A Condition-based Grey Wolf Optimizer Algorithm for Global Optimization Problems

Document Type : Persian Original Article

Authors

Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran.

Abstract

Many real-world optimization problems are complex and high-dimensional problems. In the problems, the search space grows exponentially as the problem dimension increases. Therefore, exact algorithms are not able to find the best solution in a reasonable time. As a result, approximate algorithms are applied to solve these problems. Among these algorithms, meta-heuristic algorithms have been shown a good performance in solving these problems. The Grey Wolf Optimizer (GWO) algorithm is one of the meta-heuristic algorithms. However, the structure of the algorithm limits its exploration capability and it may fall in local optima. In this case, the diversity of the population gradually decreases and sometimes, the algorithm is not able to escape from the local optima. To enhance the performance of GWO, an improved GWO algorithm called Condition-based Gray Wolf Optimization (Cb-GWO) algorithm is proposed in this study. In Cb-GWO, the exploration phase has been separated from the exploitation one and also some mechanisms have been considered to achieve better positions per iteration. Moreover, the balance between exploration and exploitation has been improved. The performance of proposed algorithm has been compared with several improved GWO algorithms, as well as Particle Swarm Optimization (PSO), Spotted Hyena Optimizer (SHO), Harris Hawk Optimization (HHO), Wild Horse Optimizer (WHO), Aquila Optimizer (AO), African Vultures Optimization Algorithm (AVOA), which are among the newest meta-heuristic algorithms. These algorithms have been evaluated by CEC2018 benchmark optimization functions and the pressure vessel design to find the best results. The experimental results showed the significant improvement of efficiency of the proposed algorithm compared with other competitor algorithms.

Keywords


[1]          Z. Beheshti, S. M. Shamsuddin, S. Hasan, and N. E. Wong, “Improved centripetal accelerated particle swarm optimization,” Int. J. Adv. Soft Comput. its Appl., vol. 8, no. 2, pp. 1–26, 2016.
[2]          R. Salgotra, U. Singh, S. Singh, G. Singh, and N. Mittal, “Self-adaptive salp swarm algorithm for engineering optimization problems,” Appl. Math. Model., vol. 89, pp. 188–207, 2021.
[3]          H. Majani and M. Nasri, “Water Streams Optimization (WSTO): A new Metaheuristic Optimization method in High-Dimensional Problems,” J. Soft Comput. Inf. Technol., vol. 10, no. 1, pp. 36–51, 2021.
[4]          R. Sabbagh Gol and N. Daneshpour, “An Improved View Selection Algorithm in Data Warehouses by Shuffled Frog Leaping Algorithm in 0/1 Knapsack Problem,” J. Soft Comput. Inf. Technol., vol. 9, no. 3, pp. 163–179, 2020.
[5]          Z. Beheshti, “UTF: Upgrade transfer function for binary meta-heuristic algorithms,” Appl. Soft Comput., vol. 106, p. 107346, 2021.
[6]          Z. Beheshti, “BMNABC: Binary Multi-Neighborhood Artificial Bee Colony for High-Dimensional Discrete Optimization Problems,” Cybern. Syst., vol. 49, no. 7–8, pp. 452–474, 2018.
[7]          S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Softw., vol. 69, pp. 46–61, 2014.
[8]          M. Liu, K. Luo, J. Zhang, and S. Chen, “A stock selection algorithm hybridizing grey wolf optimizer and support vector regression,” Expert Syst. Appl., vol. 179, p. 115078, 2021.
[9]          W. Xie, W.-Z. Wu, C. Liu, T. Zhang, and Z. Dong, “Forecasting fuel combustion-related CO2 emissions by a novel continuous fractional nonlinear grey Bernoulli model with grey wolf optimizer,” Environ. Sci. Pollut. Res., vol. 28, no. 28, pp. 38128–38144, 2021.
[10]        D. Hasterok, R. Castro, M. Landrat, K. PikoĊ„, M. Doepfert, and H. Morais, “Polish Energy Transition 2040: Energy Mix Optimization Using Grey Wolf Optimizer,” Energies , vol. 14, no. 2. 2021.
[11]        S. N. Makhadmeh et al., “Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer,” Electronics , vol. 10, no. 4. 2021.
[12]        N. Thakur, Y. K. Awasthi, and A. S. Siddiqui, “Reliability analysis and power quality improvement model using enthalpy based grey wolf optimizer,” Energy Syst., vol. 12, no. 1, pp. 31–59, 2021.
[13]        E. Uzlu, “Estimates of greenhouse gas emission in Turkey with grey wolf optimizer algorithm-optimized artificial neural networks,” Neural Comput. Appl., 2021.
[14]        M. H. Nadimi-Shahraki, S. Taghian, and S. Mirjalili, “An improved grey wolf optimizer for solving engineering problems,” Expert Syst. Appl., vol. 166, p. 113917, 2021.
[15]        K. Luo, “Enhanced grey wolf optimizer with a model for dynamically estimating the location of the prey,” Appl. Soft Comput., vol. 77, pp. 225–235, 2019.
[16]        M. Banaie-Dezfouli, M. H. Nadimi-Shahraki, and Z. Beheshti, “R-GWO: Representative-based grey wolf optimizer for solving engineering problems,” Appl. Soft Comput., vol. 106, p. 107328, 2021.
[17]        Y. Li, X. Lin, and J. Liu, “An Improved Gray Wolf Optimization Algorithm to Solve Engineering Problems,” Sustainability , vol. 13, no. 6. 2021.
[18]        M. Kohli and S. Arora, “Chaotic grey wolf optimization algorithm for constrained optimization problems,” J. Comput. Des. Eng., vol. 5, no. 4, pp. 458–472, 2018.
[19]        W. Long, J. Jiao, X. Liang, and M. Tang, “An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization,” Eng. Appl. Artif. Intell., vol. 68, pp. 63–80, 2018.
[20]        Z. Yue, S. Zhang, and W. Xiao, “A Novel Hybrid Algorithm Based on Grey Wolf Optimizer and Fireworks Algorithm,” Sensors , vol. 20, no. 7. 2020.
[21]        X. Zhang, Q. Lin, W. Mao, S. Liu, Z. Dou, and G. Liu, “Hybrid Particle Swarm and Grey Wolf Optimizer and its application to clustering optimization,” Appl. Soft Comput., vol. 101, p. 107061, 2021.
[22]        W. Long, S. Cai, J. Jiao, M. Xu, and T. Wu, “A new hybrid algorithm based on grey wolf optimizer and cuckoo search for parameter extraction of solar photovoltaic models,” Energy Convers. Manag., vol. 203, p. 112243, 2020.
[23]        N. Mittal, U. Singh, and B. S. Sohi, “Modified Grey Wolf Optimizer for Global Engineering Optimization,” Appl. Comput. Intell. Soft Comput., vol. 2016, p. 7950348, 2016.
[24]        T. Jayabarathi, T. Raghunathan, B. R. Adarsh, and P. N. Suganthan, “Economic dispatch using hybrid grey wolf optimizer,” Energy, vol. 111, pp. 630–641, 2016.
[25]        S. Padhy, S. Panda, and S. Mahapatra, “A modified GWO technique based cascade PI-PD controller for AGC of power systems in presence of Plug in Electric Vehicles,” Eng. Sci. Technol. an Int. J., vol. 20, no. 2, pp. 427–442, 2017.
[26]        N. Singh and S. B. Singh, “A novel hybrid GWO-SCA approach for optimization problems,” Eng. Sci. Technol. an Int. J., vol. 20, no. 6, pp. 1586–1601, 2017.
[27]        W. Long, S. Cai, J. Jiao, and M. Tang, “An efficient and robust grey wolf optimizer algorithm for large-scale numerical optimization,” Soft Comput., vol. 24, no. 2, pp. 997–1026, 2020.
[28]        A. Saxena, B. P. Soni, R. Kumar, and V. Gupta, “Intelligent Grey Wolf Optimizer – Development and application for strategic bidding in uniform price spot energy market,” Appl. Soft Comput., vol. 69, pp. 1–13, 2018.
[29]        A. K. Tripathi, K. Sharma, and M. Bala, “A Novel Clustering Method Using Enhanced Grey Wolf Optimizer and MapReduce,” Big Data Res., vol. 14, pp. 93–100, 2018.
[30]        C. Lu, L. Gao, and J. Yi, “Grey wolf optimizer with cellular topological structure,” Expert Syst. Appl., vol. 107, pp. 89–114, 2018.
[31]        H. Zamani, M. H. Nadimi-Shahraki, and A. H. Gandomi, “CCSA: Conscious Neighborhood-based Crow Search Algorithm for Solving Global Optimization Problems,” Appl. Soft Comput., vol. 85, p. 105583, 2019.
[32]        S. Gupta and K. Deep, “A novel Random Walk Grey Wolf Optimizer,” Swarm Evol. Comput., vol. 44, pp. 101–112, 2019.
[33]        M. H. Qais, H. M. Hasanien, and S. Alghuwainem, “Augmented grey wolf optimizer for grid-connected PMSG-based wind energy conversion systems,” Appl. Soft Comput., vol. 69, pp. 504–515, 2018.
[34]        A. Faramarzi, M. Heidarinejad, S. Mirjalili, and A. H. Gandomi, “Marine Predators Algorithm: A nature-inspired metaheuristic,” Expert Syst. Appl., vol. 152, p. 113377, Aug. 2020.
[35]        N. H. Awad, M. Z. Ali, J. J. Liang, B. Y. Qu, and P. N. Suganthan, “CEC 2017 Special Session on Single Objective Numerical Optimization Single Bound Constrained Real-Parameter Numerical Optimization Topics Outline,” 2017.
[36]        B. K. Kannan and S. N. Kramer, “An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design,” J. Mech. Des., vol. 116, no. 2, pp. 405–411, 1994.
[37]        J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the 1995 IEEE International Conference on Neural Networks, 1995, vol. 4, pp. 1942–1948.
[38]        L. Abualigah, D. Yousri, M. Abd Elaziz, A. A. Ewees, M. A. A. Al-qaness, and A. H. Gandomi, “Aquila Optimizer: A novel meta-heuristic optimization algorithm,” Comput. Ind. Eng., vol. 157, p. 107250, 2021.
[39]        B. Abdollahzadeh, F. S. Gharehchopogh, and S. Mirjalili, “African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems,” Comput. Ind. Eng., vol. 158, p. 107408, 2021.
[40]        A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen, “Harris hawks optimization: Algorithm and applications,” Futur. Gener. Comput. Syst., vol. 97, pp. 849–872, 2019.
[41]        G. Dhiman and V. Kumar, “Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications,” Adv. Eng. Softw., vol. 114, pp. 48–70, 2017.
[42]        I. Naruei and F. Keynia, “Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems,” Eng. Comput., 2021.
[43]        J. Hu et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: Insights, balance, diversity, and feature selection,” Knowledge-Based Syst., vol. 213, p. 106684, 2021.
[44]        N. Gupta, Madan and Jin, Liang and Homma, Static and dynamic neural networks: from fundamentals to advanced theory. John Wiley \& Sons, 2004.