A Hybrid TLBO Algorithm by Quadratic Approximation for Function Optimization and Its Application

  • Sukanta NamaEmail author
  • Apu Kumar Saha
  • Sushmita Sharma
Part of the Intelligent Systems Reference Library book series (ISRL, volume 172)


Recently hybrid optimization algorithms enjoy growing attention in the optimization community. However, over the last two decades, many new hybrid meta-heuristics optimization techniques are developed and are still developing. On the hybrid optimization algorithm, the most common criticism is that they are not well balanced in respect of the local search and global search of the algorithm. Viewing this, in the present work a modified adaptive based teaching factor is suggested for the basic TLBO algorithm. Also, a novel hybrid approach is proposed that combines the Teaching Learning Base Optimization (TLBO) Algorithm and Quadratic approximation (QA). The QA is applied to improve the global as well as local search capability of the method that also represents the characters of “Teacher Refresh”. For the performance investigation, the suggested algorithm is involved to solve twenty classical optimization functions and one real life optimization problem and the performances are differentiated with different state-of-the-arts methods in terms of numerical results of the solution.


Hybrid optimization method Teaching learning based optimization (TLBO) Quadratic approximation (QA) Unconstrained optimization problem 



The authors would like to thank Dr. P. N. Suganthan, School of Electrical and Electronic Engineering, NTU, Singapore for shearing the source codes of PSO variants. Also thanks to the editors, anonymous referees for their valuable suggestion towards improving the book chapter.


  1. 1.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceeding of the IEEE International Conference on Neural Networks, 1995, 1942–1948Google Scholar
  2. 2.
    Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: IEEE International Conference on Computational Intelligence, pp. 69–73 (1998)Google Scholar
  3. 3.
    Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press (1975)Google Scholar
  4. 4.
    Dorigo, M.: Optimization, Learning and Natural Algorithms. Thesis (Ph.D.), Politecnico di Milano (1992)Google Scholar
  5. 5.
    Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Rashedi, E., Nezamabadi-pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179, 2232–2248 (2009)zbMATHCrossRefGoogle Scholar
  7. 7.
    Akay, B., Karaboga, D.: Artificial bee colony algorithm for large-scale problems and engineering design optimization. J. Intell. Manuf. (2010).
  8. 8.
    Akay, B., Karaboga, D.: A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl. Soft Comput. (2010).
  9. 9.
    Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43, 303–315 (2011)CrossRefGoogle Scholar
  10. 10.
    Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)CrossRefGoogle Scholar
  11. 11.
    Kennedy, J., Mendes, R.: Population structure and particle swarm performance. In: Proceedings of IEEE Congress Evolutionary Computation, Honolulu, HI, 2002, pp. 1671–1676Google Scholar
  12. 12.
    Mendes, R., Kennedy, J., Neves, J.: The fully informed particle swarm: simpler, maybe better. IEEE Trans. Evol. Comput. 8, 204–210 (2004)CrossRefGoogle Scholar
  13. 13.
    Parsopoulos, K.E., Vrahatis, M.N.: UPSO—a unified particle swarm optimization scheme. Lect. Ser. Comput. Sci. 1, 868–873 (2004)Google Scholar
  14. 14.
    Peram, T., Veeramachaneni, K., Mohan, C.K.: Fitness-distance-ratio based particle swarm optimization. In: Proceedings of Swarm Intelligence Symposium, pp. 174–181 (2003)Google Scholar
  15. 15.
    van den Bergh, F., Engelbrecht, A.P.: A cooperative approach to particle swarm optimization. IEEE Trans. Evol. Comput. 8, 225–239 (2004)CrossRefGoogle Scholar
  16. 16.
    Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. Comput. 10(3) (2006)Google Scholar
  17. 17.
    Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(April), 398–417 (2009)CrossRefGoogle Scholar
  18. 18.
    Iorio, A., Li, X.: Solving rotated multi-objective optimization problems using differential evolution. In: Australian Conference on Artificial Intelligence, Cairns, Australia, 2004, pp. 861–872Google Scholar
  19. 19.
    Storn, R.: On the usage of differential evolution for function optimization. In: Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS), pp. 519–523. IEEE, Berkeley (1996)Google Scholar
  20. 20.
    Mallipeddi, R., Suganthan, P.N., Pan, Q.K., Tasgetiren, M.F.: Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl. Soft Comput. 11, 1679–1696 (2011)CrossRefGoogle Scholar
  21. 21.
    Pant, M., Thangaraj, R.: DE-PSO: a new hybrid meta-heuristic for solving global optimization problems. New Math. Nat. Comput. 7(3), 363–381 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Deep, K., Das, K.N.: Quadratic approximation based hybrid genetic algorithm for function optimization. Appl. Math. Comput. 203, 86–98 (2008)zbMATHGoogle Scholar
  23. 23.
    Abd-El-Wahed, W.F., Mousa, A.A., El-Shorbagy, M.A.: Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems. J. Comput. Appl. Math. 235, 1446–1453 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Zhang, L., Li, H., Jiao, Y.-C., Zhang, F.-S.: Hybrid differential evolution and the simplified quadratic interpolation for global optimization. Copyright is held by the author/owner(s). GEC’09, 12–14 June 2009, Shanghai, China. ACM 978-1-60558-326-6/09/06Google Scholar
  25. 25.
    Mirjalili, S., Mohd Hashim, S.Z.: A new hybrid PSOGSA algorithm for function optimization. In: International Conference on Computer and Information Application, ICCIA 2010Google Scholar
  26. 26.
    Deep, K., Bansal, J.C.: Hybridization of particle swarm optimization with quadratic approximation. OPSEARCH 46(1), 3–24Google Scholar
  27. 27.
    Pant, M., Thangaraj, R., Abraham, A.: A new PSO algorithm with crossover operator for global optimization problems. Innov. Hybrid Intell. Syst., ASC 44, 215–222 (2007)CrossRefGoogle Scholar
  28. 28.
    Nama, S., Saha, A.K., Ghosh, S.: A new ensemble algorithm of differential evolution and backtracking search optimization algorithm with adaptive control parameter for function optimization. Int. J. Ind. Eng. Comput. 7, 323–338 (2016)Google Scholar
  29. 29.
    Nama, S., Saha, A.K., Ghosh, S.: A hybrid symbiosis organisms search algorithm and its application to real world problems. Memetic Comput. (2016).
  30. 30.
    Satapathy, S.C., Naik, A.: A modified teaching-learning-based optimization (mTLBO) for global search. Recent Pat. Comput. Sci. 6, 60–72 (2013)CrossRefGoogle Scholar
  31. 31.
    Satapathy, S.C., Naik, A., Parvathi, K.: A teaching learning based optimization based on orthogonal design for solving global optimization problemsGoogle Scholar
  32. 32.
    Rao, R.V., Patel, V.: Comparative performance of an elitist teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Int. J. Ind. Eng. Comput. 4, 29–50 (2013)Google Scholar
  33. 33.
    Satapathy, S.C., Naik, A., Parvathi, K.: Weighted teaching-learning-based optimization for global function optimization. Appl. Math. 4, 429–439 (2013)CrossRefGoogle Scholar
  34. 34.
    Nayak, M.R., Nayak, C.K., Rout, P.K.: Application of multi-objective teaching learning based optimization algorithm to optimal power flow problem. In: 2nd International Conference on Communication, Computing & Security [ICCCS-2012], Procedia Technology, vol. 6, pp. 255–264 (2012)Google Scholar
  35. 35.
    Xia, K., et al.: Disassembly sequence planning using a simplified teaching–learning-based optimization algorithm. Adv. Eng. Inform. (2014).
  36. 36.
    Roy, P.K., Paul, C., Sultana, S.: Oppositional teaching learning based optimization approach for combined heat and power dispatch. Electr. Power Energy Syst. 57, 392–403 (2014)CrossRefGoogle Scholar
  37. 37.
    Roy, P.K., Sur, A., Pradhan, D.K.: Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization. Eng. Appl. Artif. Intell. 26, 2516–2524 (2013)Google Scholar
  38. 38.
    Venkata Rao, R.: Teaching Learning Based Optimization Algorithm: And Its Engineering Applications, 1st edn. Springer Publishing Company, Incorporated (2015)Google Scholar
  39. 39.
    Jiang, X., Zhou, J.: Hybrid DE-TLBO algorithm for solving short term hydro-thermal optimal scheduling with incommensurable objectives. In: Proceedings of the 32nd Chinese Control Conference, 26–28 July 2013, Xian, ChinaGoogle Scholar
  40. 40.
    Xie, Z., Zhang, C., Shao, X., Lin, W., Zhu, H.: An effective hybrid teaching–learning-based optimization algorithm for permutation flow shop scheduling problem. Adv. Eng. Softw. 77, 35–47 (2014)Google Scholar
  41. 41.
    Azad-Farsani, E., Zare, M., Azizipanah-Abarghooee, R., Askarian-Abyaneh, H.: A new hybrid CPSO-TLBO optimization algorithm for distribution network reconfiguration. J. Intell. Fuzzy Syst. 26(5), 2175–2184 (2014). Scholar
  42. 42.
    Dokeroglu, T.: Hybrid teaching–learning-based optimization algorithms for the quadratic assignment problem. Comput. Ind. Eng. 85, 86–101 (2015)CrossRefGoogle Scholar
  43. 43.
    Gnanambal, K., Jeyavelumani, K.R., Juriya Banu, H.: Optimal, power flow using hybrid teaching learning based optimization algorithm. GRD Journals. Global Research and Development Journal for Engineering. International Conference on Innovations in Engineering and Technology, (ICIET)—2016, July 2016. e-ISSN: 2455-5703Google Scholar
  44. 44.
    Khare, R., Kumar, Y.: A novel hybrid MOL–TLBO optimized techno-economic-socio analysis of renewable energy mix in island mode. Appl. Soft Comput. 43, 187–198 (2016)CrossRefGoogle Scholar
  45. 45.
    Sahu, B.K., Pati, T.K., Nayak, J.R., Panda, S., Kar, S.K.: A novel hybrid LUS–TLBO optimized fuzzy-PID controller for load frequency control of multi-source power system. Int. J. Electr. Power Energy Syst. 74, 58–69 (2016)CrossRefGoogle Scholar
  46. 46.
    Babazadeh, R., Tavakkoli-Moghaddam, R.: A hybrid GA-TLBO algorithm for optimizing a capacitated three-stage supply chain network. Int. J. Ind. Eng. Prod. Res. 28, 151–161 (2017)Google Scholar
  47. 47.
    Deb, S., Kalita, K., Gao, X., Tammi, K., Mahanta, P.: Optimal placement of charging stations using CSO-TLBO algorithm. In: 2017 Third International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN), Kolkata, pp. 84–89 (2017)Google Scholar
  48. 48.
    Patsariya, A., et al.: Implementation of noble TLBO-MPPT technique for SPV in hybrid DC-DC boost converter. In: 2017 International Conference on Energy, Communication, Data Analytics and Soft Computing (ICECDS), pp. 1622–1627 (2017)Google Scholar
  49. 49.
    Shahbeig, S., Helfroush, M.S., Rahideh, A.: A fuzzy multi-objective hybrid TLBO–PSO approach to select the associated genes with breast cancer. Signal Process. 131, 58–65 (2017)CrossRefGoogle Scholar
  50. 50.
    Tuo, S., Yong, L., Deng, F., Li, Y., Lin, Y., Lu, Q.: HSTLBO: a hybrid algorithm based on harmony search and teaching-learning-based optimization for complex high-dimensional optimization problems. PLoS ONE 12(4), e0175114 (2017). Scholar
  51. 51.
    Ding, Y., et al.: A novel hybrid teaching learning based optimization algorithm for function optimization. In: 2017 Chinese Automation Congress (CAC), pp. 4383–4388 (2017)Google Scholar
  52. 52.
    Singh, R., Chaudhary, H., Singh, A.K.: A new hybrid teaching–learning particle swarm optimization algorithm for synthesis of linkages to generate path. Sadhana 42(11), 1851–1870 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  53. 53.
    Chen, X., Xu, B., Yu, K., Du, W.: Teaching-learning-based optimization with learning enthusiasm mechanism and its application in chemical engineering. J. Appl. Math. (2018).
  54. 54.
    Nenavath, H., Jatoth, R.K.: Hybrid SCA–TLBO: a novel optimization algorithm for global optimization and visual tracking. Neural Comput. Appl. (2018).
  55. 55.
    Zhang, M., Pan, Y., Zhu, J., Chen, G.: BC-TLBO: a hybrid algorithm based on artificial bee colony and teaching-learning-based optimization, pp. 2410–2417 (2018).
  56. 56.
    Sevinç, E., Dökeroğlu, T.: A novel hybrid teaching-learning-based optimization algorithm for the classification of data by using extreme learning machines. Turk. J. Electr. Eng. Comput. Sci. 27, 1523–1533 (2019). Scholar
  57. 57.
    Guo, C., Lu, J., Tian, Z., Guo, W., Darvishan, A.: Optimization of critical parameters of PEM fuel cell using TLBO-DE based on Elman neural network. Energy Convers. Manag. 183, 149–158 (2019)CrossRefGoogle Scholar
  58. 58.
    Zhang, Q., Yu, G., Song, H.: A hybrid bird mating optimizer algorithm with teaching-learning-based optimization for global numerical optimization. Stat. Optim. Inf. Comput. 3 (2015).
  59. 59.
    Tang, Q., Li, Z., Zhang, L.P., Zhang, C.: Balancing stochastic two-sided assembly line with multiple constraints using hybrid teaching-learning-based optimization algorithm. Comput. Oper. Res. 82, 102–113 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Shao, W., Pi, D., Shao, Z.: A hybrid discrete optimization algorithm based on teaching–probabilistic learning mechanism for no-wait flow shop scheduling. Knowl.-Based Syst. 107, 219–234 (2016)CrossRefGoogle Scholar
  61. 61.
    Shao, W., Pi, D., Shao, Z.: A hybrid discrete teaching-learning based meta-heuristic for solving no-idle flow shop scheduling problem with total tardiness criterion. Comput. Oper. Res. 94, 89–105 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Das, S.P., Padhy, S.: A novel hybrid model using teaching–learning-based optimization and a support vector machine for commodity futures index forecasting. Int. J. Mach. Learn. Cyber. 9, 97 (2018). Scholar
  63. 63.
    González-Álvarez, D.L., Vega-Rodríguez, M.A., Rubio-Largo, Á.: Finding patterns in protein sequences by using a hybrid multiobjective teaching learning based optimization algorithm. IEEE/ACM Trans. Comput. Biol. Bioinform. 12(3), 656–666 (2015)CrossRefGoogle Scholar
  64. 64.
    Chen, D., Zou, F., Wang, J., et al.: A multi-class cooperative teaching–learning-based optimization algorithm with simulated annealing. Soft Comput. 20, 1921 (2016). Scholar
  65. 65.
    Zou, F., Wang, L., Hei, X., Chen, D., Jiang, Q., Li, H.: Bare-bones teaching-learning-based optimization. Sci. World J. 2014, 17p (2014). Article ID 136920.
  66. 66.
    Ghasemi, M., Taghizadeh, M., Ghavidel, S., Aghaei, J., Abbasian, A.: Solving optimal reactive power dispatch problem using a novel teaching–learning-based optimization algorithm. Eng. Appl. Artif. Intell. 39, 100–108 (2015)CrossRefGoogle Scholar
  67. 67.
    Wang, L., Zou, F., Hei, X., et al.: A hybridization of teaching–learning-based optimization and differential evolution for chaotic time series prediction. Neural Comput. Appl. 25, 1407 (2014). Scholar
  68. 68.
    Ghasemi, M., Ghanbarian, M.M., Ghavidel, S., Rahmani, S., Moghaddam, E.M.: Modified teaching learning algorithm and double differential evolution algorithm for optimal reactive power dispatch problem: a comparative study. Inf. Sci. 278, 231–249 (2014)MathSciNetCrossRefGoogle Scholar
  69. 69.
    Zou, F., Wang, L., Chen, D., Hei, X.: An improved teaching-learning-based optimization with differential learning and its application. Math. Probl. Eng. 2015, 19p (2015). Article ID 754562.
  70. 70.
    Dib, F., Boumhidi, I.: Hybrid algorithm DE–TLBO for optimal H∞ and PID control for multi-machine power system. Int. J. Syst. Assur. Eng. Manag. (2017). Scholar
  71. 71.
    Turgut, O.E., Coban, M.T.: Optimal proton exchange membrane fuel cell modelling based on hybrid teaching learning based optimization–differential evolution algorithm. Ain Shams Eng. J. 7(1), 347–360 (2016)CrossRefGoogle Scholar
  72. 72.
    Lim, W.H., Isa, N.A.M.: Teaching and peer-learning particle swarm optimization. Appl. Soft Comput. 18, 39–58 (2014)CrossRefGoogle Scholar
  73. 73.
    Lim, W.H., Isa, N.A.M.: Bidirectional teaching and peer-learning particle swarm optimization. Inf. Sci. 280, 111–134 (2014)CrossRefGoogle Scholar
  74. 74.
    Cheng, T., Chen, M., Fleming, P.J., et al.: A novel hybrid teaching learning based multi-objective particle swarm optimization. Neuro Comput. 222, 11–25 (2017)Google Scholar
  75. 75.
    Azizipanah-Abarghooee, R., Niknam, T., Bavafa, F., Zare, M.: Short-term scheduling of thermal power systems using hybrid gradient based modified teaching–learning optimizer with black hole algorithm. Electr. Power Syst. Res. 108, 16–34 (2014)CrossRefGoogle Scholar
  76. 76.
    Güçyetmez, M., Çam, E.: A new hybrid algorithm with genetic-teaching learning optimization (G-TLBO) technique for optimizing of power flow in wind-thermal power systems. Electr. Eng. 98, 145 (2016). Scholar
  77. 77.
    Chen, X., Bin, X., Mei, C., Ding, Y., Li, K.: Teaching–learning–based artificial bee colony for solar photovoltaic parameter estimation. Appl. Energy 212, 1578–1588 (2018)CrossRefGoogle Scholar
  78. 78.
    Tefek, M.F., Uğuz, H., Güçyetmez, M.: A new hybrid gravitational search–teaching–learning-based optimization method for energy demand estimation of Turkey. Neural Comput. Appl. (2017).
  79. 79.
    Huang, J., Gao, L., Li, X.: An effective teaching-learning-based cuckoo search algorithm for parameter optimization problems in structure designing and machining processes. Appl. Soft Comput. 36, 349–356 (2015)CrossRefGoogle Scholar
  80. 80.
    Huang, J., Gao, L., Li, X.: A teaching–learning-based cuckoo search for constrained engineering design problems. Adv. Glob. Optim. (2015).
  81. 81.
    Tuo, S., Yong, L., Zhou, T.: An improved harmony search based on teaching-learning strategy for unconstrained optimization problems. Math. Probl. Eng. (2013).
  82. 82.
    Mahdad, B., Srairi, K.: Optimal power flow improvement using a hybrid teaching-learning-based optimization and pattern search. Int. J. Mod. Educ. Comput. Sci. 10, 55–70 (2018). Scholar
  83. 83.
    Mohan, C., Shanker, K.: A random search technique for global optimization based on quadratic approximation. Asia Pac. J. Oper. Res. 11, 93–101 (1994)zbMATHGoogle Scholar
  84. 84.
    Ali, M.M., Torn, A., Viitanen, S.: A numerical comparison of some modified controlled random search algorithms. J. Glob. Optim. 11, 377–385 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  85. 85.
    Venkata Rao, R., Patel, V.: Multi-objective optimization of heat exchangers using a modified teaching-learning-based optimization algorithm. Appl. Math. Model. 37, 1147–1162 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  86. 86.
    Venkata Rao, R., Patel, V.: Multi-objective optimization of two stage thermoelectric cooler using a modified teaching–learning-based optimization algorithm. Eng. Appl. Artif. Intell. 26, 430–445 (2013)CrossRefGoogle Scholar
  87. 87.
    Crepinsek, M., Liu, S.-H., Mernik, M.: Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput. Surv. (CSUR) 45(3), 35 (2013)Google Scholar
  88. 88.
    Civicioglu, P.: Backtracking search optimization algorithm for numerical optimization problems. Appl. Math. Comput. 219, 8121–8144 (2013)MathSciNetzbMATHGoogle Scholar
  89. 89.
    Nasir, M., Das, S., Maity, D., Sengupta, S., Halder, U., Suganthan, P.N.: A dynamic neighborhood learning based particle swarm optimizer for global numerical optimization. Inf. Sci. 209, 16–36 (2012)MathSciNetCrossRefGoogle Scholar
  90. 90.
    Das, S., Suganthan, P.N.: Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Nanyang Technol. University, Kolkata, India, 2010Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Sukanta Nama
    • 1
    Email author
  • Apu Kumar Saha
    • 2
  • Sushmita Sharma
    • 2
  1. 1.Department of MathematicsRamthakur CollegeAgartala, West TripuraIndia
  2. 2.Department of MathematicsNational Institute of Technology AgartalaAgartalaIndia

Personalised recommendations