{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T19:51:26Z","timestamp":1781034686447,"version":"3.54.1"},"reference-count":101,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T00:00:00Z","timestamp":1508198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Advanced global optimization algorithms have been continuously introduced and improved to solve various complex design optimization problems for which the objective and constraint functions can only be evaluated through computation intensive numerical analyses or simulations with a large number of design variables. The often implicit, multimodal, and ill-shaped objective and constraint functions in high-dimensional and \u201cblack-box\u201d forms demand the search to be carried out using low number of function evaluations with high search efficiency and good robustness. This work investigates the performance of six recently introduced, nature-inspired global optimization methods: Artificial Bee Colony (ABC), Firefly Algorithm (FFA), Cuckoo Search (CS), Bat Algorithm (BA), Flower Pollination Algorithm (FPA) and Grey Wolf Optimizer (GWO). These approaches are compared in terms of search efficiency and robustness in solving a set of representative benchmark problems in smooth-unimodal, non-smooth unimodal, smooth multimodal, and non-smooth multimodal function forms. In addition, four classic engineering optimization examples and a real-life complex mechanical system design optimization problem, floating offshore wind turbines design optimization, are used as additional test cases representing computationally-expensive black-box global optimization problems. Results from this comparative study show that the ability of these global optimization methods to obtain a good solution diminishes as the dimension of the problem, or number of design variables increases. Although none of these methods is universally capable, the study finds that GWO and ABC are more efficient on average than the other four in obtaining high quality solutions efficiently and consistently, solving 86% and 80% of the tested benchmark problems, respectively. The research contributes to future improvements of global optimization methods.<\/jats:p>","DOI":"10.3390\/a10040120","type":"journal-article","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T11:14:35Z","timestamp":1508238875000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Comparative Study on Recently-Introduced Nature-Based Global Optimization Methods in Complex Mechanical System Design"],"prefix":"10.3390","volume":"10","author":[{"given":"Abdulbaset","family":"Saad","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7149-8422","authenticated-orcid":false,"given":"Zuomin","family":"Dong","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meysam","family":"Karimi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.amc.2015.11.001","article-title":"A hybrid PSO-GA algorithm for constrained optimization problems","volume":"274","author":"Garg","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1109\/TEVC.2013.2281531","article-title":"Ant Colony Optimization for Mixed-Variable Optimization Problems","volume":"18","author":"Liao","year":"2014","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1007\/s11269-016-1238-5","article-title":"Simulated Annealing in Optimization of Energy Production in a Water Supply Network","volume":"30","author":"Samora","year":"2016","journal-title":"Water Resour. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cie.2012.09.015","article-title":"Multi-objective reliability-redundancy allocation problem using particle swarm optimization","volume":"64","author":"Garg","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2016\/8073523","article-title":"Application of Genetic Algorithms for Driverless Subway Train Energy Optimization","volume":"2016","author":"Brenna","year":"2016","journal-title":"Int. J. Veh. Technol."},{"key":"ref_6","first-page":"1","article-title":"An Improved Ant Colony Algorithm for Solving the Path Planning Problem of the Omnidirectional Mobile Vehicle","volume":"2016","author":"Zhao","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s12647-013-0081-x","article-title":"Reliability, Availability and Maintainability Analysis of Industrial Systems Using PSO and Fuzzy Methodology","volume":"29","author":"Garg","year":"2013","journal-title":"Mapan"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Baeyens, E., Herreros, A., and Per\u00e1n, J. (2016). A Direct Search Algorithm for Global Optimization. Algorithms, 9.","DOI":"10.3390\/a9020040"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.disopt.2016.01.005","article-title":"Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning","volume":"19","author":"Morrison","year":"2016","journal-title":"Discret. Optim."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s40745-015-0040-1","article-title":"A Comprehensive Survey of Clustering Algorithms","volume":"2","author":"Xu","year":"2015","journal-title":"Ann. Data Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1137\/0906002","article-title":"The Tunneling Algorithm for the Global Minimization of Functions","volume":"6","author":"Levy","year":"1985","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1016\/j.protcy.2016.08.203","article-title":"An Artificial Bee Colony Approach for Multi-objective Job Shop Scheduling","volume":"25","author":"Scaria","year":"2016","journal-title":"Procedia Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8034573","DOI":"10.1155\/2017\/8034573","article-title":"Firefly Mating Algorithm for Continuous Optimization Problems","volume":"2017","author":"Ritthipakdee","year":"2017","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1016\/j.cor.2011.09.026","article-title":"Multiobjective cuckoo search for design optimization","volume":"40","author":"Yang","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_15","first-page":"14","article-title":"An approach for solving constrained reliability-redundancy allocation problems using cuckoo search algorithm","volume":"4","author":"Garg","year":"2015","journal-title":"Beni-Suef Univ. J. Basic Appl. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1108\/02644401211235834","article-title":"Bat algorithm: A novel approach for global engineering optimization","volume":"29","author":"Yang","year":"2012","journal-title":"Eng. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1080\/0305215X.2013.832237","article-title":"Flower pollination algorithm: A novel approach for multiobjective optimization","volume":"46","author":"Yang","year":"2014","journal-title":"Eng. Optim."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ab Wahab, M.N., Nefti-Meziani, S., and Atyabi, A. (2015). A comprehensive review of swarm optimization algorithms. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0122827"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1080\/09500340.2017.1337250","article-title":"A hybrid artificial bee colony algorithm and pattern search method for inversion of particle size distribution from spectral extinction data","volume":"64","author":"Wang","year":"2017","journal-title":"J. Mod. Opt."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.cor.2011.06.007","article-title":"A modified artificial bee colony algorithm","volume":"39","author":"Gao","year":"2012","journal-title":"Comput. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3166","DOI":"10.1016\/j.amc.2010.08.049","article-title":"Gbest-guided artificial bee colony algorithm for numerical function optimization","volume":"217","author":"Zhu","year":"2010","journal-title":"Appl. Math. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.asoc.2011.08.040","article-title":"Development and investigation of efficient artificial bee colony algorithm for numerical function optimization","volume":"12","author":"Li","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2888","DOI":"10.1016\/j.asoc.2010.11.025","article-title":"The best-so-far selection in Artificial Bee Colony algorithm","volume":"11","author":"Banharnsakun","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1016\/j.cor.2012.12.006","article-title":"An efficient and robust artificial bee colony algorithm for numerical optimization","volume":"40","author":"Xiang","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.asoc.2015.12.046","article-title":"Artificial bee colony algorithm with memory","volume":"41","author":"Li","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2961","DOI":"10.1016\/j.cor.2013.07.014","article-title":"An efficient two phase approach for solving reliability-redundancy allocation problem using artificial bee colony technique","volume":"40","author":"Garg","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","article-title":"A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm","volume":"39","author":"Karaboga","year":"2007","journal-title":"J. Glob. Optim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.swevo.2013.06.001","article-title":"A comprehensive review of firefly algorithms","volume":"13","author":"Fister","year":"2013","journal-title":"Swarm Evolut. Comput."},{"key":"ref_30","first-page":"36","article-title":"Firefly Algorithm: Recent Advances and Applications","volume":"1","author":"Yang","year":"2013","journal-title":"Int. J. Swarm Intell."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bhushan, B., and Pillai, S.S. (2013, January 22\u201323). Particle Swarm Optimization and Firefly Algorithm: Performance analysis. Proceedings of the 2013 IEEE 3rd International Advance Computing Conference (IACC), Ghaziabad, India.","DOI":"10.1109\/IAdCC.2013.6514320"},{"key":"ref_32","unstructured":"Mashhadi Farahani, S., Nasiri, B., and Meybodi, M. (2011, January 27\u201328). A multiswarm based firefly algorithm in dynamic environments. Proceedings of the Third International Conference on Signal Processing Systems (ICSPS2011), Yantai, China."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.energy.2013.12.043","article-title":"Multi-objective economic emission dispatch solution using hybrid FFA (firefly algorithm) and considering wind power penetration","volume":"67","author":"Younes","year":"2014","journal-title":"Energy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1002\/tal.1043","article-title":"Optimum design of tower structures using Firefly Algorithm","volume":"23","author":"Talatahari","year":"2014","journal-title":"Struct. Des. Tall Spec. Build."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Hassanzadeh, T., Vojodi, H., and Moghadam, A.M.E. (2011, January 26\u201328). An image segmentation approach based on maximum variance Intra-cluster method and Firefly algorithm. Proceedings of the 2011 Seventh International Conference on Natural Computation, Shanghai, China.","DOI":"10.1109\/ICNC.2011.6022379"},{"key":"ref_36","unstructured":"Bouchachia, A. (2011, January 6\u20138). Evolutionary Discrete Firefly Algorithm for Travelling Salesman Problem. Proceedings of the Adaptive and Intelligent Systems, Second International Conference (ICAIS 2011), Klagenfurt, Austria."},{"key":"ref_37","first-page":"48","article-title":"The Firefly Optimization Algorithm: Convergence Analysis and Parameter Selection","volume":"69","author":"Arora","year":"2013","journal-title":"Int. J. Comput. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Bidar, M., and Kanan, H.R. (2013, January 27\u201329). Modified firefly algorithm using fuzzy tuned parameters. Proceedings of the 13th Iranian Conference on Fuzzy Systems (IFSC), Qazvin, Iran.","DOI":"10.1109\/IFSC.2013.6675634"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2325","DOI":"10.1016\/j.compstruc.2011.08.002","article-title":"Mixed variable structural optimization using Firefly Algorithm","volume":"89","author":"Gandomi","year":"2011","journal-title":"Comput. Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"448","DOI":"10.7763\/IJMLC.2011.V1.67","article-title":"A Gaussian Firefly Algorithm","volume":"1","author":"Farahani","year":"2011","journal-title":"Int. J. Mach. Learn. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s00521-013-1367-1","article-title":"Cuckoo search: Recent advances and applications","volume":"24","author":"Yang","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1080\/08839514.2014.904599","article-title":"Cuckoo Search Algorithm for Optimization Problems\u2014A Literature Review and its Applications","volume":"28","author":"Yatim","year":"2014","journal-title":"Appl. Artif. Intell."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.chaos.2011.06.004","article-title":"Modified cuckoo search: A new gradient free optimisation algorithm","volume":"44","author":"Walton","year":"2011","journal-title":"Chaos Solitons Fractals"},{"key":"ref_44","first-page":"1","article-title":"Cuckoo search algorithm for the selection of optimal machining parameters in milling operations","volume":"64","author":"Yildiz","year":"2012","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Vazquez, R.A. (2011, January 5\u20138). Training spiking neural models using cuckoo search algorithm. Proceedings of the 2011 IEEE Congress on Eovlutionary Computation (CEC), New Orleans, LA, USA.","DOI":"10.1109\/CEC.2011.5949684"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1002\/tal.754","article-title":"Optimum design of steel frames using Cuckoo Search algorithm with L\u00e9vy flights","volume":"22","author":"Kaveh","year":"2013","journal-title":"Struct. Des. Tall Spec. Build."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Brazier, F.M.T., Nieuwenhuis, K., Pavlin, G., Warnier, M., and Badica, C. (2011). Optimizing the Semantic Web Service Composition Process Using Cuckoo Search. Intelligent Distributed Computing V. Studies in Computational Intelligence, Springer.","DOI":"10.1007\/978-3-642-24013-3"},{"key":"ref_48","unstructured":"Tein, L.H., and Ramli, R. (2010, January 3\u20134). Recent Advancements of Nurse Scheduling Models and a Potential Path. Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA 2010), Kuala Lumpur, Malaysia."},{"key":"ref_49","first-page":"117","article-title":"A new testing approach using cuckoo search to achieve multi-objective genetic algorithm","volume":"3","author":"Choudhary","year":"2011","journal-title":"J. Comput."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mechmachtheory.2012.10.010","article-title":"Cuckoo Search algorithm: A metaheuristic approach to solving the problem of optimum synthesis of a six-bar double dwell linkage","volume":"61","author":"Djordjevic","year":"2013","journal-title":"Mech. Mach. Theory"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Speed, E.R. (2010, January 21\u201323). Evolving a Mario agent using cuckoo search and softmax heuristics. Proceedings of the 2010 International IEEE Consumer Electronics Society\u2019s Games Innovations Conference (ICE-GIC), Hong Kong, China.","DOI":"10.1109\/ICEGIC.2010.5716893"},{"key":"ref_52","first-page":"65","article-title":"A New Metaheuristic Bat-Inspired Algorithm","volume":"284","author":"Yang","year":"2010","journal-title":"Nat. Inspired Cooper. Strateg. Optim."},{"key":"ref_53","first-page":"71","article-title":"Modified Bat Algorithm","volume":"20","author":"Kucuksille","year":"2014","journal-title":"Elektronika Elektrotechnika"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Afrabandpey, H., Ghaffari, M., Mirzaei, A., and Safayani, M. (2014, January 4\u20136). A Novel Bat Algorithm Based on Chaos for Optimization Tasks. Proceedings of the 2014 Iranian Conference on Intelligent Systems (ICIS), Bam, Iran.","DOI":"10.1109\/IranianCIS.2014.6802527"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Yang, X.-S. (2010). A new metaheuristic bat-inspired algorithm. Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Springer.","DOI":"10.1007\/978-3-642-12538-6_6"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Al-Betar, M., Awadallah, M.A., Faris, H., Yang, X.-S., Khader, A.T., and Al-Omari, O.A. (2017). Bat-inspired Algorithms with Natural Selection mechanisms for Global optimization. Int. J. Neurocomput.","DOI":"10.1016\/j.neucom.2017.07.039"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"453812","DOI":"10.1155\/2013\/453812","article-title":"A Novel Bat Algorithm Based on Differential Operator and L\u00e9vy Flights Trajectory","volume":"2013","author":"Xie","year":"2013","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_58","first-page":"56","article-title":"A chaotic Levy flight bat algorithm for parameter estimation in nonlinear dynamic biological systems","volume":"2","author":"Lin","year":"2012","journal-title":"Comput. Inf. Technol."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"279","DOI":"10.7763\/LNSE.2013.V1.61","article-title":"Improved Bat Algorithm (IBA) on Continuous Optimization Problems","volume":"1","author":"Yilmaz","year":"2013","journal-title":"Lect. Notes Softw. Eng."},{"key":"ref_60","first-page":"696491","article-title":"A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization","volume":"2013","author":"Wang","year":"2013","journal-title":"J. Appl. Math."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"6097484","DOI":"10.1155\/2016\/6097484","article-title":"A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization","volume":"2016","author":"Zhu","year":"2016","journal-title":"Comput. Intell. Neurosc."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.jocs.2013.10.002","article-title":"Chaotic bat algorithm","volume":"5","author":"Gandomi","year":"2013","journal-title":"J. Comput. Sci."},{"key":"ref_63","first-page":"46","article-title":"Modified Bat Algorithm for Nonlinear Optimization","volume":"16","author":"Kielkowicz","year":"2016","journal-title":"Int. J. Comput. Sci. Netw. Secur."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1016\/j.procs.2017.05.020","article-title":"Global Convergence Analysis of the Flower Pollination Algorithm: A Discrete-Time Markov Chain Approach","volume":"108","author":"He","year":"2017","journal-title":"Procedia Comput. Sci."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.eswa.2016.03.047","article-title":"A Modified Flower Pollination Algorithm for Global Optimization","volume":"57","author":"Nabil","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.enconman.2015.05.074","article-title":"Flower Pollination Algorithm based solar PV parameter estimation","volume":"101","author":"Alam","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_67","first-page":"1","article-title":"A New Hybrid Flower Pollination Algorithm for Solving Constrained Global Optimization Problems","volume":"4","author":"Henawy","year":"2014","journal-title":"Int. J. Appl. Oper. Res. Open Access J."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/547485","article-title":"Flower Pollination Algorithm with Dimension by Dimension Improvement","volume":"2014","author":"Wang","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_69","first-page":"97","article-title":"Reduction of real power loss by using Fusion of Flower Pollination Algorithm with Particle Swarm Optimization","volume":"2","author":"Kanagasabai","year":"2014","journal-title":"J. Inst. Ind. Appl. Eng."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"012032","DOI":"10.1088\/1757-899X\/165\/1\/012032","article-title":"Application of Modified Flower Pollination Algorithm on Mechanical Engineering Design Problem","volume":"165","author":"Meng","year":"2017","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Binh, H.T.T., Hanh, N.T., and Dey, N. (2016). Improved Cuckoo Search and Chaotic Flower Pollination Optimization Algorithm for Maximizing Area Coverage in Wireless Sensor Network. Neural Comput. Appl., 1\u201313.","DOI":"10.1007\/s00521-016-2823-5"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/978-3-319-11313-5_40","article-title":"Study of Flower Pollination Algorithm for Continuous Optimization","volume":"Volume 322","author":"Kowalski","year":"2015","journal-title":"Intelligent Systems' 2014"},{"key":"ref_73","first-page":"13","article-title":"A Comparative Study of Flower Pollination Algorithm and Bat Algorithm on Continuous Optimization Problems","volume":"4","author":"Sakib","year":"2014","journal-title":"Int. J. Soft Comput. Eng."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s10489-014-0645-7","article-title":"How effective is the Grey Wolf optimizer in training multi-layer perceptrons","volume":"43","author":"Mirjalili","year":"2015","journal-title":"Appl. Intell."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"3295769","DOI":"10.1155\/2017\/3295769","article-title":"Modified Discrete Grey Wolf Optimizer Algorithm for Multilevel Image Thresholding. Computational Intelligence and Neuroscience","volume":"2017","author":"Li","year":"2017","journal-title":"Comput. Intell. Neurosc."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Precup, R.-E., David, R.-C., Szedlak-Stinean, A.-I., Petriu, E.M., and Dragan, F. (2017). An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning. Algorithms, 10.","DOI":"10.3390\/a10020068"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1007\/s00521-015-1934-8","article-title":"Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer","volume":"27","author":"Kamboj","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Emary, E., Zawbaa, H.M., Grosan, C., and Ali, A. (2014, January 17\u201319). Feature Subset Selection Approach by Gray-Wolf Optimization. Proceedings of the 1st Afro-European Conference for Industrial Advancement, Addis Ababa, Ethiopia.","DOI":"10.1007\/978-3-319-13572-4_1"},{"key":"ref_79","first-page":"511","article-title":"Optimal design of double layer grids considering nonlinear behaviour by sequential grey wolf algorithm","volume":"5","author":"Gholizadeh","year":"2015","journal-title":"Int. J. Optim. Civ. Eng."},{"key":"ref_80","unstructured":"Yusof, Y., and Mustaffa, Z. (2015, January 18\u201320). Time Series Forecasting of Energy Commodity using Grey Wolf Optimizer. Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong, China."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jocs.2015.03.011","article-title":"Grey Wolf Optimizer Algorithm for the Two-stage Assembly Flowshop Scheduling Problem with Release Time","volume":"8","author":"Komaki","year":"2015","journal-title":"J. Comput. Sci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1080\/15325008.2015.1041625","article-title":"Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms","volume":"43","author":"Hasanien","year":"2015","journal-title":"Electric Power Compon. Syst."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.neucom.2015.06.083","article-title":"Binary Grey Wolf Optimization Approaches for Feature Selection","volume":"172","author":"Zawbaa","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Kohli, M., and Arora, S. (2017). Chaotic grey wolf optimization algorithm for constrained optimization problems. J. Comput. Des. Eng.","DOI":"10.1016\/j.jcde.2017.02.005"},{"key":"ref_85","first-page":"7950348","article-title":"Modified Grey Wolf Optimizer for Global Engineering Optimization","volume":"2016","author":"Mittal","year":"2016","journal-title":"Appl. Comput. Intell. Soft Comput."},{"key":"ref_86","first-page":"150","article-title":"A Literature Survey of Benchmark Functions for Global Optimization Problems","volume":"4","author":"Jamil","year":"2013","journal-title":"Int. J. Math. Modell. Numer. Optim."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1007\/s00158-016-1450-1","article-title":"Multi-start Space Reduction (MSSR) surrogate-based global optimization method","volume":"54","author":"Dong","year":"2016","journal-title":"Struct. Multidiscip. Optim"},{"key":"ref_88","unstructured":"Fernando, G.L., Cl\u00e1udio, F.L., and Zbigniew, M. (2007). Parameter Control in Evolutionary Algorithms. Parameter Setting in Evolutionary Algorithms, Springer."},{"key":"ref_89","first-page":"223","article-title":"Bat Algorithm is better than Intermittent Search Strategy","volume":"22","author":"Yang","year":"2014","journal-title":"J. Mult.-Valued Log. Soft Comput."},{"key":"ref_90","first-page":"608","article-title":"Parameter Tuning for the Artificial Bee Colony Algorithm","volume":"5796","author":"Akay","year":"2009","journal-title":"Int. Conf. Comput. Collect. Intell."},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"Mo, Y.-B., Ma, Y.-Z., and Zheng, Q. (2013, January 29\u201330). Optimal Choice of Parameters for Firefly Algorithm. Proceedings of the 2013 Fourth International Conference on Digital Manufacturing & Automation (ICDMA), Qingdao, China.","DOI":"10.1109\/ICDMA.2013.210"},{"key":"ref_92","first-page":"2959370","article-title":"An Improved Cuckoo Search Optimization Algorithm for the Problem of Chaotic Systems Parameter Estimation","volume":"2016","author":"Wang","year":"2016","journal-title":"Computat. Intell. Neurosc."},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Yang, X.-S. (2014). Nature-Inspired Optimization Algorithms, Elsevier.","DOI":"10.1016\/B978-0-12-416743-8.00010-5"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Melin, P., Castillo, O., and Kacprzyk, J. (2017). A Study of Parameters of the Grey Wolf Optimizer Algorithm for Dynamic Adaptation with Fuzzy Logic. Nature-Inspired Design of Hybrid Intelligent Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-47054-2"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/S0045-7825(01)00323-1","article-title":"Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art","volume":"191","author":"Coello","year":"2002","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"777","DOI":"10.3934\/jimo.2014.10.777","article-title":"Solving structural engineering design optimization problems using an Artificial Bee Colony algorithm","volume":"10","author":"Garg","year":"2013","journal-title":"J. Ind. Manag. Optim."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TEVC.2004.836819","article-title":"A Simple Multimembered Evolution Strategy to Solve Constrained Optimization Problems","volume":"9","author":"Coello","year":"2005","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Garg, H. (2015). A Hybrid GA-GSA Algorithm for Optimizing the Performance of an Industrial System by Utilizing Uncertain Data. Handbook of Research on Artificial Intelligence Techniques and Algorithms, IGI Global.","DOI":"10.4018\/978-1-4666-7258-1.ch020"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1016\/j.rser.2011.09.024","article-title":"Wind energy development and its environmental impact: A review","volume":"16","author":"Leung","year":"2012","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Jonkman, J., Butterfield, S., Musial, W., and Scott, G. (2009). Definition of a 5 MW Reference Wind Turbine for Offshore System Development.","DOI":"10.2172\/947422"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s40722-016-0072-4","article-title":"A multi-objective design optimization approach for floating offshore wind turbine support structures","volume":"3","author":"Karimi","year":"2017","journal-title":"J. Ocean Eng. Mar. Energy"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:47:39Z","timestamp":1760208459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,17]]},"references-count":101,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["a10040120"],"URL":"https:\/\/doi.org\/10.3390\/a10040120","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,17]]}}}