{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T15:36:53Z","timestamp":1778600213450,"version":"3.51.4"},"reference-count":81,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51875454"],"award-info":[{"award-number":["51875454"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>With the rapid development of the geometric modeling industry and computer technology, the design and shape optimization of complex curve shapes have now become a very important research topic in CAGD. In this paper, the Hybrid Artificial Hummingbird Algorithm (HAHA) is used to optimize complex composite shape-adjustable generalized cubic Ball (CSGC\u2013Ball, for short) curves. Firstly, the Artificial Hummingbird algorithm (AHA), as a newly proposed meta-heuristic algorithm, has the advantages of simple structure and easy implementation and can quickly find the global optimal solution. However, there are still limitations, such as low convergence accuracy and the tendency to fall into local optimization. Therefore, this paper proposes the HAHA based on the original AHA, combined with the elite opposition-based learning strategy, PSO, and Cauchy mutation, to increase the population diversity of the original algorithm, avoid falling into local optimization, and thus improve the accuracy and rate of convergence of the original AHA. Twenty-five benchmark test functions and the CEC 2022 test suite are used to evaluate the overall performance of HAHA, and the experimental results are statistically analyzed using Friedman and Wilkerson rank sum tests. The experimental results show that, compared with other advanced algorithms, HAHA has good competitiveness and practicality. Secondly, in order to better realize the modeling of complex curves in engineering, the CSGC\u2013Ball curves with global and local shape parameters are constructed based on SGC\u2013Ball basis functions. By changing the shape parameters, the whole or local shape of the curves can be adjusted more flexibly. Finally, in order to make the constructed curve have a more ideal shape, the CSGC\u2013Ball curve-shape optimization model is established based on the minimum curve energy value, and the proposed HAHA is used to solve the established shape optimization model. Two representative numerical examples comprehensively verify the effectiveness and superiority of HAHA in solving CSGC\u2013Ball curve-shape optimization problems.<\/jats:p>","DOI":"10.3390\/biomimetics8040377","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T09:13:44Z","timestamp":1692350024000},"page":"377","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["PSO-Incorporated Hybrid Artificial Hummingbird Algorithm with Elite Opposition-Based Learning and Cauchy Mutation: A Case Study of Shape Optimization for CSGC\u2013Ball Curves"],"prefix":"10.3390","volume":"8","author":[{"given":"Kang","family":"Chen","sequence":"first","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liuxin","family":"Chen","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jingkai No. 1 Primary School, Xi\u2019an 710018, China"},{"name":"Department of Applied Mathematics, Xi\u2019an University of Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2274-7482","authenticated-orcid":false,"given":"Gang","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Xi\u2019an University of Technology, Xi\u2019an 710054, China"},{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","unstructured":"Shi, F.Z. (2001). Computer Aided Geometric Design and Nonuniform Rational B-Splines: CAGD & NURBS, Beijing University of Aeronautics and Astronautics Press."},{"key":"ref_2","unstructured":"Wang, G.J., Wang, G.Z., and Zheng, J.M. (2001). Computer Aided Geometric Design, Higher Education Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.matcom.2022.01.018","article-title":"An enhanced chimp optimization algorithm for optimal degree reduction of Said\u2013Ball curves","volume":"197","author":"Hu","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0010-4485(74)90009-8","article-title":"Part one: Introduction of the conic lofting tile","volume":"6","author":"Consurf","year":"1974","journal-title":"Comput.-Aided Des."},{"key":"ref_5","first-page":"126","article-title":"Ball curve of high degree and its geometric properties","volume":"2","author":"Wang","year":"1987","journal-title":"Appl. Math. A J. Chin. Univ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1145\/77269.77275","article-title":"A generalized ball curve and its recursive algorithm","volume":"8","author":"Said","year":"1989","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0010-4485(95)00047-X","article-title":"Properties of two types of generalized Ball curves","volume":"28","author":"Hu","year":"1996","journal-title":"Comput.-Aided Des."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/S0167-8396(96)00047-7","article-title":"The dual basis functions for the generalized ball basis of odd degree","volume":"14","author":"Othlnan","year":"1997","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_9","first-page":"7","article-title":"Dual basis of Ball basis function and its application","volume":"19","author":"Xi","year":"1997","journal-title":"Comput. Math."},{"key":"ref_10","first-page":"123","article-title":"Properties and applications of generalized Ball curves","volume":"23","author":"Ding","year":"2000","journal-title":"Chin. J. Appl. Math."},{"key":"ref_11","first-page":"454","article-title":"Dual basis of Wang-Ball basis function and its application","volume":"16","author":"Jiang","year":"2004","journal-title":"J. Comput. Aided Des. Graph."},{"key":"ref_12","unstructured":"Hu, S.M., and Jin, T.G. (1992, January 10\u201312). Degree reductive approximation of B\u00e9zier curves. Proceedings of the Eighth Annual Symposium on Computational Geometry, Berlin, Germany."},{"key":"ref_13","first-page":"196","article-title":"Two new kinds of generalized Ball curves","volume":"23","author":"Wu","year":"2000","journal-title":"J. Appl. Math."},{"key":"ref_14","first-page":"77","article-title":"Extension of cubic Ball curve","volume":"29","author":"Wang","year":"2008","journal-title":"J. Eng. Graph."},{"key":"ref_15","first-page":"80","article-title":"The extension of the quartic Wang-Ball curve","volume":"30","author":"Wang","year":"2009","journal-title":"J. Eng. Graph."},{"key":"ref_16","first-page":"16","article-title":"Two types of shape-adjustable fifth-order generalized Ball curves","volume":"32","author":"Yan","year":"2011","journal-title":"J. Eng. Graph."},{"key":"ref_17","first-page":"69","article-title":"Construction and application of 2m+2 degree Ball curve with shape parameters","volume":"30","author":"Hu","year":"2009","journal-title":"J. Eng. Graph."},{"key":"ref_18","first-page":"187","article-title":"Generalized Wang-Ball curve","volume":"34","author":"Xiong","year":"2013","journal-title":"Numer. Comput. Comput. Appl."},{"key":"ref_19","first-page":"23","article-title":"Quadratic Ball curve with shape parameters","volume":"41","author":"Liu","year":"2011","journal-title":"J. Shandong Univ."},{"key":"ref_20","first-page":"1436","article-title":"Quartic Wang-Ball curve and surface with two parameters","volume":"35","author":"Huang","year":"2012","journal-title":"J. Hefei Univ. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"104417","DOI":"10.1016\/j.engappai.2021.104417","article-title":"An improved marine predators algorithm for shape optimization of developable Ball surfaces","volume":"105","author":"Hu","year":"2021","journal-title":"Eng. Appl. Artif. Intell"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108071","DOI":"10.1016\/j.knosys.2021.108071","article-title":"An enhanced manta ray foraging optimization algorithm for shape optimization of complex CCG-Ball curves","volume":"240","author":"Hu","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0097-8493(87)90024-0","article-title":"Algorithms for development of certain classes of ruled surfaces","volume":"11","author":"Gurunathan","year":"1987","journal-title":"Comput. Graph"},{"key":"ref_24","first-page":"3918","article-title":"Curvature variation minimizing cubic Hermite interpolants","volume":"218","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_25","first-page":"596","article-title":"A note on curvature variation minimizing cubic Hermite interpolants","volume":"259","author":"Lu","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s40314-022-01813-6","article-title":"Quintic generalized Hermite interpolation curves: Construction and shape optimization using an improved GWO algorithm","volume":"41","author":"Zheng","year":"2022","journal-title":"Comput. Appl. Math"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102889","DOI":"10.1016\/j.advengsoft.2020.102889","article-title":"Shape optimization of generalized developable H-B\u00e9zier surfaces using adaptive cuckoo search algorithm","volume":"149","author":"Hu","year":"2020","journal-title":"Adv. Eng. Softw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"115079","DOI":"10.1016\/j.eswa.2021.115079","article-title":"RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method","volume":"181","author":"Ahmadianfar","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"107638","DOI":"10.1016\/j.knosys.2021.107638","article-title":"An enhanced black widow optimization algorithm for feature selection","volume":"35","author":"Hu","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/s00500-019-03949-w","article-title":"A novel meta-heuristic optimization method based on golden ratio in nature","volume":"24","author":"Nematollahi","year":"2020","journal-title":"Soft Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1038\/scientificamerican0792-66","article-title":"Genetic algorithms","volume":"267","author":"Holland","year":"1992","journal-title":"Sci. Am."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2013a simple and efficient heuristic for global optimization over continuous Spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_34","unstructured":"Koza, J.R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1007\/s00521-015-1971-3","article-title":"Species co-evolutionary algorithm: A novel evolutionary algorithm based on the ecology and environments for optimization","volume":"31","author":"Li","year":"2019","journal-title":"Neural. Comput. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","article-title":"GSA: A gravitational search algorithm","volume":"179","author":"Rashedi","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","article-title":"SCA: A Sine Cosine Algorithm for Solving Optimization Problems","volume":"96","author":"Mirjalili","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","article-title":"Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems","volume":"51","author":"Hashim","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"71244","DOI":"10.1109\/ACCESS.2021.3079161","article-title":"Crystal structure algorithm (CryStAl): A metaheuristic optimization method","volume":"9","author":"Talatahari","year":"2021","journal-title":"IEEE Access"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107486","DOI":"10.1016\/j.knosys.2021.107486","article-title":"A novel smell agent optimization (sao): An extensive cec study and engineering application","volume":"232","author":"Salawudeen","year":"2021","journal-title":"Knowl. Based Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2011.08.006","article-title":"Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems","volume":"183","author":"Rao","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s40747-016-0022-8","article-title":"Social group optimization (SGO): A new population evolutionary optimization technique","volume":"2","author":"Satapathy","year":"2016","journal-title":"Complex Intell. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"102804","DOI":"10.1016\/j.advengsoft.2020.102804","article-title":"Student psychology based optimization algorithm: A new population based optimization algorithm for solving optimization problems","volume":"146","author":"Bikash","year":"2020","journal-title":"Adv. Eng. Softw."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s42044-018-0025-2","article-title":"Meta-heuristic bus transportation algorithm","volume":"2","author":"Bodaghi","year":"2019","journal-title":"Iran J. Comput. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"103158","DOI":"10.1016\/j.advengsoft.2022.103158","article-title":"Alpine skiing optimization: A new bio-inspired optimization algorithm","volume":"170","author":"Yuan","year":"2022","journal-title":"Adv. Eng. Softw."},{"key":"ref_47","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on NeuralNetworks, Perth, Australia."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.tcs.2005.05.020","article-title":"Ant colony optimization theory: A survey","volume":"344","author":"Dorigo","year":"2005","journal-title":"Theor. Comput. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","article-title":"Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm","volume":"89","author":"Mirjalili","year":"2015","journal-title":"Knowl. Based Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5836","DOI":"10.1007\/s10489-020-02081-9","article-title":"Moth-flame optimization algorithm based on diversity and mutation strategy","volume":"51","author":"Ma","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"101955","DOI":"10.1016\/j.jocs.2023.101955","article-title":"Identification of influential users with cost minimization via an improved moth flame optimization","volume":"67","author":"Wang","year":"2023","journal-title":"J. Comput. Sci."},{"key":"ref_52","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_53","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_54","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","article-title":"Harris hawks optimization: Algorithm and applications","volume":"97","author":"Heidari","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"103249","DOI":"10.1016\/j.engappai.2019.103249","article-title":"Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems","volume":"87","author":"Hayyolalam","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"104454","DOI":"10.1016\/j.bspc.2022.104454","article-title":"Recognition of EEG based on Improved Black Widow Algorithm optimized SVM","volume":"81","author":"Huang","year":"2023","journal-title":"Biomed. Signal Process Control"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.knosys.2018.11.024","article-title":"Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems","volume":"165","author":"Dhiman","year":"2019","journal-title":"Knowl. Based Syst."},{"key":"ref_58","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_59","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1007\/s10489-022-03438-y","article-title":"An efficient salp swarm algorithm based on scale-free informed followers with self-adaption weight","volume":"53","author":"Wang","year":"2023","journal-title":"Appl. Intell."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"107408","DOI":"10.1016\/j.cie.2021.107408","article-title":"African vultures optimization algorithm: A new nature-Inspired metaheuristic algorithm for global optimization problems","volume":"158","author":"Abdollahzadeh","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"114570","DOI":"10.1016\/j.cma.2022.114570","article-title":"Dwarf mongoose optimization algorithm","volume":"391","author":"Agushaka","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Trojovsk\u00fd, P., and Dehghani, M. (2022). Pelican Optimization Algorithm: A Novel Nature-Inspired Algorithm for Engineering Applications. Sensors, 22.","DOI":"10.3390\/s22030855"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"116924","DOI":"10.1016\/j.eswa.2022.116924","article-title":"Golden jackal optimization: A novel nature-inspired optimizer for engineering applications","volume":"198","author":"Nitish","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"114194","DOI":"10.1016\/j.cma.2021.114194","article-title":"Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications","volume":"388","author":"Zhao","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Ramadan, A., Kamel, S., Hassan, M.H., Ahmed, E.M., and Hasanien, H.M. (2022). Accurate photovoltaic models based on an adaptive opposition artificial hummingbird algorithm. Electronics, 11.","DOI":"10.3390\/electronics11030318"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"104535","DOI":"10.1016\/j.est.2022.104535","article-title":"Parameter identification and state of charge estimation of Li-Ion batteries used in electric vehicles using artificial hummingbird optimizer","volume":"51","author":"Mohamed","year":"2022","journal-title":"J. Energy Storage"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Sadoun, A.M., Najjar, I.R., Alsoruji, G.S., Abd-Elwahed, M.S., Elaziz, M.A., and Fathy, A. (2022). Utilization of improved machine learning method based on artificial hummingbird algorithm to predict the tribological Behavior of Cu-Al2O3 nanocomposites synthesized by In Situ method. Mathematics, 10.","DOI":"10.3390\/math10081266"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"40716","DOI":"10.1109\/ACCESS.2022.3167395","article-title":"Optimal planning of multiple renewable energy-integrated distribution system with uncertainties using artificial hummingbird algorithm","volume":"10","author":"Abid","year":"2022","journal-title":"IEEE Access"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"4207","DOI":"10.1007\/s00366-021-01368-w","article-title":"Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems","volume":"38","author":"Yildiz","year":"2021","journal-title":"Eng. Comput."},{"key":"ref_70","first-page":"2875","article-title":"Multi-strategy cooperative evolutionary PSO based on Cauchy mutation strategy","volume":"30","author":"Wang","year":"2018","journal-title":"J. Syst. Simul."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1007\/s42235-022-00223-y","article-title":"Differential Evolution-Boosted Sine Cosine Golden Eagle Optimizer with L\u00e9vy Flight","volume":"19","author":"Hu","year":"2022","journal-title":"J. Bionic. Eng."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"2627","DOI":"10.1007\/s00366-022-01604-x","article-title":"Sand Cat swarm optimization: A nature-inspired algorithm to solve global optimization problems","volume":"39","author":"Seyyedabbasi","year":"2022","journal-title":"Eng. Comput."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"114901","DOI":"10.1016\/j.cma.2022.114901","article-title":"An enhanced hybrid arithmetic optimization algorithm for engineering applications","volume":"394","author":"Hu","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Wilcoxon, F., Bulletin, S.B., and Dec, N. (1992). Individual Comparisons by Ranking Methods, Springer.","DOI":"10.1007\/978-1-4612-4380-9_16"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","article-title":"A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms","volume":"1","author":"Derrac","year":"2011","journal-title":"Swarm Evol. Comput."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"110454","DOI":"10.1016\/j.knosys.2023.110454","article-title":"Kepler optimization algorithm: A new metaheuristic algorithm inspired by Kepler\u2019s laws of planetary motion","volume":"268","author":"Mohamed","year":"2023","journal-title":"Knowl. Based Syst."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.future.2020.03.055","article-title":"Slime mould algorithm: A new method for stochastic optimization","volume":"111","author":"Li","year":"2022","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Zheng, J., Ji, X., Ma, Z., and Hu, G. (2023). Construction of Local-Shape-Controlled Quartic Generalized Said-Ball Model. Mathematics, 11.","DOI":"10.3390\/math11102369"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Hu, G., Wang, J., Li, M., Hussien, A.G., and Abbas, M. (2023). EJS: Multi-strategy enhanced jellyfish search algorithm for engineering applications. Mathematics, 11.","DOI":"10.3390\/math11040851"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"115878","DOI":"10.1016\/j.cma.2023.115878","article-title":"DTCSMO: An efficient hybrid starling murmuration optimizer for engineering applications, Comput","volume":"405","author":"Hu","year":"2023","journal-title":"Methods Appl. Mech. Eng."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"115676","DOI":"10.1016\/j.cma.2022.115676","article-title":"MCSA: Multi-strategy boosted chameleon-inspired optimization algorithm for engineering applications","volume":"403","author":"Hu","year":"2023","journal-title":"Comput. Methods Appl. Mech. Eng."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/8\/4\/377\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:37:00Z","timestamp":1760128620000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/8\/4\/377"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,18]]},"references-count":81,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["biomimetics8040377"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics8040377","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,18]]}}}