An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization


Yin–Yang-pair Optimization (YYPO) is a recently developed philosophy-inspired meta-heuristic algorithm, which works with two main points for exploitation and exploration, respectively, and then generates more points via splitting to search the global optimum. However, it suffers from low quality of candidate solutions in its exploration process owing to the lack of elitism. Inspired by this, a new modified algorithm named orthogonal opposition-based-learning Yin–Yang-pair Optimization (OOYO) is proposed to enhance the performance of YYPO. First, the OOYO retains the normalization operation in YYPO and starts with a single point to exploit. A set of opposite points is designed by a method of opposition-based learning with split points generated from the current optimum for exploration. Then, the points, i.e., candidate solutions, are constructed by the randomly selected split point and opposite points through the idea of orthogonal experiment design to make full use of information from the space. The proposed OOYO does not add additional time complexity and eliminates a user-defined parameter in YYPO, which facilitates parameter adjustment. The novel orthogonal opposition-based learning strategy can provide inspirations for the improvement of other optimization algorithms. Extensive test functions containing a classic test suite of 23 standard benchmark functions and 2 test suites of Swarm Intelligence Symposium 2005 and Congress on Evolutionary Computation 2020 from Institute of Electrical and Electronics Engineers are employed to evaluate the proposed algorithm. Non-parametric statistical results demonstrate that OOYO outperforms YYPO and furnishes strong competitiveness compared with other state-of-the-art algorithms. In addition, we apply OOYO to solve four well-known constrained engineering problems and a practical problem of parameters optimization in a rainstorm intensity model.

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  1. 1.

    Barshandeh S, Haghzadeh M (2020) A new hybrid chaotic atom search optimization based on tree-seed algorithm and Levy flight for solving optimization problems. Eng Comput.

    Article  Google Scholar 

  2. 2.

    Gupta S, Deep K (2020) A novel hybrid sine cosine algorithm for global optimization and its application to train multilayer perceptrons. Appl Intell 50(4):993–1026.

    Article  Google Scholar 

  3. 3.

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

    Article  Google Scholar 

  4. 4.

    Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Article  Google Scholar 

  5. 5.

    Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713.

    Article  Google Scholar 

  7. 7.

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

    MathSciNet  Article  Google Scholar 

  8. 8.

    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95 - international conference on neural networks, vol 1944, pp 1942–1948.

  9. 9.

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

    Article  Google Scholar 

  10. 10.

    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471.

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspir Comput 2(2):78–84.

    Article  Google Scholar 

  12. 12.

    Zong Woo G, Joong Hoon K, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68.

    Article  Google Scholar 

  13. 13.

    Rao RV, 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 

  14. 14.

    Punnathanam V, Kotecha P (2016) Yin-Yang-pair optimization: a novel lightweight optimization algorithm. Eng Appl Artif Intell 54:62–79.

    Article  Google Scholar 

  15. 15.

    Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12.

    Article  Google Scholar 

  16. 16.

    Muthiah-Nakarajan V, Noel MM (2016) Galactic swarm optimization: a new global optimization metaheuristic inspired by galactic motion. Appl Soft Comput 38:771–787.

    Article  Google Scholar 

  17. 17.

    Ahmadi S-A (2017) Human behavior-based optimization: a novel metaheuristic approach to solve complex optimization problems. Neural Comput Appl 28(1):233–244.

    Article  Google Scholar 

  18. 18.

    Kaveh A, Bakhshpoori T (2016) Water evaporation optimization: a novel physically inspired optimization algorithm. Comput Struct 167:69–85.

    Article  Google Scholar 

  19. 19.

    Chen J, Cai H, Wang W (2018) A new metaheuristic algorithm: car tracking optimization algorithm. Soft Comput 22(12):3857–3878.

    Article  Google Scholar 

  20. 20.

    Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84.

    Article  Google Scholar 

  21. 21.

    Mousavirad SJ, Ebrahimpour-Komleh H (2017) Human mental search: a new population-based metaheuristic optimization algorithm. Appl Intell 47(3):850–887.

    Article  Google Scholar 

  22. 22.

    Aghay Kaboli SH, Selvaraj J, Rahim NA (2017) Rain-fall optimization algorithm: a population based algorithm for solving constrained optimization problems. J Comput Sci 19:31–42.

    Article  Google Scholar 

  23. 23.

    Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70.

    Article  Google Scholar 

  24. 24.

    Klein CE, Mariani VC, Coelho LDS (2018) Cheetah based optimization algorithm: a novel swarm intelligence paradigm

  25. 25.

    Pierezan J, Coelho LDS (2018) Coyote optimization algorithm: a new metaheuristic for global optimization problems. In: 2018 IEEE congress on evolutionary computation (CEC), 8–13 July 2018 2018. pp 1–8. doi:

  26. 26.

    Shayanfar H, Gharehchopogh FS (2018) Farmland fertility: a new metaheuristic algorithm for solving continuous optimization problems. Appl Soft Comput 71:728–746.

    Article  Google Scholar 

  27. 27.

    Pijarski P, Kacejko P (2019) A new metaheuristic optimization method: the algorithm of the innovative gunner (AIG). Eng Optim 51(12):2049–2068.

    MathSciNet  Article  Google Scholar 

  28. 28.

    Yapici H, Cetinkaya N (2019) A new meta-heuristic optimizer: Pathfinder algorithm. Appl Soft Comput 78:545–568.

    Article  Google Scholar 

  29. 29.

    Morais RG, Nedjah N, Mourelle LM (2020) A novel metaheuristic inspired by Hitchcock birds’ behavior for efficient optimization of large search spaces of high dimensionality. Soft Comput 24(8):5633–5655.

    Article  Google Scholar 

  30. 30.

    Vasconcelos Segundo EHd, Mariani VC, Coelho LdS (2019) Design of heat exchangers using Falcon optimization algorithm. Appl Therm Eng 156:119–144.

    Article  Google Scholar 

  31. 31.

    Samareh Moosavi SH, Bardsiri VK (2019) Poor and rich optimization algorithm: a new human-based and multi populations algorithm. Eng Appl Artif Intell 86:165–181.

    Article  Google Scholar 

  32. 32.

    Kaur A, Jain S, Goel S (2020) Sandpiper optimization algorithm: a novel approach for solving real-life engineering problems. Appl Intell 50(2):582–619.

    Article  Google Scholar 

  33. 33.

    Shadravan S, Naji HR, Bardsiri VK (2019) The Sailfish optimizer: a novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34.

    Article  Google Scholar 

  34. 34.

    Vasconcelos Segundo EHd, Mariani VC, Coelho LdS (2019) Metaheuristic inspired on owls behavior applied to heat exchangers design. Thermal Sci Eng Progress 14:100431.

    Article  Google Scholar 

  35. 35.

    S-u-R M, Wagan AI, Shaikh MM (2020) A new metaheuristic optimization algorithm inspired by human dynasties with an application to the wind turbine micrositing problem. Appl Soft Comput 90:106176.

    Article  Google Scholar 

  36. 36.

    Gholizadeh S, Danesh M, Gheyratmand C (2020) A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames. Comput Struct 234:106250.

    Article  Google Scholar 

  37. 37.

    Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H (2020) Barnacles mating optimizer: a new bio-inspired algorithm for solving engineering optimization problems. Eng Appl Artif Intell 87:103330.

    Article  Google Scholar 

  38. 38.

    Zaeimi M, Ghoddosian A (2020) Color harmony algorithm: an art-inspired metaheuristic for mathematical function optimization. Soft Comput.

    Article  Google Scholar 

  39. 39.

    Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377.

    Article  Google Scholar 

  40. 40.

    Xu X, Hu Z, Su Q, Li Y, Dai J (2020) Multivariable grey prediction evolution algorithm: a new metaheuristic. Appl Soft Comput 89:106086.

    Article  Google Scholar 

  41. 41.

    Kaur S, Awasthi LK, Sangal AL, Dhiman G (2020) Tunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541.

    Article  Google Scholar 

  42. 42.

    Kaveh A, Dadras Eslamlou A (2020) Water strider algorithm: a new metaheuristic and applications. Structures 25:520–541.

    Article  MATH  Google Scholar 

  43. 43.

    Ghafil HN, Jármai K (2020) Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Appl Soft Comput 93:106392.

    Article  Google Scholar 

  44. 44.

    Houssein EH, Saad MR, Hashim FA, Shaban H, Hassaballah M (2020) Lévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 94:103731.

    Article  Google Scholar 

  45. 45.

    Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300.

    Article  Google Scholar 

  46. 46.

    Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Fut Gen Comput Syst 111:300–323.

    Article  Google Scholar 

  47. 47.

    Das B, Mukherjee V, Das D (2020) Student psychology based optimization algorithm: a new population based optimization algorithm for solving optimization problems. Adv Eng Softw 146:102804.

    Article  Google Scholar 

  48. 48.

    Chen T, Tang K, Chen G, Yao X (2012) A large population size can be unhelpful in evolutionary algorithms. Theor Comput Sci 436:54–70.

    MathSciNet  Article  MATH  Google Scholar 

  49. 49.

    Dhal KG, Das A, Sahoo S, Das R, Das S (2019) Measuring the curse of population size over swarm intelligence based algorithms. Evolving Syst.

    Article  Google Scholar 

  50. 50.

    Punnathanam V, Kotecha P (2016) Adaptive Yin-Yang-Pair Optimization on CEC 2016 functions. In: 2016 IEEE Region 10 Conference (TENCON), pp 2296–2299. doi:

  51. 51.

    Heidari AA, Kazemizade O, Hakimpour F (2017) A new hybrid yin-yang-pair-particle swarm optimization algorithm for uncapacitated warehouse location problems. In: Tehran's Joint ISPRS International Conferences of the 2nd Geospatial Information Research, GI Research 2017, the 4th Sensors and Models in Photogrammetry and Remote Sensing, SMPR 2017 and the 6th Earth Observation of Environmental Changes, EOEC 2017, October 7, 2017 - October 10, 2017, Tehran, Iran, 2017. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives. International Society for Photogrammetry and Remote Sensing, pp 373–379. doi:

  52. 52.

    Maharana D, Kommadath R, Kotecha P (2017) Dynamic Yin-Yang Pair Optimization and its performance on single objective real parameter problems of CEC 2017. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp 2390–2396. doi:

  53. 53.

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

    Article  Google Scholar 

  54. 54.

    Wang W-c, Xu L, Chau K-w, Xu D-m (2020) Yin-Yang firefly algorithm based on dimensionally Cauchy mutation. Expert Syst Appl 150:113216.

    Article  Google Scholar 

  55. 55.

    Fan Q, Chen Z, Li Z, Xia Z, Yu J, Wang D (2020) A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems. Eng Comput.

    Article  Google Scholar 

  56. 56.

    Seyyedabbasi A, Kiani F (2019) I-GWO and Ex-GWO: improved algorithms of the Grey Wolf Optimizer to solve global optimization problems. Eng Comput.

    Article  Google Scholar 

  57. 57.

    Tizhoosh HR (2005) Opposition-based learning: A new scheme for machine intelligence. In: International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, IAWTIC 2005, November 28, 2005 - November 30, 2005, Vienna, Austria, 2005. Proceedings - International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet. Inst. of Elec. and Elec. Eng. Computer Society, pp 695–701

  58. 58.

    Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition versus randomness in soft computing techniques. Appl Soft Comput 8(2):906–918.

    Article  Google Scholar 

  59. 59.

    Rahnamayan S, Tizhoosh HR, Salama MMA (2006) Opposition-based differential evolution for optimization of noisy problems. In: 2006 IEEE Congress on Evolutionary Computation, CEC 2006, July 16, 2006 - July 21, 2006, Vancouver, BC, Canada, 2006. 2006 IEEE Congress on Evolutionary Computation, CEC 2006. Inst. of Elec. and Elec. Eng. Computer Society, pp 1865–1872

  60. 60.

    Sharma TK, Gupta P (2018) Opposition learning based phases in artificial bee colony. Int J Syst Assur Eng Manag 9(1):262–273.

    Article  Google Scholar 

  61. 61.

    Bao X, Jia H, Lang C (2019) Dragonfly algorithm with opposition-based learning for multilevel thresholding color image segmentation. Symmetry 11(5):716

    Article  Google Scholar 

  62. 62.

    Dinkar SK, Deep K (2019) Accelerated opposition-based antlion optimizer with application to order reduction of linear time-invariant systems. Arab J Sci Eng 44(3):2213–2241.

    Article  Google Scholar 

  63. 63.

    Gupta S, Deep K (2019) An efficient grey wolf optimizer with opposition-based learning and chaotic local search for integer and mixed-integer optimization problems. Arab J Sci Eng 44(8):7277–7296.

    Article  Google Scholar 

  64. 64.

    Zhou L, Ma M, Ding L, Tang W (2019) Centroid opposition with a two-point full crossover for the partially attracted firefly algorithm. Soft Comput.

    Article  Google Scholar 

  65. 65.

    Rahnamayan S, Jesuthasan J, Bourennani F, Salehinejad H, Naterer GF (2014) Computing opposition by involving entire population. In: 2014 IEEE Congress on Evolutionary Computation, CEC 2014, July 6, 2014 - July 11, 2014, Beijing, China, 2014. Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014. Institute of Electrical and Electronics Engineers Inc., pp 1800–1807. doi:

  66. 66.

    Rizk-Allah RM (2019) An improved sine–cosine algorithm based on orthogonal parallel information for global optimization. Soft Comput 23(16):7135–7161.

    Article  Google Scholar 

  67. 67.

    Feng Z-k, Niu W-j, Cheng C-t, Lund Jay R (2018) Optimizing hydropower reservoirs operation via an orthogonal progressive optimality algorithm. J Water Resour Plan Manag 144(3):04018001.

    Article  Google Scholar 

  68. 68.

    Yiu-Wing L, Yuping W (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evol Comput 5(1):41–53.

    Article  Google Scholar 

  69. 69.

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

    Article  Google Scholar 

  70. 70.

    Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl-Based Syst 163:283–304.

    Article  Google Scholar 

  71. 71.

    Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Fut Gen Comput Syst 97:849–872.

    Article  Google Scholar 

  72. 72.

    Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191.

    Article  Google Scholar 

  73. 73.

    Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evolut Comput 9(2):159–195.

    Article  Google Scholar 

  74. 74.

    Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolut Comput 11(1):1–18.

    Article  Google Scholar 

  75. 75.

    Hansen N, Kern S (2004) Evaluating the CMA Evolution Strategy on Multimodal Test Functions. In: Yao X, Burke EK, Lozano JA et al. (eds) Parallel Problem Solving from Nature - PPSN VIII, Berlin, Heidelberg, 2004. Springer, Berlin, pp 282–291

  76. 76.

    Mirjalili S, Lewis A, Sadiq AS (2014) Autonomous particles groups for particle swarm optimization. Arab J Sci Eng 39(6):4683–4697.

    Article  MATH  Google Scholar 

  77. 77.

    Civicioglu P, Besdok E, Gunen MA, Atasever UH (2018) Weighted differential evolution algorithm for numerical function optimization: a comparative study with cuckoo search, artificial bee colony, adaptive differential evolution, and backtracking search optimization algorithms. Neural Comput Appl.

    Article  Google Scholar 

  78. 78.

    Liang JJ, Suganthan PN, Deb K (2005) Novel composition test functions for numerical global optimization. In: Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005., 8–10 June 2005. pp 68–75. doi:

  79. 79.

    Xin Y, Yong L, Guangming L (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102.

    Article  Google Scholar 

  80. 80.

    Yue CT, Price KV, Suganthan PN, Liang JJ, Ali MZ, Qu BY, Awad NH, Biswas PP (2019) Problem definitions and evaluation criteria for the CEC 2020 special session and competition on single objective bound constrained numerical optimization. Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, Computational Intelligence Laboratory

    Google Scholar 

  81. 81.

    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18.

    Article  Google Scholar 

  82. 82.

    Montgomery DC (2013) Design and analysis of experiments, 8th edn. Wiley, Hoboken

    Google Scholar 

  83. 83.

    Kumar A, Wu G, Ali MZ, Mallipeddi R, Suganthan PN, Das S (2020) A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evolut Comput 56:100693.

    Article  Google Scholar 

  84. 84.

    Dl Li, Cheng XY, Yang H, Huang P (2013) Study on artificial intelligence optimization algorithms for auto-calibration of hydrological models. J Hydraul Eng 44:95–101

    Google Scholar 

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The authors are grateful to the Henan province university scientific and technological innovation team (No: 18IRTSTHN009), Support of National Natural Science Foundation of China (No: 51509088), Project of key science and technology of the Henan province (202102310259; 202102310588). We gratefully acknowledge the critical comments and corrections of the anonymous reviewers, which improved the presentation of the paper considerably.

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Wang, Wc., Xu, L., Chau, Kw. et al. An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization. Engineering with Computers (2021).

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  • Meta-heuristic algorithm
  • Yin–Yang-pair optimization
  • Opposition-based learning
  • Orthogonal experiment design
  • Benchmark functions
  • Engineering optimization