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An improved Harris Hawks optimizer combined with extremal optimization

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Abstract

Harris Hawks optimizer (HHO) is a new swarm intelligence optimization algorithm proposed in recent years. It seeks the optimal solution by simulating the predation strategy of Harris hawks and many previous experiments show that HHO has a good effect on solving optimization problems. However, HHO also has the shortcomings of low convergence accuracy and easy to fall into local optimum. In order to improve the performance of HHO, an improved HHO hybridized with extremal optimization (IHHO-EO) is proposed. Aiming at the defect of insufficient information utilization and excessive randomization in the exploration phase of the algorithm, the own historical optimal position of Harris hawks is introduced to better guide the individuals to search for better positions and improve the global search ability. Secondly, a nonlinear prey energy escaping factor is proposed to better balance the exploration and exploitation phases. Thirdly, refracted opposition-based learning (ROBL) with a dynamic parameter is proposed and combined with HHO, which can improve the quality of solutions and convergence speed. Finally, the exploitation ability is improved by performing EO operation which has strong local search ability. The proposed algorithm is applied to 23 classical benchmark test functions and 29 CEC2017 test functions. IHHO-EO is compared with HHO, other newly proposed optimization algorithms and some improved variants of HHO. The experimental results verify the effectiveness of the added strategies. In addition, the proposed approach is applied to solving the pressure vessel design problem. The results show that IHHO-EO has an excellent performance in terms of accuracy, reliability and statistical tests.

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References

  1. Abd Elaziz M, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500

    Article  Google Scholar 

  2. Al-Betar MA, Awadallah MA, Heidari AA, Chen H, Al-Khraisat H, Li C (2021) Survival exploration strategies for Harris hawks optimizer. Expert Syst Appl 168:114243

    Article  Google Scholar 

  3. Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23:715–734

    Article  Google Scholar 

  4. Bak P, Sneppen K (1993) Punctuated equilibrium and criticality in a simple model of evolution. Phys Rev Lett 71:4083

    Article  Google Scholar 

  5. Bak P, Tang C, Wiesenfeld K (1988) Self-organized criticality. Phys Rev A 38:364

    Article  MathSciNet  MATH  Google Scholar 

  6. Balamurugan R, Ratheesh S, Venila YM (2021) Classification of heart disease using adaptive harris hawk optimization-based clustering algorithm and enhanced deep genetic algorithm. Soft Comput 1–17

  7. Boettcher S, Percus A (2000) Nature’s way of optimizing. Artif Intell 119:275–286

    Article  MATH  Google Scholar 

  8. Chen H, Heidari AA, Chen H, Wang M, Pan Z, Gandomi AH (2020) Multi-population differential evolution-assisted harris hawks optimization: framework and case studies. Fut Gen Comput Syst 111:175–198

    Article  Google Scholar 

  9. Chen MR, Huang YY, Zeng GQ, Lu KD, Yang LQ (2021) An improved bat algorithm hybridized with extremal optimization and Boltzmann selection. Expert Syst Appl 175:114812

    Article  Google Scholar 

  10. Chen MR, Li X, Zhang X, Lu YZ (2010) A novel particle swarm optimizer hybridized with extremal optimization. Appl Soft Comput 10:367–373

    Article  Google Scholar 

  11. Chen MR, Lu YZ (2008) A novel elitist multiobjective optimization algorithm: multiobjective extremal optimization. Eur J Oper Res 188:637–651

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen MR, Lu YZ, Yang G (2006) Population-based extremal optimization with adaptive lévy mutation for constrained optimization. In: International Conference on Computational and Information Science, Springer, New York, pp 144–155

  13. Dehkordi AA, Sadiq AS, Mirjalili S, Ghafoor KZ (2021) Nonlinear-based chaotic harris hawks optimizer: algorithm and internet of vehicles application. Appl Soft Comput 107574

  14. Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  15. 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 Evol Comput 1:3–18

    Article  Google Scholar 

  16. Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A (2019) A survey on new generation metaheuristic algorithms. Comput Ind Eng 137:106040

    Article  Google Scholar 

  17. Fan Q, Chen Z, Li Z, Xia Z, Lin Y (2020a) An efficient refracted salp swarm algorithm and its application in structural parameter identification. Eng Comput 1–15

  18. Fan Q, Chen Z, Xia Z (2020) A novel quasi-reflected harris hawks optimization algorithm for global optimization problems. Soft Comput 24:14825–14843

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180:2044–2064

    Article  Google Scholar 

  21. Gharehchopogh FS, Abdollahzadeh B (2021) An efficient harris hawk optimization algorithm for solving the travelling salesman problem. Cluster Comput 1–25

  22. Gölcük İ, Ozsoydan FB (2021) Quantum particles-enhanced multiple harris hawks swarms for dynamic optimization problems. Expert Syst Appl 167:114202

    Article  Google Scholar 

  23. Gutin G, Punnen AP (2006) The traveling salesman problem and its variations, vol 12. Springer, New York

    MATH  Google Scholar 

  24. Hakli H, Kiran MS (2020) An improved artificial bee colony algorithm for balancing local and global search behaviors in continuous optimization. Int J Mach Learn Cybern 11:2051–2076

    Article  Google Scholar 

  25. He F, Liu H, Liu C, Bao G (2021) Analysis of radar technology identification model for potential geologic hazard based on convolutional neural network and harris hawks optimization algorithm. Soft Comput pp 1–15

  26. He Q, Wang L (2007) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186:1407–1422

    MathSciNet  MATH  Google Scholar 

  27. He Y, Wang X (2021) Group theory-based optimization algorithm for solving knapsack problems. Knowl-Based Syst 219:104445

    Article  Google Scholar 

  28. He Y, Wang X, Gao S (2019) Ring theory-based evolutionary algorithm and its application to d \(\{\)0-1\(\}\) kp. Appl Soft Comput 77:714–722

    Article  Google Scholar 

  29. He Y, Zhang F, Mirjalili S, Zhang T (2022) Novel binary differential evolution algorithm based on taper-shaped transfer functions for binary optimization problems. Swarm Evol Comput 69:101022

    Article  Google Scholar 

  30. 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 

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

    Article  Google Scholar 

  32. Hussain K, Neggaz N, Zhu W, Houssein EH (2021) An efficient hybrid sine-cosine harris hawks optimization for low and high-dimensional feature selection. Expert Syst Appl 176:114778

    Article  Google Scholar 

  33. Hussien AG, Amin M (2021) A self-adaptive harris hawks optimization algorithm with opposition-based learning and chaotic local search strategy for global optimization and feature selection. Int J Mach Learn Cybern 1–28

  34. Jiang Q, Shao F, Lin W, Gu K, Jiang G, Sun H (2017) Optimizing multistage discriminative dictionaries for blind image quality assessment. IEEE Trans Multimed 20:2035–2048

    Article  Google Scholar 

  35. Kamboj VK, Nandi A, Bhadoria A, Sehgal S (2020) An intensify harris hawks optimizer for numerical and engineering optimization problems. Appl Soft Comput 89:106018

    Article  Google Scholar 

  36. Kannan BK, Kramer SN (1994) An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116:405–411

    Article  Google Scholar 

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

  38. Li C, Li J, Chen H, Jin M, Ren H (2021) Enhanced harris hawks optimization with multi-strategy for global optimization tasks. Expert Syst Appl 185:115499

    Article  Google Scholar 

  39. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the cec 2014 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore 635:490

  40. Long W, Wu T, Cai S, Liang X, Jiao J, Xu M (2019) A novel grey wolf optimizer algorithm with refraction learning. IEEE Access 7:57805–57819

    Article  Google Scholar 

  41. Luo J, Chen MR (2014) Improved shuffled frog leaping algorithm and its multi-phase model for multi-depot vehicle routing problem. Expert Syst Appl 41:2535–2545

    Article  Google Scholar 

  42. McCarthy J (1989) Block-conjugate-gradient method. Phys Rev D 40:2149

    Article  Google Scholar 

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

    Article  Google Scholar 

  44. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073

    Article  Google Scholar 

  45. Mirjalili S (2016) Sca: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

  46. 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 

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

    Article  Google Scholar 

  48. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  49. Nocedal J, Wright S (2006) Numerical optimization. Springer, New York

    MATH  Google Scholar 

  50. Qu C, He W, Peng X, Peng X (2020) Harris hawks optimization with information exchange. Appl Math Model 84:52–75

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  53. Rodríguez-Esparza E, Zanella-Calzada LA, Oliva D, Heidari AA, Zaldivar D, Pérez-Cisneros M, Foong LK (2020) An efficient harris hawks-inspired image segmentation method. Expert Syst Appl 155:113428

    Article  Google Scholar 

  54. 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 13:2592–2612

    Article  Google Scholar 

  55. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  58. Tanyildizi E, Demir G (2017) Golden sine algorithm: a novel math-inspired algorithm. Adv Electr Comput Eng 17:71–78

    Article  Google Scholar 

  59. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06), IEEE, pp 695–701

  60. Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. In: Simulated annealing: theory and applications. Springer, pp 7–15

  61. Wang G, Jin J (2019) Moth-flame optimization algorithm fused on refraction principle and opposite-based learning. Comput Eng Appl 55:46–51

    Google Scholar 

  62. Wang R, Zhang Z, Ng WW, Wu W (2021) An improved group theory-based optimization algorithm for discounted 0–1 knapsack problem. Adv Comput Intell 1:1–11

    Article  Google Scholar 

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

    Article  Google Scholar 

  64. Wu G (2016) Across neighborhood search for numerical optimization. Inf Sci 329:597–618

    Article  MATH  Google Scholar 

  65. Xiao C, Yu M, Wang H, Zhang B, Wang D (2021) Prognosis of electric scooter with intermittent faults: dual degradation processes approach. IEEE Trans Veh Technol 71:1411–1425

    Article  Google Scholar 

  66. Yang XS (2010a) Firefly algorithm, levy flights and global optimization. In: Research and development in intelligent systems XXVI, Springer, pp 209–218

  67. Yang XS (2010b) Nature-inspired metaheuristic algorithms. Luniver Press

  68. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102

    Article  Google Scholar 

  69. Yu M, Xiao C, Zhang B (2020) Event-triggered discrete component prognosis of hybrid systems using degradation model selection. IEEE Trans Industr Electron 68:11470–11481

    Article  Google Scholar 

  70. Yu X, Xu W, Li C (2021) Opposition-based learning grey wolf optimizer for global optimization. Knowl-Based Syst 226:107139

    Article  Google Scholar 

  71. Zeng GQ, Xie XQ, Chen MR, Weng J (2019) Adaptive population extremal optimization-based pid neural network for multivariable nonlinear control systems. Swarm Evol Comput 44:320–334

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61872153 and 61972288).

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H. Zhang: Conceptualization, Methodology, Software, Data curation, Formal analysis, Writing-original draft M. Chen and P. Li: Conceptualization, Methodology, Formal analysis, Investigation, Writing-review & editing, Supervision J. Jun-Jie:Conceptualization, Methodology, Formal analysis

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Correspondence to Min-Rong Chen or Pei-Shan Li.

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Zhang, HL., Chen, MR., Li, PS. et al. An improved Harris Hawks optimizer combined with extremal optimization. Int. J. Mach. Learn. & Cyber. 14, 655–682 (2023). https://doi.org/10.1007/s13042-022-01656-x

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