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A Novel Biologically Inspired Approach for Clustering and Multi-Level Image Thresholding: Modified Harris Hawks Optimizer

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Abstract

Biologically inspired computing deals with complex real-world problems using elegantly modeled techniques motivated by the behaviors of creatures in nature. Harris hawks optimizer (HHO), motivated by the cooperative behavior and hunting style of Harris’ hawks, is a nature-inspired optimization paradigm. As an eminent swarm intelligence method, HHO has established strong performance. However, the original HHO may face difficulties when handling practical multimodal and composition problems. To overcome these challenges, this paper investigates an improved HHO, which considers nonlinear decay energy, introduces the grey wolf optimizer (GWO) as a competitive method to modify conventional HHO, and improves the balance between its exploration and exploitation. The proposed approach combines different cognitive hunting behaviors of Harris’ hawks and grey wolf packs. The main idea of the proposed method can be described as follows: First, we generate a set of candidate solutions and then divide them into two halves. The improved HHO is employed to update the solutions in the first half, while the search phase of GWO is introduced to update the solutions in the second half. Second, we choose the best solutions for the union subpopulations and continue to conduct the iteration procedure. Furthermore, the new approach is utilized to solve the clustering problem and determine the optimal threshold values for multi-level image segmentation problems. Experimental results on 11 benchmark functions illustrate the effectiveness of the proposed approach. Extensive results on clustering and multi-level image segmentation demonstrate the efficiency of the proposed algorithm.

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References

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

    Article  Google Scholar 

  2. Storn R, Price K. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim. 1997;11(4):341–59.

    Article  MathSciNet  Google Scholar 

  3. Fogel DB. Artificial intelligence through simulated evolution. In Evolutionary Computation: The Fossil Record, Wiley-IEEE Press, 1998, pp. 227–296.

  4. Yao X, Liu Y, Lin G. Evolutionary programming made faster. IEEE Trans Evol Comput. 1999;3(2):82–102.

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Simon D. Biogeography-based optimization. IEEE Trans Evol Comput. 2008;12(6):702–13.

    Article  Google Scholar 

  7. Erol OK, Eksin I. A new optimization method: big bang-big crunch. Adv Eng Softw. 2006;37(2):106–11.

    Article  Google Scholar 

  8. Formato R. Central force optimization: a new metaheuristic with applications in applied electromagnetics. Progress In Electromagnetics Research. 2007;77:425–91.

    Article  Google Scholar 

  9. Rashedi E, Nezamabadi-Pour H, Saryazdi S. Gsa: a gravitational search algorithm. Inf Sci. 2009;179(13):2232–48.

    Article  Google Scholar 

  10. Kaveh A, Talatahari S. A novel heuristic optimization method: charged system search. Acta Mech. 2010;213(3–4):267–89.

    Article  Google Scholar 

  11. Alatas B. Acroa: artificial chemical reaction optimization algorithm for global optimization. Expert Syst Appl. 2011;38(10):13170–80.

    Article  Google Scholar 

  12. Hatamlou A. Black hole: a new heuristic optimization approach for data clustering. Inf Sci. 2013;222:175–84.

    Article  MathSciNet  Google Scholar 

  13. Glover F. Tabu search-part I. ORSA J Comput. 1989;1(3):190–206.

    Article  Google Scholar 

  14. Kumar M, Kulkarni AJ, Satapathy SC. Socio evolution & learning optimization algorithm: a socio-inspired optimization methodology. Futur Gener Comput Syst. 2018;81:252–72.

    Article  Google Scholar 

  15. Rao RV, Savsani VJ, Vakharia D. Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci. 2012;183(1):1–15.

    Article  MathSciNet  Google Scholar 

  16. Eberhart R, Kennedy J. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks. 1995;pp.1942–1948.

  17. Basturk B. An artificial bee colony (abc) algorithm for numeric function optimization. In: IEEE Swarm Intelligence Symposium, Indianapolis, IN, USA, 2006 (2006)

  18. Dorigo M, Di Caro G. Ant colony optimization: a new meta-heuristic. In: Proceedings of The 1999 Congress on Evolutionary Computation. 1999;pp.1470–1477.

  19. Jain M, Singh V, Rani A. A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput. 2019;44:148–75.

    Article  Google Scholar 

  20. Chen H, Zhang Q, Luo J, Xu Y, Zhang X. An enhanced bacterial foraging optimization and its application for training kernel extreme learning machine. Appl Soft Comput. 2020;86:105884.

  21. Tan Y, Zhu, Y. Fireworks algorithm for optimization. In: International Conference in Swarm Intelligence. 2010;pp.355–364.

  22. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H. Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst. 2019;97:849–72.

    Article  Google Scholar 

  23. Abdel-Basset M, Ding W, El-Shahat D. A hybrid Harris Hawks optimization algorithm with simulated annealing for feature selection. Artif Intell Rev. 2021;54:593–637.

    Article  Google Scholar 

  24. Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Adv Eng Softw. 2014;69:46–61.

    Article  Google Scholar 

  25. Jia HM, Lang CB, Oliva D, Song SL, Peng Z. Dynamic harris hawks optimization with mutation mechanism for satellite image segmentation. Remote Sensing. 2019;11(12):1421.

    Article  Google Scholar 

  26. Abd Elaziz M, Heidari AA, Fujita H, Moayedi H. A competitive chain-based harris hawks optimizer for global optimization and multi-level image thresholding problems. Appl Soft Comput. 2020;95:106347.

  27. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM. Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw. 2017;114:163–91.

    Article  Google Scholar 

  28. Kurtulus E, Yz AR, Sait SM, Bureerat S. HA novel hybrid Harris hawks-simulated annealing algorithm and RBF-based meta model for design optimization of highway guardrails. Materials Testing. 2020;62(3):251–60.

    Article  Google Scholar 

  29. Yu Z, Shi X, Zhou J, Chen X, Qiu X. Effective Assessment of blast-induced ground vibration using an optimized random forest model based on a Harris hawks optimization algorithm. Appl Sci. 2020;10(4):1403.

    Article  Google Scholar 

  30. Faris H, Aljarah I, Al-Betar MA, Mirjalili S. Grey wolf optimizer: a review of recent variants and applications. Neural Comput Appl. 2018;30(2):413–35.

    Article  Google Scholar 

  31. Gupta S, Deep K. A memory-based grey wolf optimizer for global optimization tasks. Appl Soft Comput. 2020;93:106367.

  32. Dhawale D, Kamboj VK. hHHO IGWO: a new Hybrid Harris Hawks optimizer for solving global optimization problems. In: Proceedings of the International Conference on Computation, Automation and Knowledge Management (ICCAKM). 2020:pp 52–57.

  33. Ridha HM, Heidari AA, Wang M, Chen H. Boosted mutation-based Harris hawks optimizer for parameters identification of single-diode solar cell models. Energy Convers Manage. 2020;209:112660.

  34. Yang XS. Nature-inspired metaheuristic algorithms. Luniver Press; 2008.

  35. Gregory TR. Understanding natural selection: Essential concepts and common misconceptions. Evolution: Education and Outreach. 2009;2(2):156–175.

  36. Alabool HM, Alarabiat D, Abualigah L, Heidari AA. Harris hawks optimization: a comprehensive review of recent variants and applications. Neural Comput Appl. 2020;33:8939–80.

    Article  Google Scholar 

  37. Mirjalili S. Sca: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst. 2016;96:120–33.

    Article  Google Scholar 

  38. Xue JK, Shen B. A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Cont Eng. 2020;8(1):22–34.

    Article  Google Scholar 

  39. Abualigah L, Yousri D, Elaziz MA, Ewees AA, Al-qaness MAA, Gandomi AH. Aquila optimizer: a novel meta-heuristic optimization algorithm. Computers & Industrial Engineering. 2021;157:107250.

  40. Digalakis JG, Margaritis KG. On benchmarking functions for genetic algorithms. Int J Comput Math. 2001;77(4):481–506.

    Article  MathSciNet  Google Scholar 

  41. Mirjalili S, Lewis A. S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput. 2013;9:1–14.

    Article  Google Scholar 

  42. Mirjalili S, Mirjalili SM, Yang XS. Binary bat algorithm. Neural Comput Appl. 2014;25(3–4):663–81.

    Article  Google Scholar 

  43. Molga M, Smutnicki C. Test functions for optimization needs. Test Functions for Optimization Needs. 2005;101.

  44. Lu XQ, Dong L, Yuan Y. Subspace clustering constrained sparse NMF for hyperspectral unmixing. IEEE Trans Geosci Remote Sens. 2020;58(5):3007–19.

    Article  Google Scholar 

  45. Mirjalili S. The ant lion optimizer. Adv Eng Softw. 2015;83:80–98.

    Article  Google Scholar 

  46. Mirjalili S. Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst. 2015;89:228–49.

    Article  Google Scholar 

  47. Akay B. A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput. 2013;13(6):3066–91.

    Article  Google Scholar 

  48. Zhang Y, Wu L. Optimal multi-level thresholding based on maximum tsallis entropy via an artificial bee colony approach. Entropy. 2011;13(4):841–59.

    Article  MathSciNet  Google Scholar 

  49. Wu G, Pedrycz W, Suganthan PN, Mallipeddi R. A variable reduction strategy for evolutionary algorithms handling equality constraints. Appl Soft Comput. 2015;37:774–86.

    Article  Google Scholar 

  50. Otsu N. A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern. 1979;9(1):62–6.

    Article  Google Scholar 

  51. Yin PY. Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Appl Math Comput. 2007;184(2):503–13.

    MathSciNet  MATH  Google Scholar 

  52. Wang Z, Bovik A, Sheikh H, Simoncelli E. Image quality assessment: from error measurement to structural similarity. IEEE Trans Image Process. 2004;13:600–13.

    Article  Google Scholar 

  53. Mlakar U, Potočnik B, Brest J. A hybrid differential evolution for optimal multilevel image thresholding. Expert Syst Appl. 2016;65:221–32.

    Article  Google Scholar 

Download references

Funding

The work described in this paper was supported partially by the National Natural Science Foundation of China (11871167,61866040), Special Support Plan for High-Level Talents of Guangdong Province (2019TQ05X571), Foundation of Guangdong Educational Committee (2019KZDZX1023, 2019GWZDXM004, 2019GWZJD003), Project of Guangdong Province Innovative Team (2020WCXTD011), and Guangdong Natural Science Foundation (2019A1515011797).

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Authors and Affiliations

  1. School of Digital Economy, Guangdong University of Finance & Economics, Guangdong, 510320, Guangzhou, China

    Jia Cai

  2. School of Statistics and Mathematics, Guangdong University of Finance & Economics, Guangzhou, Guangdong, 510320, China

    Tianhua Luo

  3. School of Economics and Finance, South China University of Technology, Guangzhou, Guangdong, 510641, China

    Guanglong Xu

  4. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan, 650500, China

    Yi Tang

Authors
  1. Jia Cai
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  2. Tianhua Luo
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  3. Guanglong Xu
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  4. Yi Tang
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Correspondence to Jia Cai.

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Cai, J., Luo, T., Xu, G. et al. A Novel Biologically Inspired Approach for Clustering and Multi-Level Image Thresholding: Modified Harris Hawks Optimizer. Cogn Comput 14, 955–969 (2022). https://doi.org/10.1007/s12559-022-09998-y

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