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A Global Best-guided Firefly Algorithm for Engineering Problems

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Abstract

The Firefly Algorithm (FA) is a highly efficient population-based optimization technique developed by mimicking the flashing behavior of fireflies when mating. This article proposes a method based on Differential Evolution (DE)/current-to-best/1 for enhancing the FA's movement process. The proposed modification increases the global search ability and the convergence rates while maintaining a balance between exploration and exploitation by deploying the global best solution. However, employing the best solution can lead to premature algorithm convergence, but this study handles this issue using a loop adjacent to the algorithm's main loop. Additionally, the suggested algorithm’s sensitivity to the alpha parameter is reduced compared to the original FA. The GbFA surpasses both the original and five-version of enhanced FAs in finding the optimal solution to 30 CEC2014 real parameter benchmark problems with all selected alpha values. Additionally, the CEC 2017 benchmark functions and the eight engineering optimization challenges are also utilized to evaluate GbFA’s efficacy and robustness on real-world problems against several enhanced algorithms. In all cases, GbFA provides the optimal result compared to other methods. Note that the source code of the GbFA algorithm is publicly available at https://www.optim-app.com/projects/gbfa.

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Data Availability Statements

Data are available from the authors upon reasonable request.

References

  1. Ghasemi, M., Mohammadi, S. K., Zare, M., Mirjalili, S., Gil, M., & Hemmati, R. (2022). A new firefly algorithm with improved global exploration and convergence with application to engineering optimization. Decision Analytics Journal, 5, 100125. https://doi.org/10.1016/j.dajour.2022.100125

    Article  Google Scholar 

  2. Shehab, M., Khader, A. T., & Al-Betar, M. A. (2017). A survey on applications and variants of the cuckoo search algorithm. Applied Soft Computing, 61, 1041–1059. https://doi.org/10.1016/j.asoc.2017.02.034

    Article  Google Scholar 

  3. Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1), 156–166. https://doi.org/10.1111/j.1540-5915.1977.tb01074.x

    Article  Google Scholar 

  4. Xin-She, Y., & Deb, S. (2009). Cuckoo search via Levy flights. In: World Congress on Nature & Biologically Inspired Computing, 2009. NaBIC 2009.

  5. Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization. ACM Computing Surveys, 35(3), 268–308. https://doi.org/10.1145/937503.937505

    Article  Google Scholar 

  6. Koza, J. R. (1994). Genetic programming II: automatic discovery of reusable programs. MIT Press.

    MATH  Google Scholar 

  7. Storn, R., & Price, K. (1997). Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.

    MathSciNet  MATH  Google Scholar 

  8. Booker, L. B., Goldberg, D. E., & Holland, J. H. (1989). Classifier systems and genetic algorithms. Artificial Intelligence, 40(1–3), 235–282. https://doi.org/10.1016/0004-3702(89)90050-7

    Article  Google Scholar 

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

    Google Scholar 

  10. Azizipanah-Abarghooee, R., Malekpour, M., Zare, M., & Terzija, V. (2016). A new inertia emulator and fuzzy-based LFC to support inertial and governor responses using Jaya algorithm. In: IEEE Power and Energy Society General Meeting.

  11. Eberhart, R., & Kennedy, J. (1995). Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks. Citeseer, pp 1942–1948.

  12. Yang, X.-S. (2010). Nature-inspired metaheuristic algorithms. Luniver Press.

    Google Scholar 

  13. Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39(3), 459–471.

    MathSciNet  MATH  Google Scholar 

  14. Niknam, T., Zare, M., Aghaei, J., & Farsani, E. A. (2011). A new hybrid evolutionary optimization algorithm for distribution feeder reconfiguration. Applied Artificial Intelligence, 25(10), 951–971. https://doi.org/10.1080/08839514.2011.621288

    Article  Google Scholar 

  15. Kirkpatrick, S., Gelatt, C. D., Jr., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.

    MathSciNet  MATH  Google Scholar 

  16. Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2009). GSA: A gravitational search algorithm. Information Sciences, 179(13), 2232–2248.

    MATH  Google Scholar 

  17. Ghasemi, M., Zare, M., Zahedi, A., Hemmati, R., Abualigah, L., & Forestiero, A. (2023). A comparative study of the Coulomb’s and Franklin’s laws inspired algorithm (CFA) with modern evolutionary algorithms for numerical optimization. In Pervasive knowledge and collective intelligence on web and social media: first EAI international conference, PerSOM 2022, Messina, Italy, November 17-18, 2022, Proceedings (pp. 111-124). Cham: Springer Nature Switzerland.

  18. Li, P., Yang, M., & Wu, Q. (2020). Confidence interval based distributionally robust real-time economic dispatch approach considering wind power accommodation risk. IEEE Transactions on Sustainable Energy, 12(1), 58–69.

    Google Scholar 

  19. Si, Z., Yang, M., Yu, Y., & Ding, T. (2021). Photovoltaic power forecast based on satellite images considering effects of solar position. Applied Energy, 302, 117514.

    Google Scholar 

  20. Wang, W., Feng, Z., & Ma, M. (2022). Climate changes and hydrological processes. Water (Basel), 14, 3922.

    Google Scholar 

  21. Wang, W., Zhao, Y., Tu, Y., Dong, R., Ma, Q., & Liu, C. (2023). Research on parameter regionalization of distributed hydrological model based on machine learning. Water, 15(3), 518.

    Google Scholar 

  22. Chang, Y., Niu, B., Wang, H., Zhang, L., Ahmad, A. M., & Alassafi, M. O. (2022). Adaptive tracking control for nonlinear system in pure-feedback form with prescribed performance and unknown hysteresis. IMA Journal of Mathematical Control and Information, 39(3), 892–911.

    MathSciNet  MATH  Google Scholar 

  23. Li, Y., Niu, B., Zong, G., Zhao, J., & Zhao, X. (2022). Command filter-based adaptive neural finite-time control for stochastic nonlinear systems with time-varying full-state constraints and asymmetric input saturation. International Journal of Systems Science, 53(1), 199–221.

    MathSciNet  MATH  Google Scholar 

  24. Liu, Z., Zheng, Z., Sudhoff, S. D., Gu, C., & Li, Y. (2015). Reduction of common-mode voltage in multiphase two-level inverters using SPWM with phase-shifted carriers. IEEE Transactions on Power Electronics, 31(9), 6631–6645.

    Google Scholar 

  25. Cheng, F., Niu, B., Zhang, L., & Chen, Z. (2022). Prescribed performance-based low-computation adaptive tracking control for uncertain nonlinear systems with periodic disturbances. IEEE Transactions on Circuits and Systems II: Express Briefs, 69(11), 4414–4418.

    Google Scholar 

  26. Zhang, H., Zhao, X., Zong, G., & Xu, N. (2022). Fully distributed consensus of switched heterogeneous nonlinear multi-agent systems with bouc-wen hysteresis input. IEEE Transactions on Network Science and Engineering, 9(6), 4198–4208.

    MathSciNet  Google Scholar 

  27. Zhang, H., Zou, Q., Ju, Y., Song, C., & Chen, D. (2022). Distance-based support vector machine to predict DNA N6-methyladenine modification. Current Bioinformatics, 17(5), 473–482.

    Google Scholar 

  28. Cao, C., Wang, J., Kwok, D., Cui, F., Zhang, Z., Zhao, D., Li, M. J., & Zou, Q. (2022). webTWAS: A resource for disease candidate susceptibility genes identified by transcriptome-wide association study. Nucleic Acids Research, 50(D1), D1123–D1130.

    Google Scholar 

  29. Wang, W., Tian, W., Chau, K., Xue, Y., Xu, L., & Zang, H. (2022). An improved bald eagle search algorithm with Cauchy mutation and adaptive weight factor for engineering optimization. Cmes-Computer Modeling In Engineering & Sciences.

  30. Wang, W., Tian, W., Chau, K., Zang, H., Ma, M., Feng, Z., & Xu, D. (2023). Multi-reservoir flood control operation using improved bald eagle search algorithm with ε constraint method. Water, 15(4), 692.

    Google Scholar 

  31. Wang, W., Xu, L., Chau, K., Zhao, Y., & Xu, D. (2021). An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization. Engineering with Computers, 38, 1–35.

    Google Scholar 

  32. Wang, W., Xu, L., Chau, K., Liu, C., Ma, Q., & Xu, D. (2023). Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems. Expert Systems with Applications, 211, 118644.

    Google Scholar 

  33. Wang, H., Wang, W., Cui, Z., Zhou, X., Zhao, J., & Li, Y. (2018). A new dynamic firefly algorithm for demand estimation of water resources. Information Sciences, 438, 95–106. https://doi.org/10.1016/j.ins.2018.01.041

    Article  MathSciNet  Google Scholar 

  34. B, S., & K, M. (2019). Firefly algorithm based feature selection for network intrusion detection. Computers & Security, 81, 148–155. https://doi.org/10.1016/j.cose.2018.11.005

    Article  Google Scholar 

  35. Altabeeb, A. M., Mohsen, A. M., & Ghallab, A. (2019). An improved hybrid firefly algorithm for capacitated vehicle routing problem. Applied Soft Computing, 84, 105728. https://doi.org/10.1016/j.asoc.2019.105728

    Article  Google Scholar 

  36. Chen, H., Wang, W., Chau, K., Xu, L., & He, J. (2021). Flood control operation of reservoir group using Yin-Yang Firefly Algorithm. Water Resources Management, 35, 5325–5345.

    Google Scholar 

  37. Sánchez, D., Melin, P., & Castillo, O. (2017). Optimization of modular granular neural networks using a firefly algorithm for human recognition. Engineering Applications of Artificial Intelligence, 64, 172–186. https://doi.org/10.1016/j.engappai.2017.06.007

    Article  Google Scholar 

  38. Bui, D.-K., Nguyen, T. N., Ngo, T. D., & Nguyen-Xuan, H. (2020). An artificial neural network (ANN) expert system enhanced with the electromagnetism-based firefly algorithm (EFA) for predicting the energy consumption in buildings. Energy, 190, 116370. https://doi.org/10.1016/j.energy.2019.116370

    Article  Google Scholar 

  39. Louzazni, M., Khouya, A., Amechnoue, K., Gandelli, A., Mussetta, M., & Crăciunescu, A. (2018). Metaheuristic algorithm for photovoltaic parameters: Comparative study and prediction with a firefly algorithm. Applied Sciences, 8(3), 339. https://doi.org/10.3390/app8030339

    Article  Google Scholar 

  40. He, L., & Huang, S. (2017). Modified firefly algorithm based multilevel thresholding for color image segmentation. Neurocomputing, 240, 152–174. https://doi.org/10.1016/j.neucom.2017.02.040

    Article  Google Scholar 

  41. Ghorbani, M. A., Deo, R. C., Yaseen, Z. M., Kashani, H. M., & Mohammadi, B. (2018). Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: case study in North Iran. Theoretical and Applied Climatology, 133(3–4), 1119–1131. https://doi.org/10.1007/s00704-017-2244-0

    Article  Google Scholar 

  42. Ibrahim, I. A., & Khatib, T. (2017). A novel hybrid model for hourly global solar radiation prediction using random forests technique and firefly algorithm. Energy Conversion and Management, 138, 413–425. https://doi.org/10.1016/j.enconman.2017.02.006

    Article  Google Scholar 

  43. Farahani, S. M., Abshouri, A. A., Nasiri, B., & Meybodi, M. R. (2012). Some hybrid models to improve firefly algorithm performance. International Journal of Artificial Intelligence, 8(12), 97–117.

    Google Scholar 

  44. Peng, H., Zhu, W., Deng, C., & Wu, Z. (2021). Enhancing firefly algorithm with courtship learning. Information Sciences, 543, 18–42. https://doi.org/10.1016/j.ins.2020.05.111

    Article  MathSciNet  MATH  Google Scholar 

  45. Hassan, B. A. (2021). CSCF: A chaotic sine cosine firefly algorithm for practical application problems. Neural Computing and Applications, 33(12), 7011–7030. https://doi.org/10.1007/s00521-020-05474-6

    Article  Google Scholar 

  46. Aydilek, I. B. (2018). A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Applied Soft Computing, 66, 232–249.

    Google Scholar 

  47. Wang, H., Zhou, X., Sun, H., Yu, X., Zhao, J., Zhang, H., & Cui, L. (2017). Firefly algorithm with adaptive control parameters. Soft Computing, 21(17), 5091–5102. https://doi.org/10.1007/s00500-016-2104-3

    Article  Google Scholar 

  48. Baykasoğlu, A., & Ozsoydan, F. B. (2015). Adaptive firefly algorithm with chaos for mechanical design optimization problems. Applied Soft Computing, 36, 152–164.

    Google Scholar 

  49. Yelghi, A., & Köse, C. (2018). A modified firefly algorithm for global minimum optimization. Applied Soft Computing, 62, 29–44. https://doi.org/10.1016/j.asoc.2017.10.032

    Article  Google Scholar 

  50. Wang, W., Xu, L., Chau, K., & Xu, D. (2020). Yin-Yang firefly algorithm based on dimensionally Cauchy mutation. Expert Systems with Applications, 150, 113216. https://doi.org/10.1016/j.eswa.2020.113216

    Article  Google Scholar 

  51. Tighzert, L., Fonlupt, C., & Mendil, B. (2019). Towards compact swarm intelligence: A new compact firefly optimisation technique. International Journal of Computer Applications in Technology, 60(2), 108–123.

    Google Scholar 

  52. Zhou, L., Ma, M., Ding, L., & Tang, W. (2019). Centroid opposition with a two-point full crossover for the partially attracted firefly algorithm. Soft Computing, 23(23), 12241–12254. https://doi.org/10.1007/s00500-019-04221-x

    Article  Google Scholar 

  53. Zhang, J., & Sanderson, A. C. (2009). JADE: Adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13(5), 945–958. https://doi.org/10.1109/TEVC.2009.2014613

    Article  Google Scholar 

  54. Zhu, G., & Kwong, S. (2010). Gbest-guided artificial bee colony algorithm for numerical function optimization. Applied Mathematics and Computation, 217(7), 3166–3173. https://doi.org/10.1016/j.amc.2010.08.049

    Article  MathSciNet  MATH  Google Scholar 

  55. Gao, W., Liu, S., & Huang, L. (2012). A global best artificial bee colony algorithm for global optimization. Journal of Computational and Applied Mathematics, 236(11), 2741–2753. https://doi.org/10.1016/j.cam.2012.01.013

    Article  MathSciNet  MATH  Google Scholar 

  56. Liang, J. J., Qu, B. Y., & Suganthan, P. N. (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.

    Google Scholar 

  57. 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 and Evolutionary Computation, 1(1), 3–18.

    Google Scholar 

  58. Mohamed, A. W., Hadi, A. A., & Jambi, K. M. (2019). Novel mutation strategy for enhancing SHADE and LSHADE algorithms for global numerical optimization. Swarm and Evolutionary Computation, 50, 100455. https://doi.org/10.1016/j.swevo.2018.10.006

    Article  Google Scholar 

  59. Mohamed, A. W., & Suganthan, P. N. (2018). Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation. Soft Computing, 22(10), 3215–3235. https://doi.org/10.1007/s00500-017-2777-2

    Article  Google Scholar 

  60. Tighzert, L., Fonlupt, C., & Mendil, B. (2018). A set of new compact firefly algorithms. Swarm and Evolutionary Computation, 40, 92–115. https://doi.org/10.1016/j.swevo.2017.12.006

    Article  Google Scholar 

  61. Yang, X.-S. (2010). Firefly algorithm, Lévy flights and global optimization. Research and Development in Intelligent Systems XXVI (pp. 209–218). Springer.

    Google Scholar 

  62. Brajević, I., & Stanimirović, P. (2018). An improved chaotic firefly algorithm for global numerical optimization. International Journal of Computational Intelligence Systems, 12(1), 131. https://doi.org/10.2991/ijcis.2018.25905187

    Article  Google Scholar 

  63. Lin, Q., Zhu, M., Li, G., Wang, W., Cui, L., Chen, J., & Lu, J. (2018). A novel artificial bee colony algorithm with local and global information interaction. Applied Soft Computing, 62, 702–735. https://doi.org/10.1016/j.asoc.2017.11.012

    Article  Google Scholar 

  64. Wu, G., Mallipeddi, R., & Suganthan, P. (2016). Problem definitions and evaluation criteria for the CEC 2017 competition and special session on constrained single objective real-parameter optimization.

  65. Wei, B., Xia, X., Yu, F., Zhang, Y., Xu, X., Wu, H., Gui, L., & He, G. (2020). Multiple adaptive strategies based particle swarm optimization algorithm. Swarm and Evolutionary Computation, 57, 100731. https://doi.org/10.1016/j.swevo.2020.100731

    Article  Google Scholar 

  66. Lei, Z., Gao, S., Gupta, S., Cheng, J., & Yang, G. (2020). An aggregative learning gravitational search algorithm with self-adaptive gravitational constants. Expert Systems with Applications, 152, 113396. https://doi.org/10.1016/j.eswa.2020.113396

    Article  Google Scholar 

  67. Li, W., & Wang, G.-G. (2021). Improved elephant herding optimization using opposition-based learning and K-means clustering to solve numerical optimization problems. Journal of Ambient Intelligence and Humanized Computing. https://doi.org/10.1007/s12652-021-03391-7

    Article  Google Scholar 

  68. Alsalibi, B., Abualigah, L., & Khader, A. T. (2021). A novel bat algorithm with dynamic membrane structure for optimization problems. Applied Intelligence, 51(4), 1992–2017. https://doi.org/10.1007/s10489-020-01898-8

    Article  Google Scholar 

  69. Hu, J., Gui, W., Heidari, A. A., Cai, Z., Liang, G., Chen, H., & Pan, Z. (2022). Dispersed foraging slime mould algorithm: Continuous and binary variants for global optimization and wrapper-based feature selection. Knowledge-Based Systems, 237, 107761. https://doi.org/10.1016/j.knosys.2021.107761

    Article  Google Scholar 

  70. Askarzadeh, A. (2016). A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Computers & Structures, 169, 1–12.

    Google Scholar 

  71. He, Q., & Wang, L. (2007). A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Applied mathematics and computation, 186(2), 1407–1422.

    MathSciNet  MATH  Google Scholar 

  72. Ray, T., & Liew, K.-M. (2003). Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Transactions on Evolutionary Computation, 7(4), 386–396.

    Google Scholar 

  73. Gandomi, A. H., Yang, X.-S., & Alavi, A. H. (2013). Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems. Engineering with Computers, 29(1), 17–35.

    Google Scholar 

  74. Huang, F., Wang, L., & He, Q. (2007). An effective co-evolutionary differential evolution for constrained optimization. Applied Mathematics and Computation, 186(1), 340–356. https://doi.org/10.1016/j.amc.2006.07.105

    Article  MathSciNet  MATH  Google Scholar 

  75. Mezura-Montes, E., & Coello, C.A.C. (2005). Useful infeasible solutions in engineering optimization with evolutionary algorithms. In: Mexican international conference on artificial intelligence. Springer, pp 652–662.

  76. Kumar, A., Wu, G., Ali, M. Z., Mallipeddi, R., Suganthan, P. N., & Das, S. (2020). A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm and Evolutionary Computation, 56, 100693. https://doi.org/10.1016/j.swevo.2020.100693

    Article  Google Scholar 

  77. Cantú, V. H., Azzaro-Pantel, C., & Ponsich, A. (2021). Constraint-handling techniques within differential evolution for solving process engineering problems. Applied Soft Computing, 108, 107442. https://doi.org/10.1016/j.asoc.2021.107442

    Article  MATH  Google Scholar 

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

    Google Scholar 

  79. Ngo, T. T., Sadollah, A., & Kim, J. H. (2016). A cooperative particle swarm optimizer with stochastic movements for computationally expensive numerical optimization problems. Journal of Computational Science, 13, 68–82.

    MathSciNet  Google Scholar 

  80. Parsopoulos, K.E., & Vrahatis, M.N. (2005). Unified particle swarm optimization for solving constrained engineering optimization problems. In: International Conference on Natural Computation. Springer, pp 582–591.

  81. Zhao, W., Zhang, Z., & Wang, L. (2020). Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications. Engineering Applications of Artificial Intelligence, 87, 103300. https://doi.org/10.1016/j.engappai.2019.103300

    Article  Google Scholar 

  82. Coello, C. A. C., & Montes, E. M. (2002). Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Advanced Engineering Informatics, 16(3), 193–203.

    Google Scholar 

  83. Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190.

    Google Scholar 

  84. Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61.

    Google Scholar 

  85. Akhtar, S., Tai, K., & Ray, T. (2002). A socio-behavioural simulation model for engineering design optimization. Engineering Optimization, 34(4), 341–354.

    Google Scholar 

  86. Shadravan, S., Naji, H. R., & Bardsiri, V. K. (2019). The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Engineering Applications of Artificial Intelligence, 80, 20–34.

    Google Scholar 

  87. Hedar, A.-R., & Fukushima, M. (2006). Derivative-free filter simulated annealing method for constrained continuous global optimization. Journal of Global Optimization, 35(4), 521–549.

    MathSciNet  MATH  Google Scholar 

  88. Mezura-Montes, E., & Hernández-Ocana, B. (2008). Bacterial foraging for engineering design problems: preliminary results. In: Memorias del 4o Congreso Nacional de Computación Evolutiva (COMCEV’2008).

  89. Zhang, J., Liang, C., Huang, Y., Wu, J., & Yang, S. (2009). An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. Applied Mathematics and Computation, 211(2), 392–416.

    MathSciNet  MATH  Google Scholar 

  90. Kaveh, A., & Dadras, A. (2017). A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software, 110, 69–84.

    Google Scholar 

  91. Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 110, 151–166.

    Google Scholar 

  92. He, S., Prempain, E., & Wu, Q. H. (2004). An improved particle swarm optimizer for mechanical design optimization problems. Engineering Optimization, 36(5), 585–605.

    MathSciNet  Google Scholar 

  93. He, Q., & Wang, L. (2007). An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Applications of Artificial Intelligence, 20(1), 89–99.

    Google Scholar 

  94. Aragón, V. S., Esquivel, S. C., & Coello, C. A. C. (2010). A modified version of a T cell algorithm for constrained optimization problems. International Journal for Numerical Methods in Engineering, 84(3), 351–378.

    MATH  Google Scholar 

  95. Montemurro, M., Vincenti, A., & Vannucci, P. (2013). The automatic dynamic penalisation method (ADP) for handling constraints with genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 256, 70–87.

    MathSciNet  MATH  Google Scholar 

  96. Hashim, F. A., Houssein, E. H., Mabrouk, M. S., Al-Atabany, W., & Mirjalili, S. (2019). Henry gas solubility optimization: A novel physics-based algorithm. Future Generation Computer Systems, 101, 646–667.

    Google Scholar 

  97. Hwang, S.-F., & He, R.-S. (2006). A hybrid real-parameter genetic algorithm for function optimization. Advanced Engineering Informatics, 20(1), 7–21.

    Google Scholar 

  98. Mazhoud, I., Hadj-Hamou, K., Bigeon, J., & Joyeux, P. (2013). Particle swarm optimization for solving engineering problems: A new constraint-handling mechanism. Engineering Applications of Artificial Intelligence, 26(4), 1263–1273.

    Google Scholar 

  99. Gandomi, A. H., Yang, X.-S., Alavi, A. H., & Talatahari, S. (2013). Bat algorithm for constrained optimization tasks. Neural Computing and Applications, 22(6), 1239–1255.

    Google Scholar 

  100. Gupta, S., & Deep, K. (2020). A memory-based Grey Wolf optimizer for global optimization tasks. Applied Soft Computing, 93, 106367. https://doi.org/10.1016/j.asoc.2020.106367

    Article  Google Scholar 

  101. Meng, X.-B., Li, H.-X., & Gao, X.-Z. (2019). An adaptive reinforcement learning-based bat algorithm for structural design problems. International Journal of Bio-Inspired Computation, 14(2), 114–124.

    Google Scholar 

  102. Wang, Y., Cai, Z., Zhou, Y., & Fan, Z. (2009). Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique. Structural and Multidisciplinary Optimization, 37(4), 395–413.

    Google Scholar 

  103. Liu, H., Cai, Z., & Wang, Y. (2010). Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Applied Soft Computing, 10(2), 629–640.

    Google Scholar 

  104. Gupta, D., Dhar, A. R., & Roy, S. S. (2021). A partition cum unification based genetic- firefly algorithm for single objective optimization. Sādhanā, 46(3), 121. https://doi.org/10.1007/s12046-021-01641-0

    Article  Google Scholar 

  105. Liu, Z., & Nishi, T. (2020). Multipopulation ensemble particle swarm optimizer for engineering design problems. Mathematical Problems in Engineering, 2020, 1–30.

    Google Scholar 

  106. Cheng, M.-Y., & Prayogo, D. (2014). Symbiotic organisms search: A new metaheuristic optimization algorithm. Computers & Structures, 139, 98–112.

    Google Scholar 

  107. Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: Theory and application. Advances in Engineering Software, 105, 30–47.

    Google Scholar 

  108. Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89, 228–249.

    Google Scholar 

  109. Song, S., Wang, P., Heidari, A. A., Wang, M., Zhao, X., Chen, H., He, W., & Xu, S. (2021). Dimension decided Harris hawks optimization with Gaussian mutation: Balance analysis and diversity patterns. Knowledge-Based Systems, 215, 106425. https://doi.org/10.1016/j.knosys.2020.106425

    Article  Google Scholar 

  110. Gupta, S., & Deep, K. (2019). A hybrid self-adaptive sine cosine algorithm with opposition based learning. Expert Systems with Applications, 119, 210–230.

    Google Scholar 

  111. Li, S., Chen, H., Wang, M., Heidari, A. A., & Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems, 111, 300–323.

    Google Scholar 

  112. Sadollah, A., Bahreininejad, A., Eskandar, H., & Hamdi, M. (2013). Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems. Applied Soft Computing, 13(5), 2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026

    Article  Google Scholar 

  113. Coello, C. A. C. (2000). Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry, 41(2), 113–127.

    Google Scholar 

  114. Ghafil, H. N., & Jármai, K. (2020). Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Applied Soft Computing, 93, 106392.

    Google Scholar 

  115. Zhao, W., Wang, L., & Zhang, Z. (2019). Supply-demand-based optimization: A novel economics-inspired algorithm for global optimization. IEEE Access, 7, 73182–73206.

    Google Scholar 

  116. Coello Coello, C. A., & Becerra, R. L. (2004). Efficient evolutionary optimization through the use of a cultural algorithm. Engineering Optimization, 36(2), 219–236.

    Google Scholar 

  117. Bernardino, H. S., Barbosa, H. J. C., & Lemonge, A. C. C. (2007). A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: 2007 IEEE Congress on Evolutionary Computation. IEEE, pp 646–653.

  118. dos Santos Coelho, L. (2010). Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Systems with Applications, 37(2), 1676–1683.

    Google Scholar 

  119. Ray, T., & Saini, P. (2001). Engineering design optimization using a swarm with an intelligent information sharing among individuals. Engineering Optimization, 33(6), 735–748.

    Google Scholar 

  120. Zhang, J., Xiao, M., Gao, L., & Pan, Q. (2018). Queuing search algorithm: A novel metaheuristic algorithm for solving engineering optimization problems. Applied Mathematical Modelling, 63, 464–490.

    MathSciNet  MATH  Google Scholar 

  121. Jia, H., Sun, K., Zhang, W., & Leng, X. (2022). An enhanced chimp optimization algorithm for continuous optimization domains. Complex & Intelligent Systems, 8(1), 65–82.

    Google Scholar 

  122. Yildiz, A. R., Abderazek, H., & Mirjalili, S. (2020). A comparative study of recent non-traditional methods for mechanical design optimization. Archives of Computational Methods in Engineering, 27(4), 1031–1048.

    MathSciNet  Google Scholar 

  123. Mezura-Montes, E., Velázquez-Reyes, J., & Coello, C.A.C. (2006). Modified differential evolution for constrained optimization. In: 2006 IEEE International Conference on Evolutionary Computation. pp 25–32.

  124. Abualigah, L., Abd Elaziz, M., Sumari, P., Geem, Z. W., & Gandomi, A. H. (2022). Reptile Search Algorithm (RSA): A nature-inspired meta-heuristic optimizer. Expert Systems with Applications, 191, 116158.

    Google Scholar 

  125. Braik, M. S. (2021). Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems. Expert Systems with Applications, 174, 114685.

    Google Scholar 

  126. Trojovsky, P., & Dehghani, M. (2022). Pelican optimization algorithm: a novel nature-inspired algorithm for engineering applications. Sensors, 22(3), 855.

    Google Scholar 

  127. Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M., & Gandomi, A. H. (2021). The arithmetic optimization algorithm. Computer Methods in Applied Mechanics and Engineering, 376, 113609.

    MathSciNet  MATH  Google Scholar 

  128. Emami, H. (2022). Stock exchange trading optimization algorithm: A human-inspired method for global optimization. The Journal of Supercomputing, 78(2), 2125–2174.

    Google Scholar 

  129. Dhiman, G., & Kumar, V. (2017). Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software, 114, 48–70.

    Google Scholar 

  130. Kamboj, V. K., Nandi, A., Bhadoria, A., & Sehgal, S. (2020). An intensify Harris Hawks optimizer for numerical and engineering optimization problems. Applied Soft Computing, 89, 106018.

    Google Scholar 

  131. Abualigah, L., Yousri, D., Abd Elaziz, M., Ewees, A. A., Al-Qaness, M. A. A., & Gandomi, A. H. (2021). Aquila optimizer: A novel meta-heuristic optimization algorithm. Computers & Industrial Engineering, 157, 107250.

    Google Scholar 

  132. Akay, B., & Karaboga, D. (2012). Artificial bee colony algorithm for large-scale problems and engineering design optimization. Journal of Intelligent Manufacturing, 23(4), 1001–1014.

    Google Scholar 

  133. Sallam, K.M., Elsayed, S.M., Chakrabortty, R.K., & Ryan, M.J. (2020). Multi-operator differential evolution algorithm for solving real-world constrained optimization problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185722.

  134. Gurrola-Ramos, J., Hernandez-Aguirre, A., & Dalmau-Cedeno, O. (2020). COLSHADE for real-world single-objective constrained optimization problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185583.

  135. Hellwig, M., & Beyer, H.-G. (2020). A modified matrix adaptation evolution strategy with restarts for constrained real-world problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185566.

  136. Wen, X., Wu, G., Fan, M., Wang, R., & Suganthan, P.N. (2020). Voting-mechanism based ensemble constraint handling technique for real-world single-objective constrained optimization. In: 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185632.

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Appendix A

Appendix A

Table 19 shows the best engineering design solutions obtained by GbFA for solving eight engineering problems.

Table 19 The best solutions for problems 1–8

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Zare, M., Ghasemi, M., Zahedi, A. et al. A Global Best-guided Firefly Algorithm for Engineering Problems. J Bionic Eng 20, 2359–2388 (2023). https://doi.org/10.1007/s42235-023-00386-2

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