{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T15:38:18Z","timestamp":1783438698687,"version":"3.54.6"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T00:00:00Z","timestamp":1654819200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T00:00:00Z","timestamp":1654819200000},"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":["12101195"],"award-info":[{"award-number":["12101195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471102"],"award-info":[{"award-number":["11471102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071112"],"award-info":[{"award-number":["12071112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic research projects for key scientific research projects in Henan Province","award":["20ZX001"],"award-info":[{"award-number":["20ZX001"]}]},{"name":"Natural Science Foundation of Henan Province for Youth","award":["202300410146"],"award-info":[{"award-number":["202300410146"]}]}],"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>Whale optimization algorithm, as a relatively novel swarm-based intelligence optimization algorithm, has been extensively utilized in numerous scientific and engineering fields. The intent of this work was to devise a modified WOA based on multi-strategy, named MSWOA, to address somewhat deficiencies of the original WOA, such as converging slowly, stagnating at local minima and poor stability. First, a tent map function is adopted to optimize the distribution of the initial population in problem domain. Second, new iteration-based update strategies of convergence factor and inertia weight are constructed to regulate the balance between global and local search capabilities and improve the optimization ability. Additionally, an optimal feedback strategy is presented in the search for prey stage to enhance the global search ability. Numerical experimental results based on 24 test benchmark functions reveal that the proposed MSWOA significantly improves the standard WOA in terms of solution accuracy and convergence speed, and outperforms the comparison algorithms. Furthermore, the results show that the inertia weight strategy has the greatest effect on the performance of basic WOA performance, followed by the convergence factor, and then the optimal feedback strategy.<\/jats:p>","DOI":"10.1007\/s44196-022-00092-7","type":"journal-article","created":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T07:02:30Z","timestamp":1654844550000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["An Improved Whale Optimization Algorithm Based on Nonlinear Parameters and Feedback Mechanism"],"prefix":"10.1007","volume":"15","author":[{"given":"Guanglei","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9859-4040","authenticated-orcid":false,"given":"Youlin","family":"Shang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kehong","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huimin","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,10]]},"reference":[{"issue":"5","key":"92_CR1","doi-asserted-by":"publisher","first-page":"6151","DOI":"10.3233\/IFS-179199","volume":"37","author":"Y Wang","year":"2019","unstructured":"Wang, Y., Wang, H.: Neural network model for energy low carbon economy and financial risk based on PSO intelligent algorithms. J. Intell. Fuzzy Syst. 37(5), 6151\u20136163 (2019). https:\/\/doi.org\/10.3233\/IFS-179199","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"6","key":"92_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.9781\/ijimai.2020.12.001","volume":"6","author":"H Rezk","year":"2021","unstructured":"Rezk, H., Arfaoui, J., Gomaa, M.R.: Optimal parameter estimation of solar PV panel based on hybrid particle swarm and grey wolf optimization algorithms. Int. J. Interact. Multim. Artif. Intell. 6(6), 145\u2013155 (2021). https:\/\/doi.org\/10.9781\/ijimai.2020.12.001","journal-title":"Int. J. Interact. Multim. Artif. Intell."},{"key":"92_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105884","author":"H Chen","year":"2020","unstructured":"Chen, H., Zhang, Q., Luo, J., Xu, Y., Zhang, X.: An enhanced bacterial foraging optimization and its application for training kernel extreme learning machine. Appl. Soft Comput. (2020). https:\/\/doi.org\/10.1016\/j.asoc.2019.105884","journal-title":"Appl. Soft Comput."},{"issue":"Supplement","key":"92_CR4","doi-asserted-by":"publisher","first-page":"3505","DOI":"10.1007\/s10586-018-2198-8","volume":"22","author":"Y Du","year":"2019","unstructured":"Du, Y., Yang, N.: Analysis of image processing algorithm based on bionic intelligent optimization. Clust. Comput. 22(Supplement), 3505\u20133512 (2019). https:\/\/doi.org\/10.1007\/s10586-018-2198-8","journal-title":"Clust. Comput."},{"issue":"2","key":"92_CR5","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s40305-017-0160-8","volume":"5","author":"J-R Li","year":"2017","unstructured":"Li, J.-R., Shang, Y.-L., Han, P.: New tunnel-filled function method for discrete global optimization. J. Oper. Res. Soc. China 5(2), 291\u2013300 (2017). https:\/\/doi.org\/10.1007\/s40305-017-0160-8","journal-title":"J. Oper. Res. Soc. China"},{"issue":"3","key":"92_CR6","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s40305-017-0172-4","volume":"5","author":"C-H Liu","year":"2017","unstructured":"Liu, C.-H., Huang, Y.-Y., Shang, Y.-L.: Polynomial convergence of primal dual path-following algorithms for symmetric cone programming based on wide neighborhoods and a new class of directions. J. Oper. Res. Soc. China 5(3), 333\u2013346 (2017). https:\/\/doi.org\/10.1007\/s40305-017-0172-4","journal-title":"J. Oper. Res. Soc. China"},{"key":"92_CR7","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2021115","author":"D Qu","year":"2021","unstructured":"Qu, D., Shang, Y., Wu, D., Sun, G.: Filled function method to optimize supply chain transportation costs. J. Ind. Manag. Optim. (2021). https:\/\/doi.org\/10.3934\/jimo.2021115","journal-title":"J. Ind. Manag. Optim."},{"issue":"2","key":"92_CR8","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s40305-020-00296-8","volume":"9","author":"Y-Y Huang","year":"2021","unstructured":"Huang, Y.-Y., Liu, C.-H., Shang, Y.-L.: Inexact operator splitting method for monotone inclusion problems. J. Oper. Res. Soc. China 9(2), 273\u2013306 (2021). https:\/\/doi.org\/10.1007\/s40305-020-00296-8","journal-title":"J. Oper. Res. Soc. China"},{"issue":"2","key":"92_CR9","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s40305-016-0118-2","volume":"4","author":"C-H Liu","year":"2016","unstructured":"Liu, C.-H., Wu, D., Shang, Y.-L.: A new infeasible-interior-point algorithm based on wide neighborhoods for symmetric cone programming. J. Oper. Res. Soc. China 4(2), 147\u2013165 (2016). https:\/\/doi.org\/10.1007\/s40305-016-0118-2","journal-title":"J. Oper. Res. Soc. China"},{"key":"92_CR10","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.ins.2013.02.041","volume":"237","author":"I Boussa\u00efd","year":"2013","unstructured":"Boussa\u00efd, I., Lepagnot, J., Siarry, P.: A survey on optimization meta-heuristics. Inf. Sci. 237, 82\u2013117 (2013). https:\/\/doi.org\/10.1016\/j.ins.2013.02.041","journal-title":"Inf. Sci."},{"key":"92_CR11","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/1063045","author":"H Yap\u0131c\u0131","year":"2017","unstructured":"Yap\u0131c\u0131, H., \u00c7etinkaya, N.: An improved particle swarm optimization algorithm using eagle strategy for power loss minimization. Math. Probl. Eng. (2017). https:\/\/doi.org\/10.1155\/2017\/1063045","journal-title":"Math. Probl. Eng."},{"key":"92_CR12","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1016\/j.knosys.2014.05.004","volume":"67","author":"A Meng","year":"2014","unstructured":"Meng, A., Chen, Y., Yin, H., Chen, S.: Crisscross optimization algorithm and its application. Knowl. Based Syst. 67, 218\u2013229 (2014). https:\/\/doi.org\/10.1016\/j.knosys.2014.05.004","journal-title":"Knowl. Based Syst."},{"key":"92_CR13","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.matcom.2021.08.013","volume":"192","author":"FA Hashim","year":"2022","unstructured":"Hashim, F.A., Houssein, E.H., Hussain, K., Mabrouk, M.S., Al-Atabany, W.: Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math. Comput. Simul. 192, 84\u2013110 (2022). https:\/\/doi.org\/10.1016\/j.matcom.2021.08.013","journal-title":"Math. Comput. Simul."},{"issue":"2","key":"92_CR14","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1111\/coin.12439","volume":"37","author":"W Polnik","year":"2021","unstructured":"Polnik, W., Stobiecki, J., Byrski, A., Kisiel-Dorohinicki, M.: Ant colony optimization-evolutionary hybrid optimization with translation of problem representation. Comput. Intell. 37(2), 891\u2013923 (2021). https:\/\/doi.org\/10.1111\/coin.12439","journal-title":"Comput. Intell."},{"key":"92_CR15","doi-asserted-by":"publisher","first-page":"130452","DOI":"10.1109\/ACCESS.2020.3009533","volume":"8","author":"WAHM Ghanem","year":"2020","unstructured":"Ghanem, W.A.H.M., Jantan, A., Ghaleb, S.A.A., Nasser, A.B.: An efficient intrusion detection model based on hybridization of artificial bee colony and dragonfly algorithms for training multilayer perceptrons. IEEE Access 8, 130452\u2013130475 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.3009533","journal-title":"IEEE Access"},{"issue":"16","key":"92_CR16","doi-asserted-by":"publisher","first-page":"2050253","DOI":"10.1142\/S0218126620502539","volume":"29","author":"P Albert","year":"2020","unstructured":"Albert, P., Nanjappan, M.: An efficient kernel FCM and artificial fish swarm optimization-based optimal resource allocation in cloud. J. Circuits Syst. Comput. 29(16), 2050253\u20131205025316 (2020). https:\/\/doi.org\/10.1142\/S0218126620502539","journal-title":"J. Circuits Syst. Comput."},{"issue":"1","key":"92_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s44196-021-00013-0","volume":"14","author":"C Mallika","year":"2021","unstructured":"Mallika, C., Selvamuthukumaran, S.: A hybrid crow search and grey wolf optimization technique for enhanced medical data classification in diabetes diagnosis system. Int. J. Comput. Intell. Syst. 14(1), 1\u201318 (2021). https:\/\/doi.org\/10.1007\/s44196-021-00013-0","journal-title":"Int. J. Comput. Intell. Syst."},{"issue":"1","key":"92_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s44196-021-00039-4","volume":"14","author":"RM Rizk-Allah","year":"2021","unstructured":"Rizk-Allah, R.M., Saleh, O., Hagag, E.A., Mousa, A.A.A.: Enhanced tunicate swarm algorithm for solving large-scale nonlinear optimization problems. Int. J. Comput. Intell. Syst. 14(1), 1\u201324 (2021). https:\/\/doi.org\/10.1007\/s44196-021-00039-4","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"92_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51\u201367 (2016). https:\/\/doi.org\/10.1016\/j.advengsoft.2016.01.008","journal-title":"Adv. Eng. Softw."},{"key":"92_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.swevo.2019.03.004","volume":"48","author":"FS Gharehchopogh","year":"2019","unstructured":"Gharehchopogh, F.S., Gholizadeh, H.: A comprehensive survey: whale optimization algorithm and its applications. Swarm Evol. Comput. 48, 1\u201324 (2019). https:\/\/doi.org\/10.1016\/j.swevo.2019.03.004","journal-title":"Swarm Evol. Comput."},{"issue":"3","key":"92_CR21","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.jcde.2017.12.006","volume":"5","author":"G Kaur","year":"2018","unstructured":"Kaur, G., Arora, S.: Chaotic whale optimization algorithm. J. Comput. Des. Eng. 5(3), 275\u2013284 (2018). https:\/\/doi.org\/10.1016\/j.jcde.2017.12.006","journal-title":"J. Comput. Des. Eng."},{"issue":"2","key":"92_CR22","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/s00357-018-9261-2","volume":"35","author":"GI Sayed","year":"2018","unstructured":"Sayed, G.I., Darwish, A., Hassanien, A.E.: A new chaotic whale optimization algorithm for features selection. J. Classif. 35(2), 300\u2013344 (2018). https:\/\/doi.org\/10.1007\/s00357-018-9261-2","journal-title":"J. Classif."},{"key":"92_CR23","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.knosys.2019.02.010","volume":"172","author":"MA El-Aziz","year":"2019","unstructured":"El-Aziz, M.A., Mirjalili, S.: A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl. Based Syst. 172, 42\u201363 (2019). https:\/\/doi.org\/10.1016\/j.knosys.2019.02.010","journal-title":"Knowl. Based Syst."},{"key":"92_CR24","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.5949","author":"H Ding","year":"2020","unstructured":"Ding, H., Wu, Z., Zhao, L.: Whale optimization algorithm based on nonlinear convergence factor and chaotic inertial weight. Concurr. Comput. Pract. Exp. (2020). https:\/\/doi.org\/10.1002\/cpe.5949","journal-title":"Concurr. Comput. Pract. Exp."},{"key":"92_CR25","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/j.eswa.2018.08.027","volume":"114","author":"Y Sun","year":"2018","unstructured":"Sun, Y., Wang, X., Chen, Y., Liu, Z.: A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst. Appl. 114, 563\u2013577 (2018). https:\/\/doi.org\/10.1016\/j.eswa.2018.08.027","journal-title":"Expert Syst. Appl."},{"issue":"Supplement","key":"92_CR26","doi-asserted-by":"publisher","first-page":"8319","DOI":"10.1007\/s10586-018-1769-z","volume":"22","author":"M Abdel-Basset","year":"2019","unstructured":"Abdel-Basset, M., Abdel-Fatah, L., Sangaiah, A.K.: An improved L\u00e9vy based whale optimization algorithm for bandwidth-efficient virtual machine placement in cloud computing environment. Clust. Comput. 22(Supplement), 8319\u20138334 (2019). https:\/\/doi.org\/10.1007\/s10586-018-1769-z","journal-title":"Clust. Comput."},{"issue":"2","key":"92_CR27","doi-asserted-by":"publisher","first-page":"238","DOI":"10.3390\/sym13020238","volume":"13","author":"Q Jin","year":"2021","unstructured":"Jin, Q., Xu, Z., Cai, W.: An improved whale optimization algorithm with random evolution and special reinforcement dual-operation strategy collaboration. Symmetry 13(2), 238 (2021). https:\/\/doi.org\/10.3390\/sym13020238","journal-title":"Symmetry"},{"key":"92_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.114901","volume":"176","author":"MM Saafan","year":"2021","unstructured":"Saafan, M.M., El-Gendy, E.M.: IWOSSA: an improved whale optimization salp swarm algorithm for solving optimization problems. Expert Syst. Appl. 176, 114901 (2021). https:\/\/doi.org\/10.1016\/j.eswa.2021.114901","journal-title":"Expert Syst. Appl."},{"issue":"3","key":"92_CR29","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1016\/j.eswa.2007.02.002","volume":"34","author":"CL dos Santos","year":"2008","unstructured":"dos Santos, C.L., Mariani, V.C.: Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization [J]. Expert Syst. Appl. 34(3), 1905\u20131913 (2008). https:\/\/doi.org\/10.1016\/j.eswa.2007.02.002","journal-title":"Expert Syst. Appl."},{"issue":"4","key":"92_CR30","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1007\/s00521-017-3131-4","volume":"31","author":"AA Ewees","year":"2019","unstructured":"Ewees, A.A., Aziz, M.A.E., Hassanien, A.E.: Chaotic multi-verse optimizer-based feature selection. Neural Comput. Appl. 31(4), 991\u20131006 (2019). https:\/\/doi.org\/10.1007\/s00521-017-3131-4","journal-title":"Neural Comput. Appl."},{"key":"92_CR31","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46\u201361 (2014). https:\/\/doi.org\/10.1016\/j.advengsoft.2013.12.007","journal-title":"Adv. Eng. Softw."},{"issue":"12","key":"92_CR32","doi-asserted-by":"publisher","first-page":"3387","DOI":"10.1007\/s00500-015-2016-7","volume":"21","author":"S Druzeta","year":"2017","unstructured":"Druzeta, S., Ivic, S.: Examination of benefits of personal fitness improvement dependent inertia for particle swarm optimization. Soft Comput. 21(12), 3387\u20133400 (2017). https:\/\/doi.org\/10.1007\/s00500-015-2016-7","journal-title":"Soft Comput."}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00092-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-022-00092-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-022-00092-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T07:40:28Z","timestamp":1654846828000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-022-00092-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,10]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["92"],"URL":"https:\/\/doi.org\/10.1007\/s44196-022-00092-7","relation":{},"ISSN":["1875-6883"],"issn-type":[{"value":"1875-6883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,10]]},"assertion":[{"value":"12 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 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 that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"38"}}