The Grey Wolf Optimizer (GWO) algorithm is an interesting swarm-based optimization algorithm for global optimization. It was inspired by the hunting strategy and leadership hierarchy of grey wolves. The GWO algorithm has been successfully tailored to solve various continuous and discrete optimization problems. However, the main drawback of GWO is that it may converge to sub-optimal solutions in early stages of its simulation process due to the loss of diversity in its population. This paper introduces a distributed variation of GWO(DGWO) that attempts to enhance the diversity of GWO by organizing its population into small independent groups (islands) based on a well-known distributed model called the island model. DGWO applies the original GWO to each island and then allows selected solutions to be exchanged among the islands based on the random ring topology and the best-worst migration policy. The island model in DGWO provides a better environment for unfit candidate solutions in each island to evolve into better solutions, which increases the likelihood of finding global optimal solutions. Another interesting feature about DGWO is that it can run in parallel devices, which means that its computational complexity can be reduced compared to the computational complexity of existing variations of GWO. DGWO was evaluated and compared to well-known swarm-based optimization algorithms using 30 CEC 2014 functions. In addition, the sensitivity of DGWO to its parameters was evaluated using 15 standard test functions. The comparative study and the sensitivity analysis for DGWO indicate that it provides competitive performance compared to the other tested algorithms. The source code of DGWO is available at: https://www.dropbox.com/s/2d16t46598u03y0/DistributedGreyWolfOptimizer.zip?dl=0.
B. H. Abed-alguni, D. J. Paul, S. K. Chalup and F. A. Henskens, "A Comparison Study of Cooperative Q-learning Algorithms for Independent Learners," Int. J. Artif. Intell., vol. 14, no. 1, pp. 71-93, 2016.
X.-S. Yang, "A New Metaheuristic Bat-inspired Algorithm," Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Springer, pp. 65-74, 2010.
X.-S. Yang and S. Deb, "Cuckoo Search via Lévy Flights," IEEE World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210-214, 2009.
B. H. Abed-alguni and F. Alkhateeb, "Novel Selection Schemes for Cuckoo Search," Arabian Journal for Science and Engineering, vol. 42, no. 8, pp. 3635-3654, 2017.
F. Alkhateeb and B. H. Abed-alguni, "A Hybrid Cuckoo Search and Simulated Annealing Algorithm," Journal of Intelligent Systems, 2017,[Online], Available: https://doi.org/10.1515/jisys-2017-0268.
B. H. Abed-alguni and F. Alkhateeb, "Intelligent Hybrid Cuckoo Search and β-hill Climbing Algorithm," Journal of King Saud University - Computer and Information Sciences, pp. 1-44, 2018,[Online], Available: https://doi.org/10.1016/j.jksuci.2018.05.003.
B. H. Abed-alguni and A. F. Klaib, "Hybrid Whale Optimization and β-hill Climbing Algorithm," International Journal of Computing Science and Mathematics, pp. 1-13, 2018.
S. Mirjalili and A. Lewis, "The Whale Optimization Algorithm," Advances in Engineering Software, vol. 95, pp. 51-67, 2016.
G. Kaur and S. Arora, "Chaotic Whale Optimization Algorithm," Journal of Computational Design and Engineering, vol. 5, no. 3, pp. 275-284 , July 2018.
S. Arora and P. Anand, "Learning Automata Based Butterfly Optimization Algorithm for Engineering Design Problems," International Journal of Computational Materials Science and Engineering, July 2018.
S. Arora and S. Singh, "Butterfly Optimization Algorithm: A Novel Approach for Global Optimization," Soft Computing, pp. 1-20, 2018.
S. Arora and S. Singh, "A Hybrid Optimization Algorithm Based on Butterfly Optimization Algorithm and Differential Evolution," International Journal of Swarm Intelligence, vol. 3, no. 2-3, pp. 152-169, 2017.
S. Arora and S. Singh, "An Improved Butterfly Optimization Algorithm for Global Optimization," Advanced Science, Engineering and Medicine, vol. 8, no. 9, pp. 711-717, 2016.
S. Arora, S. Singh and K. Yetilmezsoy, "A Modified Butterfly Optimization Algorithm for Mechanical Design Optimization Problems," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 1, p. 21, 2018.
S. Arora and P. Anand, "Chaotic Grasshopper Optimization Algorithm for Global Optimization," Neural Computing and Applications, pp. 1-21, 2018.
S. Arora and P. Anand, "Chaos-enhanced Flower Pollination Algorithms for Global Optimization," Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3853-3869, 2017.
B. H. Abed-alguni, "Bat Q-learning Algorithm," Jordanian Journal of Computers and Information Technology (JJCIT), vol. 3, no. 1, pp. 56-77, 2017.
S. J. Mousavirad and H. Ebrahimpour-Komleh, "Multilevel Image Thresholding Using Entropy of Histogram and Recently Developed Population-based Metaheuristic Algorithms," Evolutionary Intelligence, vol. 10, no. 1-2, pp. 45-75, 2017.
S. Pare, A. Bhandari, A. Kumar and G. Singh, "Rényi’s Entropy and Bat Algorithm Based Color Image Multilevel Thresholding," Machine Intelligence and Signal Analysis: Springer, pp. 71-84, 2019.
R.-E. Precup, R.-C. David, A.-I. Szedlak-Stinean, E. M. Petriu and F. Dragan, "An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning," Algorithms, vol. 10, no. 2, p. 68, 2017.
J. Vaščák, "Adaptation of Fuzzy Cognitive Maps by Migration Algorithms," Kybernetes, vol. 41, no. 3/4, pp. 429-443, 2012.
T. Jayabarathi, T. Raghunathan and A. Gandomi, "The Bat Algorithm, Variants and Some Practical Engineering Applications: A Review," Nature-Inspired Algorithms and Applied Optimization: Springer, pp. 313-330, 2018.
S. K. Sarangi, R. Panda, P. K. Das and A. Abraham, "Design of Optimal High Pass and Band Stop FIR Filters Using Adaptive Cuckoo Search Algorithm," Engineering Applications of Artificial Intelligence, vol. 70, pp. 67-80, 2018.
R.-E. Precup, R.-C. David and E. M. Petriu, "Grey Wolf Optimizer Algorithm-based Tuning of Fuzzy Control Systems with Reduced Parametric Sensitivity," IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 527-534, 2017.
N. Jayakumar, S. Subramanian, S. Ganesan and E. Elanchezhian, "Grey Wolf Optimization for Combined Heat and Power Dispatch with Cogeneration Systems," International Journal of Electrical Power & Energy Systems, vol. 74, pp. 252-264, 2016.
M. Nouiri, A. Bekrar, A. Jemai, S. Niar and A. C. Ammari, "An Effective and Distributed Particle Swarm Optimization Algorithm for Flexible Job-Shop Scheduling Problem," Journal of Intelligent Manufacturing, vol. 29, no. 3, pp. 603-615, 2018.
M. K. Marichelvam and M. Geetha, "Cuckoo Search Algorithm for Solving Real Industrial Multi-Objective Scheduling Problems," Encyclopedia of Information Science and Technology, 4th Edition: IGI Global, pp. 4369-4381, 2018.
S. Mirjalili, S. M. Mirjalili and A. Lewis, "Grey Wolf Optimizer," Advances in Engineering Software, vol. 69, pp. 46-61, 2014.
M. A. Tawhid and A. F. Ali, "A Hybrid Grey Wolf Optimizer and Genetic Algorithm for Minimizing Potential Energy Function," Memetic Computing, vol. 9, no. 4, pp. 347-359, 2017.
W. Gai, C. Qu, J. Liu and J. Zhang, "An Improved Grey Wolf Algorithm for Global Optimization," 2018Chinese Control and Decision Conference (CCDC), pp. 2494-2498, 2018.
M. A. Al-Betar and M. A. Awadallah, "Island Bat Algorithm for Optimization," Expert Systems with Applications, vol. 107, pp. 126-145, 2018.
M. A. Al-Betar, M. A. Awadallah, A. T. Khader and Z. A. Abdalkareem, "Island-based Harmony Search for Optimization Problems," Expert Systems with Applications, vol. 42, no. 4, pp. 2026-2035, 2015.
A. L. Corcoran and R. L. Wainwright, "A Parallel Island Model Genetic Algorithm for the Multiprocessor Scheduling Problem," Proceedings of the 1994 ACM Symposium on Applied Computing, pp. 483-487, 1994.
E. Emary and H. M. Zawbaa, "Impact of Chaos Functions on Modern Swarm Optimizers," PLOS One, vol. 11, no. 7, p. e0158738, 2016.
E. Emary, H. M. Zawbaa and A. E. Hassanien, "Binary Grey Wolf Optimization Approaches for Feature Selection," Neurocomputing, vol. 172, pp. 371-381, 2016.
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.
M. Pradhan, P. K. Roy and T. Pal, "Grey Wolf Optimization Applied to Economic Load Dispatch Problems," International Journal of Electrical Power & Energy Systems, vol. 83, pp. 325-334, 2016.
C. Lu, S. Xiao, X. Li and L. Gao, "An Effective Multi-objective Discrete Grey Wolf Optimizer for a Real-world Scheduling Problem in Welding Production," Advances in Engineering Software, vol. 99, pp. 161-176, 2016.
G. Komaki and V. Kayvanfar, "Grey Wolf Optimizer Algorithm for the Two-stage Assembly Flow Shop Scheduling Problem with Release Time," Journal of Computational Science, vol. 8, pp. 109-120, 2015.
M. Ruciński, D. Izzo and F. Biscani, "On the Impact of the Migration Topology on the Island Model," Parallel Computing, vol. 36, no. 10, pp. 555-571, 2010.
M. Tomassini, Spatially Structured Evolutionary Algorithms: Artificial Evolution in Space and Time, Springer, 2006.
M. Tomassini, "Spatially Structured Evolutionary Algorithms: Artificial Evolution in Space and Time (Natural Computing Series), Secaucus," Ed: NJ, USA: Springer-Verlag New York, Inc, 2005.
D. Jitkongchuen, "A Hybrid Differential Evolution with Grey Wolf Optimizer for Continuous Global Optimization," IEEE 7th International Conference on Information Technology and Electrical Engineering (ICITEE), pp. 51-54, 2015.
H. M. Zawbaa, E. Emary, C. Grosan and V. Snasel, "Large-dimensionality Small-instance Set Feature Selection: A Hybrid Bio-inspired Heuristic Approach," Swarm and Evolutionary Computation, vol. 42, pp. 29-42, 2018.
S. Saremi, S. Z. Mirjalili and S. M. Mirjalili, "Evolutionary Population Dynamics and Grey Wolf Optimizer," Neural Computing and Applications, vol. 26, no. 5, pp. 1257-1263, 2015.
L. Rodríguez, O. Castillo and J. Soria, "A Study of Parameters of the Grey Wolf Optimizer Algorithm for Dynamic Adaptation with Fuzzy Logic," Nature-Inspired Design of Hybrid Intelligent Systems: Springer, pp. 371-390, 2017.
H. Joshi and S. Arora, "Enhanced Grey Wolf Optimization Algorithm for Constrained Optimization Problems," International Journal of Swarm Intelligence, vol. 3, no. 2-3, pp. 126-151, 2017.
M. R. S. Malik, E. R. Mohideen and L. Ali, "Weighted Distance Grey Wolf Optimizer for Global Optimization Problems," IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), pp. 1-6, 2015.
E. A. Emary, H. M. A. Zawbaa and C. A. Grosan, "Experienced Grey Wolf Optimizer through Reinforcement Learning and Neural Networks," vol. 29, no. 3, pp. 681-694, 2018.
H. Joshi and S. Arora, "Enhanced Grey Wolf Optimization Algorithm for Global Optimization," Fundamenta Informaticae, vol. 153, no. 3, pp. 235-264, 2017.
M. Kohli and S. Arora, "Chaotic Grey Wolf Optimization Algorithm for Constrained Optimization Problems," Journal of Computational Design and Engineering, vol. 5, no. 4, pp. 458-472,2017.
A. A. Heidari and P. Pahlavani, "An Efficient Modified Grey Wolf Optimizer with Lévy Flight for Optimization Tasks," Applied Soft Computing, vol. 60, pp. 115-134, 2017.
M. A. Al-Betar, I. A. Doush, A. T. Khader and M. A. Awadallah, "Novel Selection Schemes for Harmony Search," Applied Mathematics and Computation, vol. 218, no. 10, pp. 6095-6117, 2012.
S. Gupta and K. Deep, "A Novel Random Walk Grey Wolf Optimizer," Swarm and Evolutionary Computation, 2018.
S. Gupta and K. Deep, "Random Walk Grey Wolf Optimizer for Constrained Engineering Optimization Problems," Computational Intelligence, 2018.
Fr et al., "A Dynamic Island-based Genetic AlgorithmsFramework," Proceedings of the 8th International Conference on Simulated Evolution and Learning, Kanpur, India, 2010.
H. T. T. Thein, "Island Model Based Differential Evolution Algorithm for Neural Network Training," Advances in Computer Science: An International Journal (ACSIJ), vol. 3, no. 1, pp. 67-73, 2014.
Z. A. Mostafa, N. H. Awad and R. M. Duwairi, "Multi-objective Differential Evolution Algorithm with A New Improved Mutation Strategy," International Journal of Artificial IntelligenceTM, vol. 14, no. 2, pp. 23-41, 2016.
J. F. Romero and C. Cotta, "Optimization by Island-structured Decentralized Particle Swarms," Computational Intelligence, Theory and Applications: Springer, pp. 25-33, 2005.
M. Randall and A. Lewis, "A Parallel Implementation of Ant Colony Optimization," Journal of Parallel and Distributed Computing, vol. 62, no. 9, pp. 1421-1432, 2002.
S. Gupta and K. Deep, "Performance of Grey Wolf Optimizer on Large Scale Problems," AIP Conference Proceedings, vol. 1802, no. 1, p. 020005, 2017, AIP Publishing.
R. Tanabe and A. S. Fukunaga, "Improving the Search Performance of SHADE Using Linear Population Size Reduction," IEEE Congress on Evolutionary Computation (CEC), pp. 1658-1665, 2014.
K. S.SreeRanjini and S. Murugan, "Memory-based Hybrid Dragonfly Algorithm for Numerical Optimization Problems," Expert Systems with Applications, vol. 83, pp. 63-78, 2017.
C. Yu, L. Kelley, S. Zheng and Y. Tan, "Fireworks Algorithm with Differential Mutation for Solving the CEC 2014 Competition Problems," IEEE Congress on Evolutionary Computation (CEC), pp. 3238-3245, 2014.
P. N. Suganthan et al., "Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-parameter Optimization," KanGAL Report, vol. 2005005, p. 2005, 2005.
B. H. Abed-alguni, "Action-Selection Method for Reinforcement Learning Based on Cuckoo Search Algorithm," Arabian Journal for Science and Engineering, pp. 1-15, 2017.
J. Liang, B. Qu and P. Suganthan, "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, 2013.
E. Emary, H. M. Zawbaa, C. Grosan and A. E. Hassenian, "Feature Subset Selection Approach by Gray-wolf Optimization," Afro-European Conference for Industrial Advancement, pp. 1-13, Springer, 2015.
B. H. Abed-alguni, S. K. Chalup, F. A. Henskens and D. J. Paul, "A Multi-agent Cooperative Reinforcement Learning Model Using a Hierarchy of Consultants, Tutors and Workers," Vietnam Journal of Computer Science, vol. 2, no. 4, pp. 213-226, 2015.