{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T10:38:18Z","timestamp":1772015898584,"version":"3.50.1"},"reference-count":111,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union: Next Generation EU through the Program Greece 2.0 National Recovery and Resilience Plan","award":["TAEDK-06195"],"award-info":[{"award-number":["TAEDK-06195"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Global optimization is used in many practical and scientific problems. For this reason, various computational techniques have been developed. Particularly important are the evolutionary techniques, which simulate natural phenomena with the aim of detecting the global minimum in complex problems. A new evolutionary method is the Eel and Grouper Optimization (EGO) algorithm, inspired by the symbiotic relationship and foraging strategy of eels and groupers in marine ecosystems. In the present work, a series of improvements are proposed that aim both at the efficiency of the algorithm to discover the total minimum of multidimensional functions and at the reduction in the required execution time through the effective reduction in the number of functional evaluations. These modifications include the incorporation of a stochastic termination technique as well as an improvement sampling technique. The proposed modifications are tested on multidimensional functions available from the relevant literature and compared with other evolutionary methods.<\/jats:p>","DOI":"10.3390\/computation12100205","type":"journal-article","created":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T12:44:31Z","timestamp":1728909871000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Refining the Eel and Grouper Optimizer with Intelligent Modifications for Global Optimization"],"prefix":"10.3390","volume":"12","author":[{"given":"Glykeria","family":"Kyrou","sequence":"first","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 47150 Kostaki Artas, Greece"}]},{"given":"Vasileios","family":"Charilogis","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 47150 Kostaki Artas, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2343-2733","authenticated-orcid":false,"given":"Ioannis G.","family":"Tsoulos","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 47150 Kostaki Artas, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1023\/A:1008395408187","article-title":"Stochastic global optimization: Problem classes and solution techniques","volume":"14","author":"Ali","year":"1999","journal-title":"J. Glob. Optim."},{"key":"ref_2","unstructured":"Floudas, C.A., and Pardalos, P.M. (2013). State of the Art in Global Optimization: Computational Methods and Applications, Springer."},{"key":"ref_3","unstructured":"Horst, R., and Pardalos, P.M. (2013). Handbook of Global Optimization, Springer Science & Business Media."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Intriligator, M.D. (2002). Mathematical Optimization and Economic Theory, Society for Industrial and Applied Mathematics, SIAM.","DOI":"10.1137\/1.9780898719215"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10013-020-00396-1","article-title":"Marco A. L\u00f3pez, a Pioneer of Continuous Optimization in Spain","volume":"48","author":"Kruger","year":"2020","journal-title":"Vietnam. J. Math."},{"key":"ref_6","first-page":"2002","article-title":"A novel adaptive genetic algorithm for global optimization of mathematical test functions and real-world problems","volume":"19","author":"Mahmoodabadi","year":"2016","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3020","DOI":"10.1002\/aic.15220","article-title":"Data-driven mathematical modeling and global optimization framework for entire petrochemical planning operations","volume":"62","author":"Li","year":"2016","journal-title":"AIChE J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.ast.2017.04.013","article-title":"Global optimization of benchmark aerodynamic cases using physics-based surrogate models","volume":"67","author":"Iuliano","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1029\/91WR02985","article-title":"Effective and efficient global optimization for conceptual rainfall-runoff models","volume":"28","author":"Duan","year":"1992","journal-title":"Water Resour. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.nima.2009.08.027","article-title":"Global optimization of an accelerator lattice using multiobjective genetic algorithms","volume":"609","author":"Yang","year":"2009","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. Accel. Spectrom. Detect. Assoc. Equip."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1002\/qua.24462","article-title":"Global optimization of clusters using electronic structure methods","volume":"113","author":"Heiles","year":"2013","journal-title":"Int. J. Quantum Chem."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2647","DOI":"10.1002\/jcc.23438","article-title":"GalaxyDock2: Protein\u2013ligand docking using beta-complex and global optimization","volume":"34","author":"Shin","year":"2013","journal-title":"J. Comput. Chem."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5482","DOI":"10.1073\/pnas.96.10.5482","article-title":"Protein structure prediction by global optimization of a potential energy function","volume":"96","author":"Liwo","year":"1999","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5251","DOI":"10.1007\/s00521-022-07916-9","article-title":"Fuzzy-based hunger games search algorithm for global optimization and feature selection using medical data","volume":"35","author":"Houssein","year":"2023","journal-title":"Neural Comput. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2635","DOI":"10.1007\/s00202-018-0716-6","article-title":"Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements","volume":"100","author":"Ion","year":"2018","journal-title":"Electr. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cuevas-Vel\u00e1squez, V., Sordo-Ward, A., Garc\u00eda-Palacios, J.H., Bianucci, P., and Garrote, L. (2020). Probabilistic model for real-time flood operation of a dam based on a deterministic optimization model. Water, 12.","DOI":"10.3390\/w12113206"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/JSTSP.2015.2496908","article-title":"A survey of stochastic simulation and optimization methods in signal processing","volume":"10","author":"Pereyra","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_18","first-page":"473","article-title":"Stochastic optimization","volume":"2","author":"Hannah","year":"2015","journal-title":"Int. Encycl. Soc. Behav. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kizielewicz, B., and Sa\u0142abun, W. (2020). A new approach to identifying a multi-criteria decision model based on stochastic optimization techniques. Symmetry, 12.","DOI":"10.3390\/sym12091551"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4937","DOI":"10.1109\/TSP.2021.3092377","article-title":"Solving stochastic compositional optimization is nearly as easy as solving stochastic optimization","volume":"69","author":"Chen","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","first-page":"179","article-title":"Interval methods for global optimization","volume":"75","author":"Wolfe","year":"1996","journal-title":"Appl. Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1137\/S0036142995281528","article-title":"Subdivision direction selection in interval methods for global optimization","volume":"34","author":"Csendes","year":"1997","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sergeyev, Y.D., Kvasov, D.E., and Mukhametzhanov, M.S. (2018). On the efficiency of nature-inspired metaheuristics in expensive global optimization with limited budget. Sci. Rep., 8.","DOI":"10.1038\/s41598-017-18940-4"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1007\/s00500-004-0363-x","article-title":"A fuzzy adaptive differential evolution algorithm","volume":"9","author":"Liu","year":"2005","journal-title":"Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"Volume 4","author":"Kennedy","year":"1995","journal-title":"Proceedings of the ICNN\u201995-International Conference on Neural Networks"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s11721-007-0002-0","article-title":"Particle swarm optimization: An overview","volume":"1","author":"Poli","year":"2007","journal-title":"Swarm Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0020-0190(02)00447-7","article-title":"The particle swarm optimization algorithm: Convergence analysis and parameter selection","volume":"85","author":"Trelea","year":"2003","journal-title":"Inf. Process. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCI.2006.329691","article-title":"Ant colony optimization","volume":"1","author":"Dorigo","year":"2006","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.ejor.2006.06.046","article-title":"Ant colony optimization for continuous domains","volume":"185","author":"Socha","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_31","unstructured":"Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company."},{"key":"ref_32","unstructured":"Michalewicz, Z. (1999). Genetic Algorithms + Data Structures = Evolution Programs, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"9329","DOI":"10.1007\/s10462-023-10403-9","article-title":"Exponential distribution optimizer (EDO): A novel math-inspired algorithm for global optimization and engineering problems","volume":"56","author":"Jameel","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6723","DOI":"10.1109\/TSMC.2020.2963943","article-title":"Enhancing learning efficiency of brain storm optimization via orthogonal learning design","volume":"51","author":"Ma","year":"2020","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhou, Y., and Tan, Y. (2009, January 18\u201321). GPU-based parallel particle swarm optimization. Proceedings of the 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway.","DOI":"10.1109\/CEC.2009.4983119"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Dawson, L., and Stewart, I. (2013, January 20\u201323). Improving Ant Colony Optimization performance on the GPU using CUDA. Proceedings of the 2013 IEEE Congress on Evolutionary Computation, Cancun, Mexico.","DOI":"10.1109\/CEC.2013.6557791"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10898-016-0411-y","article-title":"Parallel global optimization on GPU","volume":"66","author":"Barkalov","year":"2016","journal-title":"J. Glob. Optim."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hassanien, A.E., and Emary, E. (2018). Swarm Intelligence: Principles, Advances, and Applications, CRC Press.","DOI":"10.1201\/9781315222455"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1109\/JAS.2021.1004129","article-title":"A review on representative swarm intelligence algorithms for solving optimization problems: Applications and trends","volume":"8","author":"Tang","year":"2021","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Brezo\u010dnik, L., Fister, I., and Podgorelec, V. (2018). Swarm intelligence algorithms for feature selection: A review. Appl. Sci., 8.","DOI":"10.3390\/app8091521"},{"key":"ref_41","unstructured":"Chu, Y., Mi, H., Liao, H., Ji, Z., and Wu, Q.H. (2008, January 1\u20136). A fast bacterial swarming algorithm for high-dimensional function optimization. Proceedings of the 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), Hong Kong, China."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1007\/s10462-012-9342-2","article-title":"Artificial fish swarm algorithm: A survey of the state-of-the-art, hybridization, combinatorial and indicative applications","volume":"42","author":"Neshat","year":"2014","journal-title":"Artif. Intell. Rev."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1631\/FITEE.1500287","article-title":"Dolphin swarm algorithm","volume":"17","author":"Wu","year":"2016","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The whale optimization algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1483565","DOI":"10.1080\/25742558.2018.1483565","article-title":"A whale optimization algorithm (WOA) approach for clustering","volume":"5","author":"Nasiri","year":"2018","journal-title":"Cogent Math. Stat."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2019.03.004","article-title":"A comprehensive survey: Whale Optimization Algorithm and its applications","volume":"48","author":"Gharehchopogh","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"110130","DOI":"10.1016\/j.asoc.2023.110130","article-title":"A whale optimization algorithm with combined mutation and removing similarity for global optimization and multilevel thresholding image segmentation","volume":"137","author":"Wang","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"103541","DOI":"10.1016\/j.engappai.2020.103541","article-title":"Tunicate Swarm Algorithm: A new bio-inspired based metaheuristic paradigm for global optimization","volume":"90","author":"Kaur","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Wan, Y., Mao, M., Zhou, L., Zhang, Q., Xi, X., and Zheng, C. (2019). A novel nature-inspired maximum power point tracking (MPPT) controller based on SSA-GWO algorithm for partially shaded photovoltaic systems. Electronics, 8.","DOI":"10.3390\/electronics8060680"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","article-title":"Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems","volume":"114","author":"Mirjalili","year":"2017","journal-title":"Adv. Eng. Softw."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/978-981-13-1592-3_41","article-title":"Salp swarm algorithm (SSA) for training feed-forward neural networks","volume":"Volume 1","author":"Bairathi","year":"2019","journal-title":"Proceedings of the Soft Computing for Problem Solving: SocProS"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"11195","DOI":"10.1007\/s00521-019-04629-4","article-title":"Salp swarm algorithm: A comprehensive survey","volume":"32","author":"Abualigah","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_53","first-page":"108","article-title":"A comparative study of artificial bee colony algorithm","volume":"214","author":"Karaboga","year":"2009","journal-title":"Appl. Math. Comput."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s00521-019-04170-4","article-title":"A survey of symbiotic organisms search algorithms and applications","volume":"32","author":"Abdullahi","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"431","DOI":"10.3934\/mbe.2012.9.431","article-title":"A mutualism-parasitism system modeling host and parasite withmutualism at low density","volume":"9","author":"Wang","year":"2012","journal-title":"Math. Biosci. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1086\/690121","article-title":"Mimicry among unequally defended prey should be mutualistic when predators sample optimally","volume":"189","author":"Aubier","year":"2017","journal-title":"Am. Nat."},{"key":"ref_57","unstructured":"Addicott, J.F. (1985). Competition in mutualistic systems. The biology of Mutualism: Ecology and Evolution, Croom Helm."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Bshary, R., Hohner, A., Ait-el-Djoudi, K., and Fricke, H. (2006). Interspecific communicative and coordinated hunting between groupers and giant moray eels in the Red Sea. Plos Biol., 4.","DOI":"10.1371\/journal.pbio.0040431"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Mohammadzadeh, A., and Mirjalili, S. (2024). Eel and Grouper Optimizer: A Nature-Inspired Optimization Algorithm, Springer Science+Business Media, LLC.","DOI":"10.1007\/s10586-024-04545-w"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Gogu, A., Nace, D., Dilo, A., Meratnia, N., and Ortiz, J.H. (2012). Review of optimization problems in wireless sensor networks. Telecommunications Networks\u2014Current Status and Future Trends, BoD.","DOI":"10.5772\/38360"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Goudos, S.K., Boursianis, A.D., Mohamed, A.W., Wan, S., Sarigiannidis, P., Karagiannidis, G.K., and Suganthan, P.N. (2021, January 14\u201316). Large Scale Global Optimization Algorithms for IoT Networks: A Comparative Study. Proceedings of the 2021 17th International Conference on Distributed Computing in Sensor Systems (DCOSS), Pafos, Cyprus.","DOI":"10.1109\/DCOSS52077.2021.00052"},{"key":"ref_62","unstructured":"Arayapan, K., and Warunyuwong, P. (2009). Logistics Optimization: Application of Optimization Modeling in Inbound Logistics. [Master\u2019s Thesis, Malardalen University]."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"5417","DOI":"10.1109\/JIOT.2023.3306353","article-title":"A New QoS Optimization in IoT-Smart Agriculture Using Rapid Adaption Based Nature-Inspired Approach","volume":"11","author":"Singh","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_64","unstructured":"Wang, H., and Ersoy, O.K. (2005). A novel evolutionary global optimization algorithm and its application in bioinformatics. ECE Tech. Rep., 65, Available online: https:\/\/docs.lib.purdue.edu\/cgi\/viewcontent.cgi?article=1065&context=ecetr."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10589-010-9330-x","article-title":"Machine learning for global optimization","volume":"51","author":"Cassioli","year":"2012","journal-title":"Comput. Optim. Appl."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"56066","DOI":"10.1109\/ACCESS.2021.3072336","article-title":"An improved tunicate swarm algorithm for global optimization and image segmentation","volume":"9","author":"Houssein","year":"2021","journal-title":"IEEE Access"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1109\/TMTT.2019.2915298","article-title":"High-dimensional global optimization method for high-frequency electronic design","volume":"67","author":"Torun","year":"2019","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Wang, L., Kan, J., Guo, J., and Wang, C. (2019). 3D path planning for the ground robot with improved ant colony optimization. Sensors, 19.","DOI":"10.3390\/s19040815"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/j.procs.2016.02.095","article-title":"Analysis of k-means and k-medoids algorithm for big data","volume":"78","author":"Arora","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Ahmed, M., Seraj, R., and Islam, S.M.S. (2020). The k-means algorithm: A comprehensive survey and performance evaluation. Electronics, 9.","DOI":"10.3390\/electronics9081295"},{"key":"ref_71","unstructured":"MacQueen, J.B. (July, January 21). Some Methods for classification and Analysis of Multivariate Observations. Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1016\/j.camwa.2003.07.011","article-title":"Quasi-random initial population for genetic algorithms","volume":"47","author":"Maaranen","year":"2004","journal-title":"Comput. Math. Appl."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Paul, P.V., Dhavachelvan, P., and Baskaran, R. (2013, January 20\u201321). A novel population initialization technique for genetic algorithm. Proceedings of the 2013 International Conference on Circuits, Power and Computing Technologies (ICCPCT), Nagercoil, India.","DOI":"10.1109\/ICCPCT.2013.6528933"},{"key":"ref_74","first-page":"4474","article-title":"Unconventional initialization methods for differential evolution","volume":"219","author":"Ali","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.eswa.2016.05.009","article-title":"A population initialization method for evolutionary algorithms based on clustering and Cauchy deviates","volume":"60","author":"Bajer","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Kazimipour, B., Li, X., and Qin, A.K. (2014, January 6\u201311). A review of population initialization techniques for evolutionary algorithms. Proceedings of the 2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, China.","DOI":"10.1109\/CEC.2014.6900618"},{"key":"ref_77","unstructured":"Jain, B.J., Pohlheim, H., and Wegener, J. (2001, January 7\u201311). On termination criteria of evolutionary algorithms. Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, Francisc, CA, USA."},{"key":"ref_78","unstructured":"Zielinski, K., Weitkemper, P., Laur, R., and Kammeyer, K.D. (2006, January 18\u201320). Examination of stopping criteria for differential evolution based on a power allocation problem. Proceedings of the 10th International Conference on Optimization of Electrical and Electronic Equipment, Brasov, Romania."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Ghoreishi, S.N., Clausen, A., and J\u00f8rgensen, B.N. (2017, January 1\u20133). Termination Criteria in Evolutionary Algorithms: A Survey. Proceedings of the IJCCI, Funchal, Portugal.","DOI":"10.5220\/0006577903730384"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"109478","DOI":"10.1016\/j.asoc.2022.109478","article-title":"Maximum number of generations as a stopping criterion considered harmful","volume":"128","author":"Ravber","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Charilogis, V., and Tsoulos, I.G. (2022). Toward an ideal particle swarm optimizer for multidimensional functions. Information, 13.","DOI":"10.3390\/info13050217"},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Kyrou, G., Charilogis, V., and Tsoulos, I.G. (2024). EOFA: An Extended Version of the Optimal Foraging Algorithm for Global Optimization Problems. Computation, 12.","DOI":"10.3390\/computation12080158"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Charilogis, V., Tsoulos, I.G., and Stavrou, V.N. (2023). An Intelligent Technique for Initial Distribution of Genetic Algorithms. Axioms, 12.","DOI":"10.3390\/axioms12100980"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1007\/s42979-023-02227-9","article-title":"An improved parallel particle swarm optimization","volume":"4","author":"Charilogis","year":"2023","journal-title":"SN Comput. Sci."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"225","DOI":"10.3390\/analytics3020013","article-title":"Improving the Giant-Armadillo Optimization Method","volume":"3","author":"Kyrou","year":"2024","journal-title":"Analytics"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1016\/j.phpro.2012.03.206","article-title":"A clustering method based on K-means algorithm","volume":"25","author":"Li","year":"2012","journal-title":"Phys. Procedia"},{"key":"ref_87","first-page":"1577","article-title":"K-means clustering algorithm applications in data mining and pattern recognition","volume":"6","author":"Ali","year":"2017","journal-title":"Int. J. Sci. Res. (IJSR)"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/3477.764879","article-title":"Genetic K-means algorithm","volume":"29","author":"Krishna","year":"1999","journal-title":"IEEE Trans. Syst. Man Cybern. Part B (Cybern.)"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"80716","DOI":"10.1109\/ACCESS.2020.2988796","article-title":"Unsupervised K-means clustering algorithm","volume":"8","author":"Sinaga","year":"2020","journal-title":"IEEE Access"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"118656","DOI":"10.1016\/j.eswa.2022.118656","article-title":"FC-Kmeans: Fixed-centered K-means algorithm","volume":"211","author":"Ay","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_91","first-page":"22","article-title":"Comprehensive review of K-Means clustering algorithms","volume":"12","author":"Oti","year":"2021","journal-title":"Criterion"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s10898-004-9972-2","article-title":"A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems","volume":"31","author":"Ali","year":"2005","journal-title":"J. Glob. Optim."},{"key":"ref_93","unstructured":"Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., G\u00fcm\u00fcs, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., and Schweiger, C.A. (2013). Handbook of Test Problems in Local and Global Optimization, Springer Science & Business Media."},{"key":"ref_94","first-page":"578","article-title":"Improved particle swarm algorithms for global optimization","volume":"196","author":"Ali","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_95","first-page":"129","article-title":"A PSO based approach: Scout particle swarm algorithm for continuous global optimization problems","volume":"6","author":"Koyuncu","year":"2019","journal-title":"J. Comput. Des. Eng."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1145\/264029.264043","article-title":"Enhanced simulated annealing for globally minimizing functions of many-continuous variables","volume":"23","author":"Siarry","year":"1997","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.cpc.2008.01.040","article-title":"GenMin: An enhanced genetic algorithm for global optimization","volume":"178","author":"Tsoulos","year":"2008","journal-title":"Comput. Phys. Commun."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"100973","DOI":"10.1016\/j.swevo.2021.100973","article-title":"A prescription of methodological guidelines for comparing bio-inspired optimization algorithms","volume":"67","author":"LaTorre","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"ref_99","unstructured":"Li, X., Engelbrecht, A., and Epitropakis, M.G. (2013). Benchmark Functions for CEC\u20192013 Special Session and Competition on Niching Methods for Multimodal Function Optimization, Technology Report; RMIT University, Evolutionary Computation and Machine Learning Group."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1145\/962437.962444","article-title":"Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization","volume":"29","author":"Gaviano","year":"2003","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"ref_101","unstructured":"Jones, J.E. (1924). On the Determination of Molecular Fields.\u2014II. From the Equation of State of a Gas, Royal Society."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/BF01589118","article-title":"A Tolerant Algorithm for Linearly Constrained Optimization Calculations","volume":"45","author":"Powell","year":"1989","journal-title":"Math. Program"},{"key":"ref_103","first-page":"598","article-title":"Modifications of real code genetic algorithm for global optimization","volume":"203","author":"Tsoulos","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1016\/j.mcm.2008.06.013","article-title":"A new method to simulate the triangular distribution","volume":"49","author":"Stein","year":"2009","journal-title":"Math. Comput. Model."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"6982","DOI":"10.1080\/03610918.2016.1222422","article-title":"An extended Maxwell distribution: Properties and applications","volume":"46","author":"Sharma","year":"2017","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"3638","DOI":"10.1007\/s10489-020-01707-2","article-title":"Uniform distribution driven adaptive differential evolution","volume":"50","author":"Sengupta","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1504\/IJRAM.2009.030702","article-title":"Practical risk assessment with triangular distributions","volume":"13","author":"Glickman","year":"2009","journal-title":"Int. J. Risk Assess. Manag."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s40745-020-00288-8","article-title":"The Maxwell\u2013Weibull distribution in modeling lifetime datasets","volume":"7","author":"Ishaq","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_109","first-page":"26069","article-title":"Multi-swap k-means++","volume":"36","author":"Beretta","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1016\/0167-8191(96)00024-5","article-title":"A high-performance, portable implementation of the MPI message passing interface standard","volume":"22","author":"Gropp","year":"1996","journal-title":"Parallel Comput."},{"key":"ref_111","unstructured":"Chandra, R. (2001). Parallel Programming in OpenMP, Academic Press."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/10\/205\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:13:13Z","timestamp":1760112793000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/10\/205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,14]]},"references-count":111,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["computation12100205"],"URL":"https:\/\/doi.org\/10.3390\/computation12100205","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,14]]}}}