Skip to main content
Log in

A chaotic teaching learning based optimization algorithm for clustering problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper presents a teaching learning based algorithm for solving optimization problems. This algorithm is inspired through classroom teaching pattern either students can learn from teachers or from other students. But, the teaching learning based optimization (TLBO) algorithm suffers with premature convergence and lack of tradeoff between local search and global search. Hence, to address the above mentioned shortcomings of TLBO algorithm, a chaotic version of TLBO algorithm is proposed with different chaotic mechanisms. Further, a local search method is also incorporated for effective tradeoff between local and global search and also to improve the quality of solution. The performance of proposed algorithm is evaluated on some benchmark test functions taken from Congress on Evolutionary Computation 2014 (CEC’14). The results revealed that proposed algorithm provides better and effective results to solve benchmark test functions. Moreover, the proposed algorithm is also applied to solve clustering problems. It is found that proposed algorithm gives better clustering results in comparison to other algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Stützle T (1998) Local search algorithms for combinatorial problems. Darmstadt University of Technology PhD Thesis, p 20

  2. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220 (4598):671–680

    Article  MathSciNet  MATH  Google Scholar 

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

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

  5. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  6. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9-10):781–798

    Article  Google Scholar 

  7. Karaboğa D, Baştürk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. LNCS: Ad Soft Comput: Found Fuzzy Logic Soft Comput 4529:789–798

    Article  MATH  Google Scholar 

  8. Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. Springer, Berlin, pp 169–178

  9. Kashan AH (2011) An efficient algorithm for constrained global optimization and application to mechanical engineering design: league championship algorithm (LCA). Comput Aided Des 43(12):1769–1792

    Article  Google Scholar 

  10. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166

    Article  Google Scholar 

  11. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3-4):267–289

    Article  MATH  Google Scholar 

  12. Kumar Y, Sahoo G (2014) A charged system search approach for data clustering. Progress Artif Intell 2(2-3):153–166

    Article  Google Scholar 

  13. Kaveh A, Share MAM, Moslehi M (2013) Magnetic charged system search: a new meta-heuristic algorithm for optimization. Acta Mech 224(1):85–107

    Article  MATH  Google Scholar 

  14. Kumar Y, Sahoo G (2015) Hybridization of magnetic charge system search and particle swarm optimization for efficient data clustering using neighborhood search strategy. Soft Comput 19(12):3621–3645

    Article  Google Scholar 

  15. Kumar Y, Gupta S, Kumar D, Sahoo G (2016) A clustering approach based on charged particles. In: Optimization algorithms-methods and applications. InTech

  16. Rao R, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315

    Article  Google Scholar 

  17. Sahoo AJ, Kumar Y (2014) Modified teacher learning based optimization method for data clustering. In: Advances in signal processing and intelligent recognition systems. Springer, Cham, pp 429–437

  18. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13(5):2592–2612

    Article  Google Scholar 

  19. Dos Santos Coelho L, Mariani VC (2008) Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization. Expert Syst Appl 34(3):1905–1913

    Article  Google Scholar 

  20. Talatahari S, Azar BF, Sheikholeslami R, Gandomi AH (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simul 17(3):1312–1319

    Article  MathSciNet  MATH  Google Scholar 

  21. Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076–1085

    MathSciNet  MATH  Google Scholar 

  22. Gharooni-fard G, Moein-darbari F, Deldari H, Morvaridi A (2010) Scheduling of scientific workflows using a chaos-genetic algorithm. Procedia Comput Sci 1(1):1445–1454

    Article  Google Scholar 

  23. Alatas B (2010) Chaotic harmony search algorithms. Appl Math Comput 216(9):2687–2699

    MATH  Google Scholar 

  24. Mingjun J, Huanwen T (2004) Application of chaos in simulated annealing. Chaos Solitons Fractals 21(4):933–941

    Article  MATH  Google Scholar 

  25. Alatas B, Akin E, Ozer AB (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals 40(4):1715–1734

    Article  MathSciNet  MATH  Google Scholar 

  26. Talatahari S, Azar BF, Sheikholeslami R, Gandomi AH (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simul 17(3):1312–1319

    Article  MathSciNet  MATH  Google Scholar 

  27. Gong W, Wang S (2009) Chaos ant colony optimization and application. In: 2009 Fourth International conference on internet computing for science and engineering (ICICSE). IEEE, pp 301–303

  28. Alatas B (2010) Chaotic bee colony algorithms for global numerical optimization. Expert Syst Appl 37(8):5682–5687

    Article  Google Scholar 

  29. Alatas B (2011) Uniform big bang–chaotic big crunch optimization. Commun Nonlinear Sci Numer Simul 16(9):3696–3703

    Article  MATH  Google Scholar 

  30. Kumar Y, Sahoo G (2014) A chaotic charged system search approach for data clustering. Informatica 38(3):249–261

    MathSciNet  Google Scholar 

  31. Rao R, Savsani VJ, Balic J (2012) Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems. Eng Optim 44(12):1447–1462

    Article  Google Scholar 

  32. Rao R, Savsani VJ, Vakharia DP (2012) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inform Sci 183(1):1–15

    Article  MathSciNet  Google Scholar 

  33. Zhile YANG, Kang LI, Qun NIU, Yusheng XUE, Foley A (2014) A self-learning TLBO based dynamic economic/environmental dispatch considering multiple plug-in electric vehicle loads. J Modern Power Syst Clean Energy 2(4):298–307

    Article  Google Scholar 

  34. Chen CH (2013) Group leader dominated teaching-learning based optimization. In: 2013 international conference on parallel and distributed computing, applications and technologies (PDCAT). IEEE, pp 304–308

  35. Yang Z, Li K, Foley A, Zhang C (2014) A new self-learning TLBO algorithm for RBF neural modelling of batteries in electric vehicles. In: 2014 IEEE congress on evolutionary computation (CEC). IEEE, pp 2685–2691

  36. Sahoo AJ, Kumar Y (2014) Modified teacher learning based optimization method for data clustering. In: Advances in signal processing and intelligent recognition systems. Springer, Cham, pp 429–437

  37. Rao R, Patel V (2013) An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Scientia Iranica 20(3):710–720

    Google Scholar 

  38. Satapathy SC, Naik A (2014) Modified teaching–learning-based optimization algorithm for global numerical optimization—a comparative study. Swarm Evol Compu 16:28–37

    Article  Google Scholar 

  39. 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 

  40. Zou F, Wang L, Hei X, Chen D (2015) Teaching–learning-based optimization with learning experience of other learners and its application. Appl Soft Comput 37:725–736

    Article  Google Scholar 

  41. Ouyang HB, Gao L, Kong XY, Zou DX, Li S (2015) Teaching-learning based optimization with global crossover for global optimization problems. Appl Math Comput 265:533–556

    MathSciNet  MATH  Google Scholar 

  42. Ghasemi M, Taghizadeh M, Ghavidel S, Aghaei J, Abbasian A (2015) Solving optimal reactive power dispatch problem using a novel teaching–learning-based optimization algorithm. Eng Appl Artif Intel 39:100–108

    Article  Google Scholar 

  43. Zou F, Wang L, Hei X, Chen D, Yang D (2014) Teaching–learning-based optimization with dynamic group strategy for global optimization. Inform Sci 273:112–131

    Article  Google Scholar 

  44. Lim WH, Isa NAM (2014) An adaptive two-layer particle swarm optimization with elitist learning strategy. Inform Sci 273:49–72

    Article  MathSciNet  Google Scholar 

  45. 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 

  46. Gandomi AH, Alavi AH (2011) Multi-stage genetic programming: a new strategy to nonlinear system modeling. Inform Sci 181(23):5227–5239

    Article  Google Scholar 

  47. Gandomi AH, Yang XS, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255

    Article  Google Scholar 

  48. Yang XS, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237

    Article  MathSciNet  Google Scholar 

  49. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol 1, pp 281–297

  50. Maulik U, Bandyopadhyay S (2000) Genetic algorithm-based clustering technique. Pattern Recogn 33(9):1455–1465

    Article  Google Scholar 

  51. Maulik U, Bandyopadhyay S (2000) Genetic algorithm-based clustering technique. Pattern Recogn 33(9):1455–1465

    Article  Google Scholar 

  52. Shelokar PS, Jayaraman VK, Kulkarni BD (2004) An ant colony approach for clustering. Anal Chim Acta 509(2):187–195

    Article  Google Scholar 

  53. Kao YT, Zahara E, Kao IW (2008) A hybridized approach to data clustering. Expert Syst Appl 34(3):1754–1762

    Article  Google Scholar 

  54. Kumar Y, Sahoo G (2014) A hybrid data clustering approach based on cat swarm optimization and K-harmonic mean algorithm. J Inf Comput Sci 9(3):196–209

    Google Scholar 

  55. Kumar Y, Sahoo G (2015) A hybrid data clustering approach based on improved cat swarm optimization and K-harmonic mean algorithm. Ai Commun 28(4):751–764

    Article  MathSciNet  Google Scholar 

  56. Sahoo G (2017) A two-step artificial bee colony algorithm for clustering. Neural Comput Applic 28(3):537–551

    Article  Google Scholar 

  57. Kumar Y, Sahoo G (2017) Gaussian cat swarm optimisation algorithm based on Monte Carlo method for data clustering. Int J Comput Sci Eng 14(2):198–210

    MathSciNet  Google Scholar 

  58. Jordehi AR (2014) A chaotic-based big bang–big crunch algorithm for solving global optimisation problems. Neural Comput Applic 25(6):1329–1335

    Article  Google Scholar 

  59. Jordehi AR (2015) A chaotic artificial immune system optimisation algorithm for solving global continuous optimisation problems. Neural Comput Applic 26(4):827–833

    Article  Google Scholar 

  60. Jordehi AR (2015) Chaotic bat swarm optimisation (CBSO). Appl Soft Comput 26:523–530

    Article  Google Scholar 

  61. Jordehi AR (2015) Seeker optimisation (human group optimisation) algorithm with chaos. J Exper Theor Artif Intell 27(6):753–762

    Article  Google Scholar 

  62. Kumar Y, Sahoo G (2017) An improved cat swarm optimization algorithm based on opposition-based learning and cauchy operator for clustering. JIPS (J Inf Process Syst) 13(4):1000– 1013

    Google Scholar 

  63. Rai D (2017) Comments on “A note on multi-objective improved teaching-learning based optimization algorithm (MO-ITLBO)”. Int J Ind Eng Comput 8(2):179–190

    Google Scholar 

  64. Rao R (2016) Review of applications of TLBO algorithm and a tutorial for beginners to solve the unconstrained and constrained optimization problems. Decis Sci Lett 5(1):1–30

    MathSciNet  Google Scholar 

  65. Tuo S, Yong L, Li Y, Lin Y, Lu Q (2017) HSTLBO: a hybrid algorithm based on harmony search and teaching-learning-based optimization for complex high-dimensional optimization problems. PloS one 12(4):e0175114

    Article  Google Scholar 

  66. Yu K, Wang X, Wang Z (2016) An improved teaching-learning-based optimization algorithm for numerical and engineering optimization problems. J Intell Manuf 27(4):831–843

    Article  Google Scholar 

  67. Khuat TT, Le MH (2017) A genetic algorithm with multi-parent crossover using quaternion representation for numerical function optimization. Appl Intell 46(4):810–826

    Article  Google Scholar 

  68. Wang HB, Zhang KP, Tu XY (2015) A mnemonic shuffled frog leaping algorithm with cooperation and mutation. Appl Intell 43(1):32–48

    Article  Google Scholar 

  69. Yi J, Gao L, Li X, Gao J (2016) An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems. Appl Intell 44(3):725–753

    Article  Google Scholar 

  70. Guo W, Chen M, Wang L, Wu Q (2016) Backtracking biogeography-based optimization for numerical optimization and mechanical design problems. Appl Intell 44(4):894–903

    Article  Google Scholar 

  71. Yi W, Gao L, Li X, Zhou Y (2015) A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. Appl Intell 42(4):642–660

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yugal Kumar.

Ethics declarations

Conflict of interests

There is no conflict of interest.

Appendix

Appendix

List of abbreviations

1

SA

Simulated Annealing

2

GA

Genetic Algorithm

3

PSO

Particle Swarm Optimization

4

ACO

Ant Colony Optimization

5

HS

Harmony Search

6

ABC

Artificial Bee Colony

7

FA

Firefly Algorithm

8

LCA

League Championship Algorithm

9

WCA

Water Cycle Algorithm

10

CSS

Charged System Search

11

MCSS

Magnetic Charged System Search

12

TLBO

Teacher Learning Based Optimization

13

I-TLBO

Improved Teacher Learning Based Optimization

14

MBA

Mine Blast Algorithm

15

COA

Chaos Optimization based Algorithms

16

ICSO

Improved Cat Swarm Optimization

17

SD

Standard Deviation

18

M-TLBO

Modified Teacher Learning Based Optimization

19

BA

Bat Algorithm

20

FPA

Flower Pollination Algorithm

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, Y., Singh, P.K. A chaotic teaching learning based optimization algorithm for clustering problems. Appl Intell 49, 1036–1062 (2019). https://doi.org/10.1007/s10489-018-1301-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-018-1301-4

Keywords

Navigation