{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T20:41:34Z","timestamp":1779309694547,"version":"3.51.4"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62066005"],"award-info":[{"award-number":["62066005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Program for Young Innovative Research Team in China University of Political Science and Law","award":["21CXTD02"],"award-info":[{"award-number":["21CXTD02"]}]},{"DOI":"10.13039\/501100009329","name":"Scientific Research and Technology Development Program of Guangxi","doi-asserted-by":"publisher","award":["AD21196006"],"award-info":[{"award-number":["AD21196006"]}],"id":[{"id":"10.13039\/501100009329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U21A20464"],"award-info":[{"award-number":["U21A20464"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Intell Syst"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, a curve approximation approach using bio-inspired polar coordinate bald eagle search algorithm (PBES) is proposed. PBES algorithm is inspired by the spiral mechanism of bald eagle during predation. By introducing polar coordinate, the spiral predation process of the bald eagle will become more intuitive, which is more conducive for the algorithm to polar coordinate optimization problems. The initialization stage of PBES algorithm is modified to make the distribution of initialized individuals more uniform and some parameters are introduced to strengthen the exploration and exploitation capabilities of algorithm. The performance of the PBES algorithm is tested in three aspects: polar coordinate transcendental equation, curve approximation and robotic manipulator. The experimental results show that the PBES algorithm is superior to the well-known metaheuristic algorithms as it is effectively applicable for curve approximation problem.<\/jats:p>","DOI":"10.1007\/s44196-022-00084-7","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T19:02:36Z","timestamp":1651518156000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Curve Approximation Approach Using Bio-inspired Polar Coordinate Bald Eagle Search Algorithm"],"prefix":"10.1007","volume":"15","author":[{"given":"Yunhui","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4404-952X","authenticated-orcid":false,"given":"Yongquan","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qifang","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binwen","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,5,2]]},"reference":[{"key":"84_CR1","first-page":"608","volume-title":"Calculus of One Variable","author":"SI Grossman","year":"1984","unstructured":"Grossman, S.I.: Polar coordinates. In: Calculus of One Variable, vol. 12, 2nd edn., pp. 608\u2013640. Elsevier, Cambridge (1984)","edition":"2"},{"issue":"1","key":"84_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0030-4018(75)90078-4","volume":"14","author":"RMA Azzam","year":"1975","unstructured":"Azzam, R.M.A.: Polar curves for transmission ellipsometry. Opt. Commun. 14(1), 145\u2013147 (1975)","journal-title":"Opt. Commun."},{"key":"84_CR3","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.jmathb.2014.10.001","volume":"36","author":"KC Moore","year":"2014","unstructured":"Moore, K.C., Paoletti, T., Musgrave, S.: Complexities in students\u2019 construction of the polar coordinate system. J. Math. Behav. 36, 135\u2013149 (2014)","journal-title":"J. Math. Behav."},{"key":"84_CR4","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.enganabound.2013.10.014","volume":"38","author":"J Rong","year":"2014","unstructured":"Rong, J., Wen, L., Xiao, J.: Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements. Eng. Anal. Bound. Elem. 38, 83\u201393 (2014)","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"2","key":"84_CR5","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1006\/jcph.1999.6382","volume":"157","author":"K Mohseni","year":"2000","unstructured":"Mohseni, K., Colonius, T.: Numerical treatment of polar coordinate singularities. J Comput Phys 157(2), 787\u2013795 (2000)","journal-title":"J Comput Phys"},{"issue":"10","key":"84_CR6","doi-asserted-by":"publisher","first-page":"2555","DOI":"10.1016\/j.patcog.2011.03.015","volume":"44","author":"T Ahmad","year":"2011","unstructured":"Ahmad, T., Hu, J., Wang, S.: Pair-polar coordinate-based cancelable fingerprint templates. Pattern Recogn. 44(10), 2555\u20132564 (2011)","journal-title":"Pattern Recogn."},{"issue":"2","key":"84_CR7","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/j.measurement.2010.10.007","volume":"44","author":"X Lei","year":"2011","unstructured":"Lei, X., et al.: Roundness error evaluation algorithm based on polar coordinate transform. Measurement 44(2), 345\u2013350 (2011)","journal-title":"Measurement"},{"key":"84_CR8","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/0-387-27705-6_6","volume-title":"Handbook of Nature-Inspired and Innovative Computing","author":"J Kennedy","year":"2006","unstructured":"Kennedy, J.: Swarm intelligence. In: Zomaya, A.Y. (ed.) Handbook of Nature-Inspired and Innovative Computing, pp. 187\u2013219. Springer, Berlin (2006)"},{"key":"84_CR9","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","volume":"51","author":"FA Hashim","year":"2020","unstructured":"Hashim, F.A., Hussain, K., Houssein, E.H., et al.: Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl. Intell. 51, 1531\u20131551 (2020)","journal-title":"Appl. Intell."},{"key":"84_CR10","volume-title":"Bioinspired Computation in Combinatorial Optimization. Natural Computing Series","author":"F Neumann","year":"2010","unstructured":"Neumann, F., Witt, C.: Combinatorial optimization and computational complexity. In: Bioinspired Computation in Combinatorial Optimization. Natural Computing Series. Springer, Berlin (2010)"},{"key":"84_CR11","volume-title":"LSHADE Algorithm with Rank-Based Selective Pressure Strategy for Solving CEC2017 Benchmark Problems. IEEE Congress on Evolutionary Computation (CEC)","author":"V Stanovov","year":"2018","unstructured":"Stanovov, V., Akhmedova, S., Semenkin, E.: LSHADE Algorithm with Rank-Based Selective Pressure Strategy for Solving CEC2017 Benchmark Problems. IEEE Congress on Evolutionary Computation (CEC). IEEE, Rio de Janeiro (2018)"},{"issue":"8","key":"84_CR12","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1108\/k.1998.27.8.979.4","volume":"27","author":"J Galletly","year":"1998","unstructured":"Galletly, J.: Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Kybernetes 27(8), 979\u2013980 (1998)","journal-title":"Kybernetes"},{"key":"84_CR13","volume-title":"Robots and Biological Systems: Towards a New Bionics? NATO ASI Series (Series F: Computer and Systems Sciences)","author":"G Beni","year":"1993","unstructured":"Beni, G., Wang, J.: Swarm intelligence in cellular robotic systems. In: Dario, P., Sandini, G., Aebischer, P. (eds.) Robots and Biological Systems: Towards a New Bionics? NATO ASI Series (Series F: Computer and Systems Sciences), vol. 102. Springer, Berlin (1993)"},{"key":"84_CR14","unstructured":"Webster, B., Bernhard, P. J.: A local search optimization algorithm based on natural principles of gravitation. In: Proceedings of the International Conference on Information and Knowledge Engineering. IKE'03, June 23\u201326, Las Vegas, Nevada, USA, Vol 1 (2003)."},{"key":"84_CR15","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1023\/A:1022602019183","volume":"3","author":"DE Goldberg","year":"1988","unstructured":"Goldberg, D.E., Holland, J.H.: Genetic algorithms and machine learning. Mach. Learn. 3, 95\u201399 (1988)","journal-title":"Mach. Learn."},{"key":"84_CR16","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn, R., Price, K.: Differential evolution\u2013a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341\u2013359 (1997)","journal-title":"J. Glob. Optim."},{"key":"84_CR17","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/4235.771163","volume":"3","author":"X Yao","year":"1999","unstructured":"Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3, 82\u2013102 (1999)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"84_CR18","unstructured":"Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. MHS'95. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, pp. 39\u201343 (2002)"},{"key":"84_CR19","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MCI.2006.329691","volume":"1","author":"M Dorigo","year":"2006","unstructured":"Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1, 28\u201339 (2006)","journal-title":"IEEE Comput. Intell. Mag."},{"key":"84_CR20","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","volume":"39","author":"D Karaboga","year":"2007","unstructured":"Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J. Glob. Optim. 39, 459\u2013471 (2007)","journal-title":"J. Glob. Optim."},{"key":"84_CR21","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-642-04944-6_14","volume-title":"Stochastic Algorithms: Foundations and Applications. Lecture Notes in Computer Science","author":"XS Yang","year":"2009","unstructured":"Yang, X.S.: Firefly algorithms for multimodal optimization. In: Watanabe, O., Zeugmann, T. (eds.) Stochastic Algorithms: Foundations and Applications. Lecture Notes in Computer Science, pp. 169\u2013178. Springer, Berlin (2009)"},{"key":"84_CR22","first-page":"65","volume-title":"Nature Inspired Cooperative Strategies for Optimization, NICSO 2010","author":"X-S Yang","year":"2010","unstructured":"Yang, X.-S.: A new metaheuristic bat-inspired algorithm. In: Gonz\u00e1lez, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N. (eds.) Nature Inspired Cooperative Strategies for Optimization, NICSO 2010, pp. 65\u201374. Springer, Berlin (2010)"},{"key":"84_CR23","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00366-011-0241-y","volume":"29","author":"AH Gandomi","year":"2013","unstructured":"Gandomi, A.H., Yang, X.-S., Alavi, A.H.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29, 17\u201335 (2013)","journal-title":"Eng. Comput."},{"key":"84_CR24","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1007\/s00521-015-1920-1","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S.: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27, 1053\u20131073 (2016)","journal-title":"Neural Comput. Appl."},{"key":"84_CR25","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","volume":"89","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili, S.: Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl.-Based Syst. 89, 228\u2013249 (2015)","journal-title":"Knowl.-Based Syst."},{"key":"84_CR26","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","volume":"114","author":"S Mirjalili","year":"2017","unstructured":"Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., Mirjalili, S.M.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163\u2013191 (2017)","journal-title":"Adv. Eng. Softw."},{"key":"84_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113377","volume":"152","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi, A., Heidarinejad, M., Mirjalili, S., Gandomi, A.H.: Marine Predators algorithm: a nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020)","journal-title":"Expert Syst. Appl."},{"issue":"1","key":"84_CR28","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/j.future.2020.03.055","volume":"111","author":"S Li","year":"2020","unstructured":"Li, S., Chen, H., Wang, M., et al.: Slime mould algorithm: A new method for stochastic optimization. Futur. Gener. Comput. Syst. 111(1), 300\u2013323 (2020)","journal-title":"Futur. Gener. Comput. Syst."},{"key":"84_CR29","doi-asserted-by":"publisher","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","volume":"179","author":"E Rashedi","year":"2009","unstructured":"Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179, 2232\u20132248 (2009)","journal-title":"Inf. Sci."},{"key":"84_CR30","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.swevo.2019.03.013","volume":"48","author":"YA Anita","year":"2019","unstructured":"Anita, Y.A.: AEFA: Artificial electric field algorithm for global optimization. Swarm Evol. Comput. 48, 93\u2013108 (2019)","journal-title":"Swarm Evol. Comput."},{"key":"84_CR31","doi-asserted-by":"publisher","first-page":"105190","DOI":"10.1016\/j.knosys.2019.105190","volume":"191","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi, A., Heidarinejad, M., Stephens, B., Mirjalili, S.: Equilibrium optimizer: A novel optimization algorithm. Knowl. Based Syst. 191, 105190 (2020)","journal-title":"Knowl. Based Syst."},{"key":"84_CR32","doi-asserted-by":"publisher","first-page":"13170","DOI":"10.1016\/j.eswa.2011.04.126","volume":"38","author":"B Alatas","year":"2011","unstructured":"Alatas, B.: ACROA: artificial chemical reaction optimization algorithm for global optimization. Expert Syst. Appl. 38, 13170\u201313180 (2011)","journal-title":"Expert Syst. Appl."},{"key":"84_CR33","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1016\/j.future.2019.07.015","volume":"101","author":"FA Hashim","year":"2019","unstructured":"Hashim, F.A., Houssein, E.H., Mabrouk, M.S., Al-Atabany, W., Mirjalili, S.: Henry gas solubility optimization: a novel physics-based algorithm. Future Gener. Comput. Syst. 101, 646\u2013667 (2019)","journal-title":"Future Gener. Comput. Syst."},{"key":"84_CR34","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","volume":"96","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S.: SCA: a sine cosine algorithm for solving optimization problems. Knowl.-Based Syst. 96, 120\u2013133 (2016)","journal-title":"Knowl.-Based Syst."},{"issue":"36\/38","key":"84_CR35","first-page":"3902","volume":"194","author":"SL Kang","year":"2005","unstructured":"Kang, S.L., Zong, W.G.: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput. Methods Appl. Mech. Eng. 194(36\/38), 3902\u20133933 (2005)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"84_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2011.08.006","volume":"183","author":"RV Rao","year":"2012","unstructured":"Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching\u2013Learning-Based Optimization: an optimization method for continuous non-linear large scale problems. Inf. Sci. 183(1), 1\u201315 (2012)","journal-title":"Inf. Sci."},{"key":"84_CR37","doi-asserted-by":"crossref","unstructured":"Loucera, C., G\u00e1lvez, A., Iglesias, A.: Simulated annealing algorithm for Bezier curve approximation. In International Conference on Cyberworlds, pp. 182\u2013189 (2014)","DOI":"10.1109\/CW.2014.33"},{"issue":"8","key":"84_CR38","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1016\/j.cad.2004.09.008","volume":"37","author":"W Li","year":"2005","unstructured":"Li, W., Xu, S., Zhao, G., Goh, L.: Adaptive knot placement in B-spline curve approximation. Comput. Aided Des. 37(8), 791\u2013797 (2005)","journal-title":"Comput. Aided Des."},{"key":"84_CR39","doi-asserted-by":"crossref","unstructured":"Laube, P., Franz, M., Umlauf, G.: Deep Learning parametrization for B-Spline curve approximation. In: International Conference on 3D Vision (3DV), pp. 691\u2013699 (2018)","DOI":"10.1109\/3DV.2018.00084"},{"issue":"4","key":"84_CR40","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1515\/jag-2018-0015","volume":"13","author":"J Bureick","year":"2019","unstructured":"Bureick, J., Alkhatib, H., Neumann, I.: Fast converging elitist genetic algorithm for knot adjustment in B-spline curve approximation. J. Appl. Geodesy 13(4), 317\u2013328 (2019)","journal-title":"J. Appl. Geodesy"},{"key":"84_CR41","doi-asserted-by":"publisher","first-page":"2237","DOI":"10.1007\/s10462-019-09732-5","volume":"53","author":"HA Alsattar","year":"2020","unstructured":"Alsattar, H.A., Zaidan, A.A., Zaidan, B.B.: Novel meta-heuristic bald eagle search optimisation algorithm. Artif. Intell. Rev. 53, 2237\u20132264 (2020)","journal-title":"Artif. Intell. Rev."},{"key":"84_CR42","doi-asserted-by":"publisher","DOI":"10.13195\/j.kzyjc.2020.1025","author":"HM Jia","year":"2021","unstructured":"Jia, H.M., Jiang, Z.C., Li, Y.: Simultaneous feature selection optimization based on improved bald eagle search algorithm. Control Dec. (2021). https:\/\/doi.org\/10.13195\/j.kzyjc.2020.1025","journal-title":"Control Dec."},{"key":"84_CR43","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1007\/s12652-020-02182-w","volume":"12","author":"SA Angayarkanni","year":"2021","unstructured":"Angayarkanni, S.A., Sivakumar, R., Ramana Rao, Y.V.: Hybrid Grey Wolf: Bald Eagle search optimized support vector regression for traffic flow forecasting. J. Ambient Intell. Hum. Comput. 12, 1293\u20131304 (2021)","journal-title":"J. Ambient Intell. Hum. Comput."},{"key":"84_CR44","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.3390\/pr9071127","volume":"9","author":"A Ramadan","year":"2021","unstructured":"Ramadan, A., Kamel, S., Hassan, M.H., Khurshaid, T., Rahmann, C.: An improved bald eagle search algorithm for parameter estimation of different photovoltaic models. Processes 9, 1127 (2021)","journal-title":"Processes"},{"issue":"6","key":"84_CR45","doi-asserted-by":"crossref","first-page":"e13683","DOI":"10.1002\/ep.13683","volume":"40","author":"AG Karthik","year":"2021","unstructured":"Karthik, A.G., Saravanakumar, R., Vijayakumar, P.: Bald eagle search optimization on dual fueled reactivity controlled combustion ignition based engine characteristics by altering low reactive fuels. Environ. Prog. Sustain. Energy 40(6), e13683 (2021)","journal-title":"Environ. Prog. Sustain. Energy"},{"key":"84_CR46","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/s11107-020-00923-7","volume":"41","author":"M Sarkar","year":"2021","unstructured":"Sarkar, M., Kumar, A., Maji, B.: PAPR reduction using twin symbol hybrid optimization-based PTS and multi-chaotic-DFT sequence-based encryption in CP-OFDM system. Photon Netw. Commun. 41, 148\u2013162 (2021)","journal-title":"Photon Netw. Commun."},{"key":"84_CR47","first-page":"1","volume":"13","author":"J Zhou","year":"2021","unstructured":"Zhou, J., Wang, Q.: Forecasting carbon price with secondary decomposition algorithm and optimized extreme learning machine. Sustainability 13, 1\u201317 (2021)","journal-title":"Sustainability"},{"key":"84_CR48","doi-asserted-by":"publisher","DOI":"10.1002\/ep.13740","author":"V Palanivel","year":"2021","unstructured":"Palanivel, V., Govindasamy, K., Arunachalam, G.K.: Optimization and prediction of pulsating heat pipe compound parabolic solar collector performances by hybrid deep belief network based bald eagle search optimizer. Environ. Prog. Sustain. Energy (2021). https:\/\/doi.org\/10.1002\/ep.13740","journal-title":"Environ. Prog. Sustain. Energy"},{"key":"84_CR49","doi-asserted-by":"crossref","unstructured":"Kang, Z., Ren, F., Zhang, H., Lu, X., Li, Q.: Diagnosis method of transformer winding fault based on bald eagle search optimizing support vector machines. In: IEEE 4th International Electrical and Energy Conference (CIEEC), pp 1\u20135 (2021)","DOI":"10.1109\/CIEEC50170.2021.9510337"},{"key":"84_CR50","doi-asserted-by":"publisher","first-page":"104712","DOI":"10.1016\/j.compbiomed.2021.104712","volume":"136","author":"GI Sayed","year":"2021","unstructured":"Sayed, G.I., Soliman, M.M., Hassanien, A.E.: A novel melanoma prediction model for imbalanced data using optimized squeeze net by bald eagle search optimization. Comput. Biol. Med. 136, 104712 (2021)","journal-title":"Comput. Biol. Med."},{"issue":"1","key":"84_CR51","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.1016\/j.asoc.2010.04.005","volume":"11","author":"W Matthysen","year":"2010","unstructured":"Matthysen, W., Engelbrecht, A.P.: A polar coordinate particle swarm optimiser. Appl. Soft Comput. 11(1), 1322\u20131399 (2010)","journal-title":"Appl. Soft Comput."},{"key":"84_CR52","doi-asserted-by":"crossref","unstructured":"Sierra, A., Echeverra, A.: The polar evolution strategy. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 2301\u20132306 (2006)","DOI":"10.1109\/CEC.2006.1688592"},{"key":"84_CR53","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s11063-020-10271-2","volume":"52","author":"Z Xiang","year":"2020","unstructured":"Xiang, Z., Zhou, Y., Luo, Q., et al.: PSSA: polar coordinate salp swarm algorithm for curve design problems. Neural Process Lett. 52, 615\u2013645 (2020)","journal-title":"Neural Process Lett."},{"key":"84_CR54","first-page":"1794","volume":"18","author":"S Liu","year":"2006","unstructured":"Liu, S., Zhang, X., Sun, D., Lin, M., Wen, S.: New-style Particle Swarm Optimization Algorithm based on polar coordination system and complex number operation. J. Syst. Simul. 18, 1794\u20131798 (2006)","journal-title":"J. Syst. Simul."},{"key":"84_CR55","first-page":"1576","volume":"24","author":"S Pang","year":"2012","unstructured":"Pang, S., Zou, H., Su, Q.: Improved multi-objective particle swarm optimization in polar coordinates. J. Syst. Simul. 24, 1576\u20131581 (2012)","journal-title":"J. Syst. Simul."},{"issue":"2","key":"84_CR56","first-page":"34","volume":"29","author":"J Liu","year":"2016","unstructured":"Liu, J., Wei, J.: An improved NSGA-II algorithm based on polar coordinate. Transformation 29(2), 34\u201337 (2016)","journal-title":"Transformation"},{"key":"84_CR57","doi-asserted-by":"publisher","first-page":"98","DOI":"10.5539\/mas.v11n8p98","volume":"11","author":"RMH Al-Sayyed","year":"2017","unstructured":"Al-Sayyed, R.M.H., Fakhouri, H.N., Rodan, A., Pattinson, C.: Polar particle swarm algorithm for solving cloud data migration optimization problem. Mod. Appl. Sci. 11, 98\u2013117 (2017)","journal-title":"Mod. Appl. Sci."},{"key":"84_CR58","first-page":"2248","volume":"32","author":"S Wei","year":"2010","unstructured":"Wei, S., Sun, Y., Jia, X.: Improved artificial fish swarm algorithm based on polar coordinate coding. Syst. Eng. Electron. 32, 2248\u20132251 (2010)","journal-title":"Syst. Eng. Electron."},{"key":"84_CR59","first-page":"161","volume":"47","author":"Y Wu","year":"2017","unstructured":"Wu, Y., Zhou, Y.: A drosophila optimization algorithm based on polar coding. Math. Pract. Cognit. 47, 161\u2013170 (2017)","journal-title":"Math. Pract. Cognit."},{"key":"84_CR60","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-021-02102-9","author":"CW Lin","year":"2021","unstructured":"Lin, C.W., Hong, S.: High-order histogram-based local clustering patterns in polar coordinate for facial recognition and retrieval. Vis. Comput. (2021). https:\/\/doi.org\/10.1007\/s00371-021-02102-9","journal-title":"Vis. Comput."},{"key":"84_CR61","doi-asserted-by":"publisher","first-page":"242","DOI":"10.18517\/ijaseit.7.1.1794","volume":"7","author":"M Shatnawi","year":"2017","unstructured":"Shatnawi, M., Nasrudin, M.F., Sahran, S.: A new initialization technique in polar coordinates for particle swarm optimization and polar PSO. Int. J. Adv. Sci. Eng. Inf. Technol. 7, 242\u2013249 (2017)","journal-title":"Int. J. Adv. Sci. Eng. Inf. Technol."},{"key":"84_CR62","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1186\/s13104-018-4008-z","volume":"11","author":"S Thota","year":"2018","unstructured":"Thota, S., Srivastav, V.K.: Quadratically convergent algorithm for computing real root of non-linear transcendental equations. BMC Res. Notes 11, 909 (2018)","journal-title":"BMC Res. Notes"},{"key":"84_CR63","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/s40819-019-0600-8","volume":"5","author":"VK Srivastav","year":"2019","unstructured":"Srivastav, V.K., Thota, S., Kumar, M.: A new trigonometrical algorithm for computing real root of non-linear transcendental equations. Int. J. Appl. Comput. Math. 5, 44 (2019)","journal-title":"Int. J. Appl. Comput. Math."},{"key":"84_CR64","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-8396(84)90003-7","volume":"1","author":"W B\u00f6hm","year":"1984","unstructured":"B\u00f6hm, W., Farin, G., Kahmann, J.: A survey of curve and surface methods in CAGD. Comput. Aided Geom. Des. 1, 1\u201360 (1984)","journal-title":"Comput. Aided Geom. Des."},{"key":"84_CR65","doi-asserted-by":"publisher","first-page":"951","DOI":"10.1038\/nbt0803-951","volume":"21","author":"K Kreeger","year":"2003","unstructured":"Kreeger, K.: The learning curve. Nat. Biotechnol. 21, 951\u2013952 (2003)","journal-title":"Nat. Biotechnol."},{"issue":"8","key":"84_CR66","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.2106\/00004623-196042080-00012","volume":"42","author":"JR Cobb","year":"1960","unstructured":"Cobb, J.R.: The problem of the primary curve. J. Bone Jt. Surg. 42(8), 1413\u20131425 (1960)","journal-title":"J. Bone Jt. Surg."},{"issue":"1","key":"84_CR67","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1109\/TAC.1959.6429401","volume":"4","author":"EC Levy","year":"1959","unstructured":"Levy, E.C.: Complex-curve fitting. IRE Trans. Autom. Control. 4(1), 37\u201343 (1959)","journal-title":"IRE Trans. Autom. Control."},{"issue":"5","key":"84_CR68","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1109\/34.55108","volume":"12","author":"HJ Wolfson","year":"1990","unstructured":"Wolfson, H.J.: On curve matching. IEEE Trans. Pattern Anal. Mach. Intell. 12(5), 483\u2013489 (1990)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"60","key":"84_CR69","doi-asserted-by":"publisher","first-page":"233","DOI":"10.2307\/2001941","volume":"11","author":"JC Holladay","year":"1957","unstructured":"Holladay, J.C.: A smoothest curve approximation. Math. Tables Other Aids Comput. 11(60), 233\u2013243 (1957)","journal-title":"Math. Tables Other Aids Comput."},{"key":"84_CR70","doi-asserted-by":"publisher","first-page":"77","DOI":"10.3847\/1538-4357\/aba59a","volume":"900","author":"JR Farah","year":"2020","unstructured":"Farah, J.R., Pesce, D.W., Johnson, M.D., et al.: On the approximation of the black hole shadow with a simple polar curve. ApJ 900, 77 (2020)","journal-title":"ApJ"},{"key":"84_CR71","doi-asserted-by":"publisher","first-page":"18821","DOI":"10.1007\/s00500-020-05114-0","volume":"24","author":"EK Ueda","year":"2020","unstructured":"Ueda, E.K., Sato, A.K., Martins, T.C., et al.: Curve approximation by adaptive neighborhood simulated annealing and piecewise B\u00e9zier curves. Soft Comput. 24, 18821\u201318839 (2020)","journal-title":"Soft Comput."},{"key":"84_CR72","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1080\/00220973.1993.9943832","volume":"62","author":"DW Zimmerman","year":"1993","unstructured":"Zimmerman, D.W., Zumbo, B.D.: Relative power of the Wilcoxon test, the Friedman test, and repeated-measures ANOV A on ranks. J. Exp. Educ. 62, 75\u201386 (1993)","journal-title":"J. Exp. Educ."},{"key":"84_CR73","doi-asserted-by":"publisher","first-page":"5040","DOI":"10.1007\/s10489-020-02071-x","volume":"51","author":"C Tang","year":"2021","unstructured":"Tang, C., Zhou, Y., Tang, Z.: Teaching-learning-based pathfinder algorithm for function and engineering optimization problems. Appl. Intell. 51, 5040\u20135066 (2021)","journal-title":"Appl. Intell."},{"issue":"10","key":"84_CR74","doi-asserted-by":"publisher","first-page":"6101","DOI":"10.1002\/int.22543","volume":"36","author":"F Liu","year":"2021","unstructured":"Liu, F., Huang, H., Li, B., et al.: A parallel learning particle swarm optimizer for inverse kinematics of robotic manipulator. Int. J. Intell. Syst. 36(10), 6101\u20136132 (2021)","journal-title":"Int. J. Intell. Syst."},{"issue":"1","key":"84_CR75","first-page":"75","volume":"22","author":"S Dereli","year":"2019","unstructured":"Dereli, S., K\u00f6ker, R., \u00d6ylek, \u0130, Ay, M.: A comprehensive research on the use of swarm algorithms in the inverse kinematics solution. Politeknik Dergisi 22(1), 75\u201379 (2019)","journal-title":"Politeknik Dergisi"},{"key":"84_CR76","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1007\/s10462-019-09683-x","volume":"53","author":"S Dereli","year":"2020","unstructured":"Dereli, S., K\u00f6ker, R.: A meta-heuristic proposal for inverse kinematics solution of 7-DOF serial robotic manipulator: quantum behaved particle swarm algorithm. Artif. Intell. Rev. 53, 949\u2013964 (2020)","journal-title":"Artif. Intell. Rev."},{"key":"84_CR77","doi-asserted-by":"crossref","unstructured":"Sun, J., Cao, G., Li, W., Liang, Y., Huang, S.: Analytical inverse kinematic solution using the D\u2013H method for a 6-DOF Robot. In: International Conference on Ubiquitous Robots and Ambient Intelligence, pp. 714\u2013716 (2017)","DOI":"10.1109\/URAI.2017.7992807"},{"issue":"5","key":"84_CR78","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1080\/17415977.2019.1602124","volume":"28","author":"S Dereli","year":"2020","unstructured":"Dereli, S., K\u00f6ker, R.: Calculation of the inverse kinematics solution of the 7-DOF redundant robot manipulator by the firefly algorithm and statistical analysis of the results in terms of speed and accuracy. Inverse Probl. Sci. Eng. 28(5), 601\u2013613 (2020)","journal-title":"Inverse Probl. Sci. Eng."},{"issue":"1","key":"84_CR79","doi-asserted-by":"crossref","first-page":"1","DOI":"10.47852\/bonviewJCCE877829","volume":"1","author":"Y Lei","year":"2022","unstructured":"Lei, Y.: Research on microvideo character perception and recognition based on target detection technology. J. Comput. Cognit. Eng. 1(1), 1\u20135 (2022)","journal-title":"J. Comput. Cognit. Eng."},{"issue":"1","key":"84_CR80","doi-asserted-by":"crossref","first-page":"32","DOI":"10.47852\/bonviewJCCE19919","volume":"1","author":"Y Yang","year":"2022","unstructured":"Yang, Y., Song, X.: Research on face intelligent perception technology integrating deep learning under different illumination intensities. J. Comput. Cognit. Eng. 1(1), 32\u201336 (2022)","journal-title":"J. Comput. Cognit. Eng."},{"key":"84_CR81","doi-asserted-by":"publisher","DOI":"10.47852\/bonviewJCCE20514","author":"M Yang","year":"2022","unstructured":"Yang, M.: Research on vehicle automatic driving target perception technology based on improved MSRPN algorithm. J. Comput. Cognit. Eng. (2022). https:\/\/doi.org\/10.47852\/bonviewJCCE20514","journal-title":"J. Comput. Cognit. Eng."}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00084-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-022-00084-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00084-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T16:01:29Z","timestamp":1727107289000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-022-00084-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,2]]},"references-count":81,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["84"],"URL":"https:\/\/doi.org\/10.1007\/s44196-022-00084-7","relation":{},"ISSN":["1875-6883"],"issn-type":[{"value":"1875-6883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,2]]},"assertion":[{"value":"16 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}}],"article-number":"30"}}