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Duck swarm algorithm: theory, numerical optimization, and applications

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Abstract

A swarm intelligence-based optimization algorithm, named Duck Swarm Algorithm (DSA), is proposed in this study, which is inspired by the searching for food sources and foraging behaviors of the duck swarm. Two rules are modeled from the finding food and foraging of the duck, which corresponds to the exploration and exploitation phases of the proposed DSA, respectively. The performance of the DSA is verified by using multiple CEC benchmark functions, where its statistical (best, mean, standard deviation, and average running-time) results are compared with seven well-known algorithms like Particle swarm optimization (PSO), Firefly algorithm (FA), Chicken swarm optimization (CSO), Grey wolf optimizer (GWO), Sine cosine algorithm (SCA), and Marine-predators algorithm (MPA), and Archimedes optimization algorithm (AOA). Moreover, the Wilcoxon rank-sum test, Friedman test, and convergence curves of the comparison results are utilized to prove the superiority of the DSA against other algorithms. The results demonstrate that DSA is a high-performance optimization method in terms of convergence speed and exploration–exploitation balance for solving the numerical optimization problems. Also, DSA is applied for the optimal design of six engineering constrained optimization problems and the node optimization deployment task of the Wireless Sensor Network (WSN). Overall, the comparison results revealed that the DSA is a promising and very competitive algorithm for solving different optimization problems.

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References

  1. Zhou, X., Cai, X., Zhang, H., Zhang, Z., Jin, T., Chen, H., Deng, W.: Multi-strategy competitive-cooperative co-evolutionary algorithm and its application. Inf. Sci. 635, 328–344 (2023)

    Article  Google Scholar 

  2. Hu, G., Guo, Y., Wei, G., Abualigah, L.: Genghis Khan shark optimizer: a novel nature-inspired algorithm for engineering optimization. Adv. Eng. Inform. 58, 102210 (2023)

    Article  Google Scholar 

  3. Hu, Y., Huang, T., Yu, Y., An, Y., Cheng, M., Zhou, W., Xian, W.: An energy-aware service placement strategy using hybrid meta-heuristic algorithm in IoT environments. Clust. Comput. 26(5), 2913–2919 (2023)

    Article  Google Scholar 

  4. Alrefai, N., Ibrahim, O.: Optimized feature selection method using particle swarm intelligence with ensemble learning for cancer classification based on microarray datasets. Neural Comput. Appl. 34(16), 13513–13528 (2022)

    Article  Google Scholar 

  5. Holland, J.H.: Genetic algorithms. Sci. Am. 267(1), 66–72 (1992)

    Article  ADS  Google Scholar 

  6. Kirkpatrick, S., Gelatt, J.C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  7. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: the IEEE International Conference on Neural Networks, Perth pp. 1942–1948 (1995)

  8. Sastry K, Goldberg D, Kendall G (2005) Genetic algorithms. Search Methodologies. Springer, Boston, MA.

  9. Xi, M., Sun, J., Xu, W.: An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl. Math. Comput. 205(2), 751–759 (2008)

    Article  Google Scholar 

  10. Zhan, Z.H., Zhang, J., Li, Y., Chung, H.S.H.: Adaptive particle swarm optimization. IEEE Trans. Syst. Man Cybern. B 39(6), 1362–1381 (2009)

    Article  Google Scholar 

  11. Chen, P., Shahandashti, S.M.: Hybrid of genetic algorithm and simulated annealing for multiple project scheduling with multiple resource constraints. Autom. Constr. 18(4), 434–443 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. SIMULATION 76(2), 60–68 (2001)

    Article  Google Scholar 

  14. Dorigo, M., Di Car, G.: Ant colony optimization: a new meta-heuristic. In: IEEE Congress on Evolutionary Computation, IEEE, pp. 1470–1477 (2002)

  15. Yang, X.S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, Bristol (2008)

    Google Scholar 

  16. Yang, X. S, Deb, S.: Cuckoo search via Lévy flights. In: World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210–214, (2009)

  17. Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Koza, J.R.: Genetic Programming, on the Programming of Computers by Means of Natural Selection and Genetics. MIT Press, Cambridge (1992)

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Kuo, R.J., Zulvia, F.E.: The gradient evolution algorithm: a new metaheuristic. Inf. Sci. 316, 246–265 (2015)

    Article  Google Scholar 

  24. Kiran, M.S.: TSA: Tree-seed algorithm for continuous optimization. Expert Syst. Appl. 42(19), 6686–6698 (2015)

    Article  Google Scholar 

  25. Gandomi, A.H., Yang, X.S., Alavi, A.H.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29(1), 17–35 (2013)

    Article  Google Scholar 

  26. Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., Mirjalili, S.M.: Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Hashim, F.A., Houssein, E.H., Mabrouk, M.S., Al-Atabany, W., Mirjalili, S.: Henry gas solubility optimization: a novel physics-based algorithm. Futur. Gener. Comput. Syst. 101, 646–667 (2019)

    Article  Google Scholar 

  34. Hashim, F.A., Hussain, K., Houssein, E.H., Mabrouk, M.S., Al-Atabany, W.: Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl. Intell. 51(3), 1531–1551 (2021)

    Article  Google Scholar 

  35. Faramarzi, A., Heidarinejad, M., Stephens, B., Mirjalili, S.: Equilibrium optimizer: a novel optimization algorithm. Knowl.-Based Syst. 191, 105190 (2020)

    Article  Google Scholar 

  36. Ahmadianfar, I., Bozorg-Haddad, O., Chu, X.: Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf. Sci. 540, 131–159 (2020)

    Article  MathSciNet  Google Scholar 

  37. Atashpaz-Gargari, E., Lucas, C.: Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE Congress on Evolutionary Computation, IEEE, pp. 4661–4667, (2007)

  38. 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(3), 303–315 (2011)

    Article  Google Scholar 

  39. Kumar, M., Kulkarni, A.J., Satapathy, S.C.: Socio evolution & learning optimization algorithm: a socio-inspired optimization methodology. Futur. Gener. Comput. Syst. 81, 252–272 (2018)

    Article  Google Scholar 

  40. Askari, Q., Younas, I., Saeed, M.: Political optimizer: a novel socio-inspired meta-heuristic for global optimization. Knowl.-Based Syst. 195, 105709 (2020)

    Article  Google Scholar 

  41. Abdollahzadeh, B., Soleimanian, G. F, Mirjalili, S.: Artificial gorilla troops optimizer: a new nature‐inspired metaheuristic algorithm for global optimization problems. International Journal of Intelligent Systems pp. 1–72 (2021)

  42. Abdel-Basset, M., El-Shahat, D., Jameel, M., Abouhawwash, M.: Young’s double-slit experiment optimizer: a novel metaheuristic optimization algorithm for global and constraint optimization problems. Comput. Methods Appl. Mech. Eng. 403, 115652 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  43. Gharehchopogh, F.S.: An improved Harris Hawks optimization algorithm with multi-strategy for community detection in social network. J. Bionic Eng. 20(3), 1175–1197 (2023)

    Article  Google Scholar 

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

    Article  Google Scholar 

  45. Meng, X., Liu, Y., Gao, X., Zhang, H.: A new bio-inspired algorithm: chicken swarm optimization: advances in swarm intelligence. ICSI 2014. Lecture Notes in Computer Science: Springer, pp. 86–94, (2014)

  46. Xue, J., Shen, B.: A novel swarm intelligence optimization approach: sparrow search algorithm. Syst. Sci. Control Eng. 8(1), 22–34 (2020)

    Article  Google Scholar 

  47. Bohling, M.: Severe michigan winter could leave some diving ducks stranded on land. Michigan State University Extension. (2014)

  48. Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), IEEE, pp 69–73, (1998)

  49. Zhang, M., Long, D., Qin, T., Yang, J.: A chaotic hybrid butterfly optimization algorithm with particle swarm optimization for high-dimensional optimization problems. Symmetry 12(11), 18 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  51. Wilcoxon, F.: Individual comparisons by ranking methods. Biom. Bull. 1(6), 80–83 (1945)

    Article  Google Scholar 

  52. Meddis, R.: Unified analysis of variance by ranks. Br. J. Math. Stat. Psychol. 33(1), 84–98 (1980)

    Article  MathSciNet  Google Scholar 

  53. Shi, Y.: An optimization algorithm based on brainstorming process. Int. J. Swarm Intell. Res. 2(4), 35–62 (2011)

    Article  Google Scholar 

  54. Cheng, S., Shi, Y., Qin, Q., Zhang, Q., Bai, R.: Population diversity maintenance in brain storm optimization algorithm. J. Artif. Intell. Soft Comput. Res. 4(2), 83–97 (2014)

    Article  Google Scholar 

  55. Hussain, K., Salleh, M.N.M., Cheng, S., Shi, Y.: On the exploration and exploitation in popular swarm-based metaheuristic algorithms. Neural Comput. Appl. 31(11), 7665–7683 (2019)

    Article  Google Scholar 

  56. Ray, T., Saini, P.: Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng. Optim. 3(33), 735–748 (2001)

    Article  Google Scholar 

  57. Arora, J.S.: Introduction to Optimum Design. Elsevier Press, Amsterdam (2017)

    Google Scholar 

  58. Hashim, F.A., Houssein, E.H., Hussain, K., Mabrouk, M.S., Al-Atabany, W.: Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math. Comput. Simul 192, 84–110 (2022)

    Article  MathSciNet  Google Scholar 

  59. Deb, K.: Optimal design of a welded beam via genetic algorithms. AIAA J. 29, 2013–2015 (1991)

    Article  ADS  Google Scholar 

  60. Kumar, A., Wu, G., Ali, M.Z., Mallipeddi, R., Suganthan, P.N., Swagatam, D.: A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol. Comput. 56, 100693 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  62. He, Q., Wang, L.: An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng. Appl. Artif. Intell. 20, 89–99 (2007)

    Article  Google Scholar 

  63. Mezura-Montes, E., Coello, C.A., Vela´zquez-Reyes, J., Mun˜oz-Da´vila, L.: Multiple trial vectors in differential evolution for engineering design. Eng. Optim. 39(5), 567–589 (2007)

    Article  MathSciNet  Google Scholar 

  64. Abdollahzadeh, B., Gharehchopogh, F.S., Mirjalili, S.: African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems. Comput. Ind. Eng. 158, 107408 (2021)

    Article  Google Scholar 

  65. Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M., Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Methods Appl. Mech. Eng. 376, 113609 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  66. Chen, L., Feng, C., Ma, Y.: Improved Harris Hawks optimization for global optimization and engineering design. Clust. Comput. 24, 1–25 (2023)

    Google Scholar 

  67. Zhang, M., Wang, D., Yang, M., Tan, W., Yang, J.: HPSBA: a modified hybrid framework with convergence analysis for solving wireless sensor network coverage optimization problem. Axioms 11(12), 675 (2022)

    Article  Google Scholar 

  68. Dao, T.K., Nguyen, T.D., Nguyen, V.T.: An improved honey badger algorithm for coverage optimization in wireless sensor network. J. Internet Technol. 24(2), 363–377 (2023)

    Article  Google Scholar 

  69. Jin, Z., Jiang, J., Kong, Z., Pan, C., Ruan, X.: A novel coverage optimization scheme based on enhanced marine predator algorithm for urban sensing systems. IEEE Sens. J. Early Access (2023). https://doi.org/10.1109/JSEN.2023.3287582

    Article  Google Scholar 

  70. Xia, F., Yang, M., Zhang, M., Zhang, J.: Joint light-sensitive balanced butterfly optimizer for solving the NLO and NCO problems of WSN for environmental monitoring. Biomimetics 8(5), 393 (2023)

    Article  PubMed  PubMed Central  Google Scholar 

  71. Fortune, S.: Voronoi diagrams and Delaunay triangulations. In Handbook of discrete and computational geometry, pp. 705–721 (2017)

  72. Zhang, J., Piao, M.J., Zhang, D.G., Zhang, T., Dong, W.M.: An approach of multi-objective computing task offloading scheduling based NSGS for IOV in 5G. Clust. Comput. 25(6), 4203–4219 (2022)

    Article  Google Scholar 

  73. Bacanin, N., Antonijevic, M., Bezdan, T., Zivkovic, M., Venkatachalam, K., Malebary, S.: Energy efficient offloading mechanism using particle swarm optimization in 5G enabled edge nodes. Clust. Comput. 26(1), 587–598 (2023)

    Article  Google Scholar 

  74. Gharehchopogh, F.S., Abdollahzadeh, B., Barshandeh, S., Arasteh, B.: A multi-objective mutation-based dynamic Harris Hawks optimization for botnet detection in IoT. Internet Things 24, 100952 (2023)

    Article  Google Scholar 

  75. Shen, Y., Zhang, C., Gharehchopogh, F.S., Mirjalili, S.: An improved whale optimization algorithm based on multi-population evolution for global optimization and engineering design problems. Expert Syst. Appl. 215, 119269 (2023)

    Article  Google Scholar 

  76. Zhang, M., Wen, G., Zhong, J., Chen, D., Wang, C., Huang, X., Zhang, S.: MLP-like model with convolution complex transformation for auxiliary diagnosis through medical images. IEEE J. Biomed. Health Inform. 27(9), 4385–4396 (2023)

    Article  PubMed  Google Scholar 

  77. Özbay, E., Özbay, F.A., Gharehchopogh, F.S.: Peripheral blood smear images classification for acute lymphoblastic leukemia diagnosis with an improved convolutional neural network. J. Bionic Eng. 4, 1–17 (2023)

    Google Scholar 

  78. Jain, R., Sharma, N.: A quantum inspired hybrid SSA–GWO algorithm for SLA based task scheduling to improve QoS parameter in cloud computing. Clust. Comput. 26, 3587–3610 (2023)

    Article  Google Scholar 

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MZ: Conceptualization, Methodology, Writing—original draft, Writing—review and editing. GW: Supervision, Writing—review and editing.

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Correspondence to Mengjian Zhang.

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Zhang, M., Wen, G. Duck swarm algorithm: theory, numerical optimization, and applications. Cluster Comput (2024). https://doi.org/10.1007/s10586-024-04293-x

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