bio-Inspired Computation 4(4):229–236

    Article  Google Scholar 

  13. 13.

    Jati GK, Manurung HM (2012) Discrete cuckoo search for traveling salesman problem. Computing and Convergence Technology (ICCCT), 2012 7th International Conference on. IEEE, pp. 993–997

  14. 14.

    Khan K, Sahai A (2013) Neural-based cuckoo search of employee health and safety (hs). International Journal of Intelligent Systems and Applications 5(2):76

    Article  Google Scholar 

  15. 15.

    Lin JH, Lee IH (2012) Emotional chaotic cuckoo search for the reconstruction of chaotic dynamics. In source: 11th WSEAS Int. Conf. on COmputational Intelligence, Man-Machine Systems and Cybernetics (CIMMACS'12), pp. 123–128

  16. 16.

    Nawi NM, Khan A, Rehman MZ (2013) A new cuckoo search based Levenberg-Marquardt (CSLM) algorithm. International Conference on Computational Science and Its Applications. Springer Berlin Heidelberg, pp. 438–451

  17. 17.

    Subotic M, et al (2012) Parallelized cuckoo search algorithm for unconstrained optimization. Proceedings of the 5th WSEAS congress on Applied Computing conference, and Proceedings of the 1st international conference on Biologically Inspired Computation. World Scientific and Engineering Academy and Society (WSEAS), pp. 151–156

  18. 18.

    Tuba M, Subotic M, Stanarevic N (2011) Modified cuckoo search algorithm for unconstrained optimization problems. Proceedings of the 5th European conference on European computing conference. World Scientific and Engineering Academy and Society (WSEAS), pp. 263–268

  19. 19.

    Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons Fractals 44(9):710–718

    Article  Google Scholar 

  20. 20.

    Zhang Y, Wang L, Wu Q (2012) Modified Adaptive Cuckoo Search (MACS) algorithm and formal description for global optimisation. Int J Comput Appl Technol 44(2):73–79

    Article  Google Scholar 

  21. 21.

    Yang X-S, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40(6):1616–1624

    MathSciNet  MATH  Article  Google Scholar 

  22. 22.

    Zhou Y, Zheng H (2013) A novel complex valued cuckoo search algorithm. The Scientific World Journal 2013

  23. 23.

    Zheng H, Zhou Y (2012) A novel cuckoo search optimization algorithm based on Gauss distribution. J Comput Inf Syst 8(10):4193–4200

    Google Scholar 

  24. 24.

    Huang L, Dung S, Yu S, Wang J, Lul K (2016) Chaos-enhanced Cuckoo search optimization algorithms for global optimization. Appl Math Model 40(5):3860–3875

    MathSciNet  Article  Google Scholar 

  25. 25.

    Balasubbareddy M, Sivanagaraju S, Suresh CV (2015) Multi-objective optimization in the presence of practical constraints using non-dominated sorting hybrid cuckoo search algorithm. Engineering Science and Technology, an International Journal 18(4):603–615

    Article  Google Scholar 

  26. 26.

    Rakhshani H, Rahati A (2016) Snap-Drift Cuckoo Search: A novel cuckoo search optimization algorithm. Appl Soft Comput 52:771–794

    Article  Google Scholar 

  27. 27.

    Mahmoudi S, Lotfi S (2015) Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem. Appl Soft Comput 33:48–64

    Article  Google Scholar 

  28. 28.

    Mlakar Uros IF Jr, Fister I (2016) Hybrid self-adaptive cuckoo search for global optimization. Swarm and Evolutionary Computation 29:47–72

    Article  Google Scholar 

  29. 29.

    Wang Z, Li Y (2015) Irreversibility analysis for optimization design of plate fin heat exchangers using a multi-objective cuckoo search algorithm. Energy Convers Manag 101:126–135

    Article  Google Scholar 

  30. 30.

    Devabalaji KR, Yuvaraj T, Ravi K (2016) An efficient method for solving the optimal sitting and sizing problem of capacitor banks based on cuckoo search algorithm. Ain Shams Engineering Journal

  31. 31.

    Bhandari AK et al (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41(7):3538–3560

    Article  Google Scholar 

  32. 32.

    Amiri E, Mahmoudi S (2016) Efficient protocol for data clustering by fuzzy Cuckoo Optimization Algorithm. Appl Soft Comput 41:15–21

    Article  Google Scholar 

  33. 33.

    Mellal MA, Williams EJ (2015) Cuckoo optimization algorithm with penalty function for combined heat and power economic dispatch problem. Energy 93:1711–1718

    Article  Google Scholar 

  34. 34.

    Nguyen TT, Vo DN, Dinh BH (2016) Cuckoo search algorithm for combined heat and power economic dispatch. Int J Electr Power Energy Syst 81:204–214

    Article  Google Scholar 

  35. 35.

    Sanajaoba S, Fernandez E (2016) Maiden application of Cuckoo Search algorithm for optimal sizing of a remote hybrid renewable energy System. Renew Energy 96:1–10

    Article  Google Scholar 

  36. 36.

    Abd-Elazim SM, Ali ES (2016) Optimal location of STATCOM in multimachine power system for increasing loadability by Cuckoo Search algorithm. Int J Electr Power Energy Syst 80:240–251

    Article  Google Scholar 

  37. 37.

    Huang J, Gao L, Li X (2015) An effective teaching-learning-based cuckoo search algorithm for parameter optimization problems in structure designing and machining processes. Appl Soft Comput 36:349–356

    Article  Google Scholar 

  38. 38.

    Asadi M, Song Y, Sunden B, Xie G (2014) Economic optimization design of shell-and-tube heat exchangers by a cuckoo-search-algorithm. Appl Therm Eng 73(1):1032–1040

    Article  Google Scholar 

  39. 39.

    Zineddine M (2015) Vulnerabilities and mitigation techniques toning in the cloud: A cost and vulnerabilities coverage optimization approach using Cuckoo search algorithm with Lévy flights. Computers & Security 48:1–18

    Article  Google Scholar 

  40. 40.

    Khajeh M, Golzary AR (2014) Synthesis of zinc oxide nanoparticles–chitosan for extraction of methyl orange from water samples: Cuckoo optimization algorithm–artificial neural network. Spectrochim Acta A Mol Biomol Spectrosc 131:189–194

    Article  Google Scholar 

  41. 41.

    Li X, Yin M (2015) Modified cuckoo search algorithm with self-adaptive parameter method. Inf Sci 298:80–97

    Article  Google Scholar 

  42. 42

    Din M, Pal SK, Muttoo SK, Anjali J (2016) Applying Cuckoo Search for analysis of LFSR based cryptosystem. Perspect Sci 8:435–439

    Article  Google Scholar 

  43. 43.

    Yang X-S (2014) Swarm intelligence based algorithms: a critical analysis. Evol Intel 7(1):17–28

    Article  Google Scholar 

  44. 44.

    Qin AK, Li X (2013) Differential evolution on the CEC-2013 single-objective continuous optimization testbed." Evolutionary Computation (CEC), 2013 IEEE Congress on. IEEE

  45. 45.

    Lam AYS, Li VOK, James JQ (2012) Real-coded chemical reaction optimization. IEEE Trans Evol Comput 16(3):339–353

    Article  Google Scholar 

  46. 46.

    Price, Kenneth, Rainer M. Storn, and Jouni A. Lampinen (2006) Differential evolution: a practical approach to global optimization. Springer Science & Business Media

  47. 47.

    Chen W-N, Zhang J, Lin Y, Chen N, Zhan Z-H, Chung HS-H, Li Y, Shi Y-H (2013) Particle swarm optimization with an aging leader and challengers. IEEE Trans Evol Comput 17(2):241–258

    Article  Google Scholar 

  48. 48.

    Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Article  Google Scholar 

  49. 49.

    Vrugt JA, Robinson BA, Hyman JM (2009) Self-adaptive multimethod search for global optimization in real-parameter spaces. IEEE Trans Evol Comput 13(2):243–259

    Article  Google Scholar 

  50. 50.

    Mohapatra P, Das KN, Roy S (2017) A modified competitive swarm optimizer for large scale optimization problems. Appl Soft Comput 59:340–362

    Article  Google Scholar 

  51. 51.

    Cheng R, Jin Y (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191–204

    Article  Google Scholar 

  52. 52.

    Yang Z, Tang K, Yao X (2008) Multilevel cooperative coevolution for large scale optimization. Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on. IEEE

  53. 53.

    Ros R, Hansen N (2008) A simple modification in CMA-ES achieving linear time and space complexity. International Conference on Parallel Problem Solving from Nature. Springer, Berlin

  54. 64.

    Hsieh ST, Sun TY, Liu CC, Tsai SJ (2008) Solving large scale global optimization using improved particle swarm optimizer. In Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on (pp. 1777–1784). IEEE

  55. 55.

    LaTorre A, Muelas S, Peña J-M (2015) A comprehensive comparison of large scale global optimizers. Inf Sci 316:517–549

    Article  Google Scholar 

  56. 56.

    Tang K, Yáo X, Suganthan PN, MacNish C, Chen YP, Chen CM, Yang Z (2007) Benchmark functions for the CEC’2008 special session and competition on large scale global optimization. Nature Inspired Computation and Applications Laboratory, USTC, China, 24

  57. 57.

    Li X, Tang K, Omidvar MN, Yang Z, Qin K, China H (2013) Benchmark functions for the CEC 2013 special session and competition on large-scale global optimization. Gene 7(33):8

    Google Scholar 

  58. 58.

    LaTorre A, Muelas S, Peña J-M (2013) Large scale global optimization: Experimental results with mos-based hybrid algorithms. Evolutionary Computation (CEC), 2013 IEEE Congress on. IEEE

  59. 59.

    Liu J, Tang K (2013) Scaling up covariance matrix adaptation evolution strategy using cooperative coevolution. International Conference on Intelligent Data Engineering and Automated Learning. Springer, Berlin

  60. 60.

    LaTorre A, Muelas S, Peña J-M (2011) A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test. Soft Comput 15(11):2187–2199

    Article  Google Scholar 

  61. 61.

    Yang Z, Tang K, Yao X (2011) Scalability of generalized adaptive differential evolution for large-scale continuous optimization. Soft Comput 15(11):2141–2155

    Article  Google Scholar 

  62. 62.

    Coello CA (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  63. 63.

    He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99

    Article  Google Scholar 

  64. 64.

    Mezura-Montes E, Coello CA (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    MathSciNet  MATH  Article  Google Scholar 

  65. 65.

    Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  66. 66.

    Mirjalili S (2015) Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Article  Google Scholar 

  67. 67.

    Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7):340–349

    Article  Google Scholar 

  68. 68.

    Arora JS (2004) Introduction to optimum design. Elsevier

  69. 69.

    Belegundu AD (1983) Study of mathematical programming methods for structural optimization. Dissertation Abstracts International Part B: Science and Engineering [DISS. ABST INT PT B- SCI & ENG], Volume 43, Issue 12

  70. 70.

    Yang XS (2011) Nature-inspired metaheuristic algorithms, Luniver Press

  71. 71.

    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Article  Google Scholar 

  72. 72.

    Zahara E, Kao YT (2009) Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36:3880–3886

    Article  Google Scholar 

  73. 73.

    Li MD, Zhao H, Weng XW, Han T (2016) A novel nature-inspired algorithm for optimization: Virus colony search. Adv Eng Softw 92:65–88

    Article  Google Scholar 

  74. 74.

    Yang X-S, Deb S (2010) Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation 1(4):330–343

    MATH  Article  Google Scholar 

  75. 75.

    Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  76. 76.

    Zheng H, Zhou Y (2013) A cooperative coevolutionary cuckoo search algorithm for optimization problem. Journal of Applied Mathematics 2013

  77. 77.

    Qu C, He W (2016) A cuckoo search algorithm with complex local search method for solving engineering structural optimization problem. MATEC Web of Conferences. Vol. 40. EDP Sciences

  78. 78.

    Hsieh T-J (2014) A bacterial gene recombination algorithm for solving constrained optimization problems. Appl Math Comput 231:187–204

    MathSciNet  MATH  Google Scholar 

  79. 79.

    Shayeghi H, Ghasemi A (2014) A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch. Energy Convers Manag 79:344–354

    Article  Google Scholar 

  80. 80.

    Mirjalili S (2016) SCA: A Sine Cosine Algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

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Correspondence to Kalaipriyan Thirugnanasambandam.

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Thirugnanasambandam, K., Prakash, S., Subramanian, V. et al. Reinforced cuckoo search algorithm-based multimodal optimization. Appl Intell 49, 2059–2083 (2019). https://doi.org/10.1007/s10489-018-1355-3

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Keywords

  • Cuckoo search
  • Multimodal optimization
  • Evolutionary algorithm
  • Self-adaptive
  • Non-linear optimization