{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T23:37:09Z","timestamp":1772321829673,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"crossref","award":["no.12271326, no. 61806120, no. 61502290, no. 61401263, no. 61672334, no. 61673251"],"award-info":[{"award-number":["no.12271326, no. 61806120, no. 61502290, no. 61401263, no. 61672334, no. 61673251"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"crossref","award":["no. 2015M582606"],"award-info":[{"award-number":["no. 2015M582606"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Industrial Research Project of Science and Technology in Shaanxi Province","award":["no. 2015GY016, no. 2017JQ6063"],"award-info":[{"award-number":["no. 2015GY016, no. 2017JQ6063"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Fund for the Central Universities","doi-asserted-by":"crossref","award":["no. GK202003071"],"award-info":[{"award-number":["no. GK202003071"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["no. 2022JM-354"],"award-info":[{"award-number":["no. 2022JM-354"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Memetic Comp."],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s12293-023-00398-9","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T03:02:26Z","timestamp":1694142146000},"page":"391-403","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A point crowding-degree based evolutionary algorithm for many-objective optimization"],"prefix":"10.1007","volume":"15","author":[{"given":"Cai","family":"Dai","sequence":"first","affiliation":[]},{"given":"Cheng","family":"Peng","sequence":"additional","affiliation":[]},{"given":"Xiujuan","family":"Lei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"398_CR1","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s12293-022-00353-0","volume":"15","author":"N Luo","year":"2023","unstructured":"Luo N, Ye Y, Lin W, Lin Q, Leung VCM (2023) A novel multimodal multiobjective memetic algorithm with a local detection mechanism and a clustering-based selection strategy. Memetic Comput 15:31\u201343","journal-title":"Memetic Comput"},{"key":"398_CR2","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s12293-023-00387-y","volume":"15","author":"Q Jiang","year":"2023","unstructured":"Jiang Q, Cui J, Wang L, Lin Y, Wu Y, Hei X (2023) A regularity model-based multi-objective estimation of distribution memetic algorithm with auto-controllable population diversity. Memetic Comput 15:45\u201370","journal-title":"Memetic Comput"},{"key":"398_CR3","doi-asserted-by":"crossref","unstructured":"Wei Z, Gao W, Gong M, Yen GG (2022) A bi-objective evolutionary algorithm for multimodal multi-objective optimization. IEEE Trans Evol Comput 1\u20131","DOI":"10.1109\/TEVC.2022.3217258"},{"issue":"7","key":"398_CR4","doi-asserted-by":"publisher","first-page":"6024","DOI":"10.1109\/TCYB.2021.3117359","volume":"52","author":"Z Wei","year":"2022","unstructured":"Wei Z, Gao W, Li G, Zhang Q (2022) A penalty-based differential evolution for multimodal optimization. IEEE Trans Cybern 52(7):6024\u20136033","journal-title":"IEEE Trans Cybern"},{"key":"398_CR5","unstructured":"Gao W, Wei Z, Gong M, Yen GG (2021) Solving expensive multimodal optimization problem by a decomposition differential evolution algorithm. IEEE Trans Cybern 1\u201311"},{"issue":"1","key":"398_CR6","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1109\/TCYB.2021.3108563","volume":"53","author":"W Gao","year":"2023","unstructured":"Gao W, Li Y (2023) Solving a new test set of nonlinear equation systems by evolutionary algorithm. IEEE Trans Cybern 53(1):406\u2013415","journal-title":"IEEE Trans Cybern"},{"key":"398_CR7","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s12532-022-00231-3","volume":"15","author":"M Lapucci","year":"2023","unstructured":"Lapucci M, Mansueto P, Schoen F (2023) A memetic procedure for global multi-objective optimization. Math Program Comput 15:227\u2013267","journal-title":"Math Program Comput"},{"key":"398_CR8","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s12293-021-00324-x","volume":"13","author":"R Saikia","year":"2021","unstructured":"Saikia R, Sharma D (2021) Reference-lines-steered memetic multi-objective evolutionary algorithm with adaptive termination criterion. Memetic Comput 13:49\u201367","journal-title":"Memetic Comput"},{"key":"398_CR9","doi-asserted-by":"publisher","first-page":"108158","DOI":"10.1016\/j.asoc.2021.108158","volume":"114","author":"H Ge","year":"2022","unstructured":"Ge H, Zhang N, Sun L, Wang X, Hou Y (2022) A memetic evolution system with statistical variable classification for large-scale many-objective optimization. Appl Soft Comput 114:108158","journal-title":"Appl Soft Comput"},{"issue":"2","key":"398_CR10","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182\u2013197","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"398_CR11","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"Q Zhang","year":"2007","unstructured":"Zhang Q, Li H (2007) MOEA\/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712\u2013731","journal-title":"IEEE Trans Evol Comput"},{"issue":"8","key":"398_CR12","doi-asserted-by":"publisher","first-page":"2912","DOI":"10.1109\/TCYB.2018.2832640","volume":"49","author":"ZG Chen","year":"2019","unstructured":"Chen ZG, Zhan ZH, Lin Y, Gong YJ, Gu TL, Zhao F, Yuan HQ, Chen X, Li Q, Zhang J (2019) Multiobjective cloud workflow scheduling: a multiple populations ant colony system approach. IEEE Trans Cybern 49(8):2912\u20132926","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"398_CR13","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1109\/TCYB.2018.2872803","volume":"50","author":"M Wu","year":"2020","unstructured":"Wu M, Li K, Kwong S, Zhang Q (2020) Evolutionary many-objective optimization based on adversarial decomposition. IEEE Trans Cybern 50(2):753\u2013764","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"398_CR14","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1162\/EVCO_a_00075","volume":"21","author":"D Hadka","year":"2013","unstructured":"Hadka D, Reed P (2013) Borg: an auto-adaptive many-objective evolutionary computing framework. Evol Comput 21(2):231\u2013259","journal-title":"Evol Comput"},{"issue":"2","key":"398_CR15","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1109\/TEVC.2013.2258025","volume":"18","author":"Z He","year":"2014","unstructured":"He Z, Yen GG, Zhang J (2014) Fuzzy-based pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18(2):269\u2013285","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"398_CR16","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1109\/TEVC.2012.2227145","volume":"17","author":"S Yang","year":"2013","unstructured":"Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721\u2013736","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"398_CR17","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1109\/TEVC.2014.2378512","volume":"19","author":"X Zhang","year":"2015","unstructured":"Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 19(6):761\u2013776","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"398_CR18","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1109\/TEVC.2013.2262178","volume":"18","author":"M Li","year":"2014","unstructured":"Li M, Yang S, Liu X (2014) Shift-based density estimation for pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348\u2013365","journal-title":"IEEE Trans Evol Comput"},{"issue":"9","key":"398_CR19","doi-asserted-by":"publisher","first-page":"2689","DOI":"10.1109\/TCYB.2016.2638902","volume":"47","author":"Y Liu","year":"2017","unstructured":"Liu Y, Gong D, Sun J, Jin Y (2017) A many-objective evolutionary algorithm using a one-by-one selection strategy. IEEE Trans Cybern 47(9):2689\u20132702","journal-title":"IEEE Trans Cybern"},{"issue":"1","key":"398_CR20","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1109\/TEVC.2005.851275","volume":"10","author":"L While","year":"2006","unstructured":"While L, Hingston P, Barone L, Huband S (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10(1):29\u201338","journal-title":"IEEE Trans Evol Comput"},{"key":"398_CR21","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/978-3-540-31880-4_5","volume-title":"International conference on evolutionary multi-criterion optimization","author":"M Emmerich","year":"2005","unstructured":"Emmerich M, Beume N, Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. International conference on evolutionary multi-criterion optimization. Springer, Berlin, Heidelberg, pp 62\u201376"},{"key":"398_CR22","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1162\/EVCO_a_00009","volume":"19","author":"J Bader","year":"2011","unstructured":"Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19:45\u201376","journal-title":"Evol Comput"},{"key":"398_CR23","doi-asserted-by":"crossref","unstructured":"Brockhoff D, Wagner T, Trautmann H (2012) On the properties of the R2 indicator. In: GECCO\u201912 - proceedings of the 14th international conference on genetic and evolutionary computation, 07\/07","DOI":"10.1145\/2330163.2330230"},{"issue":"2","key":"398_CR24","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1109\/TEVC.2003.810761","volume":"7","author":"PAN Bosman","year":"2003","unstructured":"Bosman PAN, Thierens D (2003) The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans Evol Comput 7(2):174\u2013188","journal-title":"IEEE Trans Evol Comput"},{"key":"398_CR25","doi-asserted-by":"crossref","unstructured":"G\u00f3mez RH, Coello CAC (2015) Improved metaheuristic based on the R2 indicator for many-objective optimization. In: Proceedings of the 2015 annual conference on genetic and evolutionary computation, Madrid, Spain, pp 679\u2013686","DOI":"10.1145\/2739480.2754776"},{"key":"398_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30217-9_84","volume-title":"Indicator-based selection in multiobjective search","author":"E Zitzler","year":"2004","unstructured":"Zitzler E, K\u00fcnzli S (2004) Indicator-based selection in multiobjective search. Springer, Berlin, Heidelberg"},{"key":"398_CR27","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1109\/TEVC.2011.2161872","volume":"16","author":"O Schutze","year":"2012","unstructured":"Schutze O, Esquivel X, Lara A, Coello C (2012) Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization. Evol Comput IEEE Trans 16:504\u2013522","journal-title":"Evol Comput IEEE Trans"},{"issue":"6","key":"398_CR28","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1109\/TCYB.2016.2550502","volume":"47","author":"H Wang","year":"2017","unstructured":"Wang H, Jin Y, Yao X (2017) Diversity assessment in many-objective optimization. IEEE Trans Cybern 47(6):1510\u20131522","journal-title":"IEEE Trans Cybern"},{"issue":"3","key":"398_CR29","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1109\/MCI.2019.2919398","volume":"14","author":"Y Tian","year":"2019","unstructured":"Tian Y, Cheng R, Zhang X, Li M, Jin Y (2019) Diversity assessment of multi-objective evolutionary algorithms: performance metric and benchmark problems [research frontier]. IEEE Comput Intell Mag 14(3):61\u201374","journal-title":"IEEE Comput Intell Mag"},{"issue":"5","key":"398_CR30","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1109\/TEVC.2016.2519378","volume":"20","author":"R Cheng","year":"2016","unstructured":"Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(5):773\u2013791","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"398_CR31","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","volume":"18","author":"K Deb","year":"2014","unstructured":"Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577\u2013601","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"398_CR32","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1109\/TEVC.2016.2592479","volume":"21","author":"S Jiang","year":"2017","unstructured":"Jiang S, Yang S (2017) A strength pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimization. IEEE Trans Evol Comput 21(3):329\u2013346","journal-title":"IEEE Trans Evol Comput"},{"key":"398_CR33","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1145\/1007730.1007731","volume":"6","author":"L Parsons","year":"2004","unstructured":"Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. SIGKDD Explor. 6:90\u2013105","journal-title":"SIGKDD Explor."},{"issue":"2","key":"398_CR34","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1109\/TEVC.2010.2058117","volume":"15","author":"SF Adra","year":"2011","unstructured":"Adra SF, Fleming PJ (2011) Diversity management in evolutionary many-objective optimization. IEEE Trans Evol Comput 15(2):183\u2013195","journal-title":"IEEE Trans Evol Comput"},{"key":"398_CR35","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.ins.2018.01.006","volume":"436\u2013437","author":"J Sun","year":"2018","unstructured":"Sun J, Gong D, Zeng X, Geng N (2018) An ensemble framework for assessing solutions of interval programming problems. Inf Sci 436\u2013437:146\u2013161","journal-title":"Inf Sci"},{"key":"398_CR36","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341\u2013359","journal-title":"J Global Optim"},{"key":"398_CR37","first-page":"115","volume":"9","author":"R Agrawal","year":"2000","unstructured":"Agrawal R, Deb K, Agrawal R (2000) Simulated binary crossover for continuous search space. Complex Systems 9:115\u2013148","journal-title":"Complex Systems"},{"key":"398_CR38","doi-asserted-by":"crossref","unstructured":"Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694\u2013716","DOI":"10.1109\/TEVC.2014.2373386"},{"issue":"2","key":"398_CR39","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1109\/TEVC.2018.2866854","volume":"23","author":"Y Tian","year":"2019","unstructured":"Tian Y, Cheng R, Zhang X, Su Y, Jin Y (2019) A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans Evol Comput 23(2):331\u2013345","journal-title":"IEEE Trans Evol Comput"},{"issue":"9","key":"398_CR40","doi-asserted-by":"publisher","first-page":"5880","DOI":"10.1109\/TSMC.2019.2956288","volume":"51","author":"Y Tian","year":"2021","unstructured":"Tian Y, He C, Cheng R, Zhang X (2021) A multistage evolutionary algorithm for better diversity preservation in multiobjective optimization. IEEE Trans Syst Man Cybern Syst 51(9):5880\u20135894","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"1","key":"398_CR41","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1109\/TEVC.2016.2587808","volume":"21","author":"Y Xiang","year":"2017","unstructured":"Xiang Y, Zhou Y, Li M, Chen Z (2017) A vector angle-based evolutionary algorithm for unconstrained many-objective optimization. IEEE Trans Evol Comput 21(1):131\u2013152","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"398_CR42","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1109\/MCI.2017.2742868","volume":"12","author":"Y Tian","year":"2017","unstructured":"Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [Educational Forum]. IEEE Comput Intell Mag 12(4):73\u201387. https:\/\/doi.org\/10.1109\/MCI.2017.2742868","journal-title":"IEEE Comput Intell Mag"},{"key":"398_CR43","unstructured":"Cheng MLR, Tian Y, Xiang X, Zhang X, Yang S, Jin Y, Yao X (2017) Benchmark functions for the CEC\u20192018 competition on many-objective optimization.\u2019 CERCIA, School Comput. Sci., Univ. Birmingham Edgbaston, Birmingham, U.K., vol. Tech. Rep. CSR-17-01"},{"issue":"2","key":"398_CR44","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","volume":"7","author":"E Zitzler","year":"2003","unstructured":"Zitzler E, Thiele L, Laumanns M, Fonseca CM, Fonseca VGd (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117\u2013132","journal-title":"IEEE Trans Evol Comput"},{"key":"398_CR45","volume-title":"Principles and procedures of statistics: A biometrical approach","author":"JHTRDG Steel","year":"1997","unstructured":"Steel JHTRDG, Dickey DA (1997) Principles and procedures of statistics: A biometrical approach. McGraw-Hill, New York, NY"}],"container-title":["Memetic Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12293-023-00398-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12293-023-00398-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12293-023-00398-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T21:13:55Z","timestamp":1701292435000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12293-023-00398-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,8]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["398"],"URL":"https:\/\/doi.org\/10.1007\/s12293-023-00398-9","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2247305\/v1","asserted-by":"object"}]},"ISSN":["1865-9284","1865-9292"],"issn-type":[{"value":"1865-9284","type":"print"},{"value":"1865-9292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,8]]},"assertion":[{"value":"7 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 August 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}