{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T10:03:13Z","timestamp":1772100193307,"version":"3.50.1"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"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 Foundation of China","doi-asserted-by":"publisher","award":["62001500"],"award-info":[{"award-number":["62001500"]}],"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":["62071480"],"award-info":[{"award-number":["62071480"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s00500-025-10970-9","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:37:25Z","timestamp":1768991845000},"page":"835-852","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A many-objective evolutionary algorithm based on reference vectors and hyper-distance"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3290-9318","authenticated-orcid":false,"given":"Xujian","family":"Wang","sequence":"first","affiliation":[]},{"given":"Yongjin","family":"Jing","sequence":"additional","affiliation":[]},{"given":"Fenggan","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Minli","family":"Yao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"issue":"1","key":"10970_CR1","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(1):45\u201376","journal-title":"Evol Comput"},{"issue":"7","key":"10970_CR2","doi-asserted-by":"publisher","first-page":"3367","DOI":"10.1109\/TCYB.2019.2899225","volume":"50","author":"H Chen","year":"2020","unstructured":"Chen H, Tian Y, Pedrycz W, Wu G, Wang R, Wang L (2020) Hyperplane assisted evolutionary algorithm for many-objective optimization problems. IEEE Trans Cybern 50(7):3367\u20133380","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"10970_CR3","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1109\/TETCI.2017.2669104","volume":"1","author":"R Cheng","year":"2017","unstructured":"Cheng R, Rodemann T, Fischer M, Olhofer M, Jin Y (2017) Evolutionary many-objective optimization of hybrid electric vehicle control: from general optimization to preference articulation. IEEE Trans Emerg Top Comput Intell 1(2):97\u2013111","journal-title":"IEEE Trans Emerg Top Comput Intell"},{"issue":"5","key":"10970_CR4","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"},{"key":"10970_CR5","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1016\/j.swevo.2018.11.003","volume":"44","author":"SS Das","year":"2019","unstructured":"Das SS, Islam MM, Arafat NA (2019) Evolutionary algorithm using adaptive fuzzy dominance and reference point for many-objective optimization, swarm. Evol Comput 44:1092\u20131107","journal-title":"Evol Comput"},{"issue":"3","key":"10970_CR6","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I Das","year":"1998","unstructured":"Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631\u2013657","journal-title":"SIAM J Optim"},{"issue":"4","key":"10970_CR7","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"},{"key":"10970_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116499","volume":"195","author":"J Dong","year":"2022","unstructured":"Dong J, Gong W, Ming F (2022) A two-stage evolutionary algorithm based on three indicators for constrained multi-objective optimization. Expert Syst Appl 195:116499","journal-title":"Expert Syst Appl"},{"issue":"7","key":"10970_CR9","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1109\/TSMC.2017.2654301","volume":"48","author":"M Elarbi","year":"2018","unstructured":"Elarbi M, Bechikh S, Gupta A, Ben Said L, Ong Y-S (2018) A new decomposition-based NSGA-II for many-objective optimization. IEEE Trans Syst Man Cybern Syst 48(7):1191\u20131210","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"2","key":"10970_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3376916","volume":"53","author":"JG Falc\u00f3n-Cardona","year":"2020","unstructured":"Falc\u00f3n-Cardona JG, Coello Coello CA (2020) Indicator-based multi-objective evolutionary algorithms: a comprehensive survey. ACM Comput Surv 53(2):1\u201335","journal-title":"ACM Comput Surv"},{"key":"10970_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.108677","volume":"246","author":"R Fan","year":"2022","unstructured":"Fan R, Wei L, Hu Z, Sun H (2022) MMOEA-SP: a multistage many-objective evolutionary algorithm based on sampling points. Knowl Based Syst 246:108677","journal-title":"Knowl Based Syst"},{"issue":"4","key":"10970_CR12","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1109\/TEVC.2018.2874465","volume":"23","author":"H Ge","year":"2019","unstructured":"Ge H, Zhao M, Sun L, Wang Z, Tan G, Zhang Q, Chen CLP (2019) A many-objective evolutionary algorithm with two interacting processes: cascade clustering and reference point incremental learning. IEEE Trans Evol Comput 23(4):572\u2013586","journal-title":"IEEE Trans Evol Comput"},{"key":"10970_CR13","doi-asserted-by":"crossref","unstructured":"G\u00f3mez RH, Coello Coello CA (2013) MOMBI: a new metaheuristic for many-objective optimization based on the R2 indicator. In: Proc. IEEE congr. evol. comput., Cancun, Mexico, pp 2488\u20132495","DOI":"10.1109\/CEC.2013.6557868"},{"issue":"2","key":"10970_CR14","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":"2","key":"10970_CR15","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1109\/TSMC.2020.3003926","volume":"52","author":"C He","year":"2022","unstructured":"He C, Cheng R, Yazdani D (2022) Adaptive offspring generation for evolutionary large-scale multiobjective optimization. IEEE Trans Syst Man Cybern Syst 52(2):786\u2013798","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"10970_CR16","doi-asserted-by":"crossref","unstructured":"G\u00f3mez RH, Coello Coello CA (2015) Improved metaheuristic based on the R2 indicator for many-objective optimization. In: Proc. annu. conf. genet. evol. comput., Madrid, Spain, pp 679\u2013686","DOI":"10.1145\/2739480.2754776"},{"issue":"2","key":"10970_CR17","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1109\/TEVC.2016.2587749","volume":"21","author":"H Ishibuchi","year":"2017","unstructured":"Ishibuchi H, Setoguchi Y, Masuda H, Nojima Y (2017) Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans Evol Comput 21(2):169\u2013190","journal-title":"IEEE Trans Evol Comput"},{"issue":"10","key":"10970_CR18","doi-asserted-by":"publisher","first-page":"2202","DOI":"10.1109\/TCYB.2014.2367526","volume":"45","author":"S Jiang","year":"2015","unstructured":"Jiang S, Zhang J, Ong Y-S, Zhang AN, Tan PS (2015) A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans Cybern 45(10):2202\u20132213","journal-title":"IEEE Trans Cybern"},{"issue":"12","key":"10970_CR19","doi-asserted-by":"publisher","first-page":"2416","DOI":"10.1109\/TSMC.2018.2818175","volume":"49","author":"Q Kang","year":"2019","unstructured":"Kang Q, Song X, Zhou M, Li L (2019) A collaborative resource allocation strategy for decomposition-based multiobjective evolutionary algorithms. IEEE Trans Syst Man Cybern Syst 49(12):2416\u20132423","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"3","key":"10970_CR20","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1162\/106365602760234108","volume":"10","author":"M Laumanns","year":"2002","unstructured":"Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multiobjective optimization. Evol Comput 10(3):263\u2013282","journal-title":"Evol Comput"},{"issue":"1","key":"10970_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2792984","volume":"48","author":"B Li","year":"2015","unstructured":"Li B, Li J, Tang K, Yao X (2015a) Many-objective evolutionary algorithms: a survey. ACM Comput Surv 48(1):1\u201335","journal-title":"ACM Comput Surv"},{"key":"10970_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106661","volume":"96","author":"L Li","year":"2020","unstructured":"Li L, Li G, Chang L (2020) A many-objective particle swarm optimization with grid dominance ranking and clustering. Appl Soft Comput 96:106661","journal-title":"Appl Soft Comput"},{"issue":"3","key":"10970_CR23","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":"5","key":"10970_CR24","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1109\/TEVC.2015.2504730","volume":"20","author":"M Li","year":"2016","unstructured":"Li M, Yang S, Liu X (2016) Pareto or non-Pareto: bi-criterion evolutionin multiobjective optimization. IEEE Trans Evol Comput 20(5):645\u2013665","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"10970_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3300148","volume":"52","author":"M Li","year":"2020","unstructured":"Li M, Yao X (2020) Quality evaluation of solution sets in multiobjective optimisation: a survey. ACM Comput Surv 52(2):1\u201338","journal-title":"ACM Comput Surv"},{"issue":"5","key":"10970_CR26","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1109\/TEVC.2014.2373386","volume":"19","author":"K Li","year":"2015","unstructured":"Li K, Deb K, Zhang Q, Kwong S (2015b) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694\u2013716","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"10970_CR27","doi-asserted-by":"publisher","first-page":"1417","DOI":"10.1109\/TCYB.2019.2918087","volume":"51","author":"Z Liang","year":"2021","unstructured":"Liang Z, Hu K, Ma X, Zhu Z (2021) A many-objective evolutionary algorithm based on a two-round selection strategy. IEEE Trans Cybern 51(3):1417\u20131429","journal-title":"IEEE Trans Cybern"},{"issue":"3","key":"10970_CR28","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1109\/TEVC.2013.2281533","volume":"18","author":"H Liu","year":"2014","unstructured":"Liu H, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450\u2013455","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"10970_CR29","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1109\/TEVC.2017.2725902","volume":"22","author":"H Liu","year":"2018","unstructured":"Liu H, Chen L, Zhang Q, Deb K (2018) Adaptively allocating search effort in challenging many-objective optimization problems. IEEE Trans Evol Comput 22(3):433\u2013448","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"10970_CR30","first-page":"439","volume":"24","author":"Y Liu","year":"2020","unstructured":"Liu Y, Ishibuchi H, Masuyama N, Nojima Y (2020a) Adapting reference vectors and scalarizing functions by growing neural gas to handle irregular pareto fronts. IEEE Trans Evol Comput 24(3):439\u2013453","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"10970_CR31","doi-asserted-by":"publisher","first-page":"2698","DOI":"10.1109\/TCYB.2020.3020630","volume":"52","author":"Q Liu","year":"2022","unstructured":"Liu Q, Jin Y, Heiderich M, Rodemann T, Yu G (2022) An adaptive reference vector-guided evolutionary algorithm using growing neural gas for many-objective optimization of irregular problems. IEEE Trans Cybern 52(5):2698\u20132711","journal-title":"IEEE Trans Cybern"},{"key":"10970_CR32","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.ins.2020.03.104","volume":"537","author":"S Liu","year":"2020","unstructured":"Liu S, Yu Q, Lin Q, Tan KC (2020b) An adaptive clustering-based evolutionary algorithm for many-objective optimization problems. Inf Sci 537:261\u2013283","journal-title":"Inf Sci"},{"key":"10970_CR33","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1016\/j.ins.2018.06.063","volume":"509","author":"Z Liu","year":"2020","unstructured":"Liu Z, Wang Y, Huang P (2020c) AnD: a many-objective evolutionary algorithm with angle-based selection and shift-based density estimation. Inf Sci 509:400\u2013419","journal-title":"Inf Sci"},{"key":"10970_CR34","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1016\/j.asoc.2016.11.009","volume":"50","author":"Y Liu","year":"2017","unstructured":"Liu Y, Gong D, Sun X, Zhang Y (2017) Many-objective evolutionary optimization based on reference points. Appl Soft Comput 50:344\u2013355","journal-title":"Appl Soft Comput"},{"issue":"4","key":"10970_CR35","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1109\/TEVC.2020.2978158","volume":"24","author":"X Ma","year":"2020","unstructured":"Ma X, Yu Y, Li X, Qi Y, Zhu Z (2020) A survey of weight vector adjustment methods for decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evol Comput 24(4):634\u2013649","journal-title":"IEEE Trans Evol Comput"},{"issue":"10","key":"10970_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TSMC.2022.3143657","volume":"52","author":"F Ming","year":"2022","unstructured":"Ming F, Gong W, Wang L (2022a) A two-stage evolutionary algorithm with balanced convergence and diversity for many-objective optimization. IEEE Trans Syst Man Cybern Syst 52(10):1\u201313","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"10970_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2022.101055","volume":"70","author":"F Ming","year":"2022","unstructured":"Ming F, Gong W, Wang L (2022b) A tri-population based co-evolutionary framework for constrained multi-objective optimization problems. Swarm Evol Comput 70:101055","journal-title":"Swarm Evol Comput"},{"key":"10970_CR38","doi-asserted-by":"crossref","unstructured":"Brockhoff D, Wagner T, Trautmann H (2012) On the properties of the R2 indicator. In: Proc. annu. conf. genet. evol. comput., New York, NY, USA, 2012, pp 465\u2013472","DOI":"10.1145\/2330163.2330230"},{"issue":"2","key":"10970_CR39","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1109\/TEVC.2018.2848921","volume":"23","author":"T Pamulapati","year":"2019","unstructured":"Pamulapati T, Mallipeddi R, Suganthan PN (2019) Isde+ - an indicator for multi and many-objective optimization. IEEE Trans Evol Comput 23(2):346\u2013352","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"10970_CR40","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1109\/TEVC.2006.876362","volume":"11","author":"FD Pierro","year":"2007","unstructured":"Pierro FD, Khu ST, Savic DA (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11(1):17\u201345","journal-title":"IEEE Trans Evol Comput"},{"key":"10970_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2022.101082","volume":"71","author":"MSS Raju","year":"2022","unstructured":"Raju MSS, Mallipeddi R, Das KN (2022) A twin-archive guided decomposition based multi\/many-objective evolutionary algorithm. Swarm Evol Comput 71:101082","journal-title":"Swarm Evol Comput"},{"issue":"5","key":"10970_CR42","doi-asserted-by":"publisher","first-page":"3645","DOI":"10.1109\/TCYB.2020.3015998","volume":"52","author":"J Shen","year":"2022","unstructured":"Shen J, Wang P, Wang X (2022) A controlled strengthened dominance relation for evolutionary many-objective optimization. IEEE Trans Cybern 52(5):3645\u20133657","journal-title":"IEEE Trans Cybern"},{"issue":"5","key":"10970_CR43","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1109\/TSMCC.2012.2188285","volume":"42","author":"VA Shim","year":"2012","unstructured":"Shim VA, Tan KC, Cheong CY (2012) A hybrid estimation of distribution algorithm with decomposition for solving the multiobjective multiple traveling salesman problem. IEEE Trans Syst Man Cybern Part C (Appl Rev) 42(5):682\u2013691","journal-title":"IEEE Trans Syst Man Cybern Part C (Appl Rev)"},{"issue":"2","key":"10970_CR44","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1109\/TEVC.2018.2791283","volume":"23","author":"Y Sun","year":"2019","unstructured":"Sun Y, Yen GG, Zhang Y (2019) IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput 23(2):173\u2013187","journal-title":"IEEE Trans Evol Comput"},{"key":"10970_CR45","doi-asserted-by":"crossref","unstructured":"Tian Y, Zhang X, Cheng R, Jin Y (2016) A multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric. In: Proc. IEEE Congr. Evol. Comput., Vancouver, BC, Canada","DOI":"10.1109\/CEC.2016.7748352"},{"issue":"2","key":"10970_CR46","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":"4","key":"10970_CR47","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1109\/TEVC.2017.2749619","volume":"22","author":"Y Tian","year":"2018","unstructured":"Tian Y, Cheng R, Zhang X, Cheng F, Jin Y (2018) An indicator based multi-objective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput 22(4):609\u2013622","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"10970_CR48","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 plat-form for evolutionary multi-objective optimization. IEEE Comput Intell Mag 12(4):73\u201387","journal-title":"IEEE Comput Intell Mag"},{"issue":"3","key":"10970_CR49","first-page":"440","volume":"21","author":"A Trivedi","year":"2017","unstructured":"Trivedi A, Srinivasan D, Sanyal K, Ghosh A (2017) A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput 21(3):440\u2013462","journal-title":"IEEE Trans Evol Comput"},{"key":"10970_CR50","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-023-01161-w","author":"X Wang","year":"2024","unstructured":"Wang X, Zhang F, Yao M (2024) A many-objective evolutionary algorithm with metric-based reference vector adjustment. Complex Intell Syst. https:\/\/doi.org\/10.1007\/s40747-023-01161-w","journal-title":"Complex Intell Syst"},{"issue":"1","key":"10970_CR51","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1109\/TEVC.2019.2909636","volume":"24","author":"Y Xiang","year":"2020","unstructured":"Xiang Y, Zhou Y, Yang X, Huang H (2020) A many-objective evolutionary algorithm with pareto-adaptive reference points. IEEE Trans Evol Comput 24(1):99\u2013113","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"10970_CR52","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 problems. IEEE Trans Evol Comput 21(1):131\u2013152","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"10970_CR53","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"},{"key":"10970_CR54","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.knosys.2017.08.006","volume":"135","author":"X Ye","year":"2017","unstructured":"Ye X, Liu S, Yin Y, Jin Y (2017) User-oriented many-objective cloud work-flow scheduling based on an improved knee point driven evolutionary algorithm. Knowledge-Based Syst 135:113\u2013124","journal-title":"Knowledge-Based Syst"},{"issue":"2","key":"10970_CR55","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1109\/TCYB.2018.2871673","volume":"50","author":"X Zhang","year":"2020","unstructured":"Zhang X, Zhou K, Pan H, Zhang L, Zeng X, Jin Y (2020) A network reduction-based multiobjective evolutionary algorithm for community detection in large-scale complex networks. IEEE Trans Cybern 50(2):703\u2013716","journal-title":"IEEE Trans Cybern"},{"issue":"6","key":"10970_CR56","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"},{"key":"10970_CR57","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.118333","volume":"209","author":"J Zhang","year":"2022","unstructured":"Zhang J, Cao J, Zhao F, Chen Z (2022) An angle-based many-objective evolutionary algorithm with shift-based density estimation and sum of objectives. Expert Syst Appl 209:118333","journal-title":"Expert Syst Appl"},{"issue":"1","key":"10970_CR58","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.swevo.2011.03.001","volume":"1","author":"A Zhou","year":"2011","unstructured":"Zhou A, Qu B, Li H, Zhao S, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1(1):32\u201349","journal-title":"Swarm Evol Comput"},{"key":"10970_CR59","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/j.ins.2021.05.080","volume":"574","author":"J Zhou","year":"2021","unstructured":"Zhou J, Gao L, Li X, Zhang C, Hu C (2021a) Hyperplane-driven and projection-assisted search for solving many-objective optimization problem. Inf Sci 574:394\u2013412","journal-title":"Inf Sci"},{"key":"10970_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106872","volume":"99","author":"J Zhou","year":"2021","unstructured":"Zhou J, Yao X, Gao L, Hu C (2021b) An indicator and adaptive region division based evolutionary algorithm for many-objective optimization. Appl Soft Comput 99:106872","journal-title":"Appl Soft Comput"},{"issue":"6","key":"10970_CR61","doi-asserted-by":"publisher","first-page":"2073","DOI":"10.1109\/TCYB.2018.2819360","volume":"49","author":"Y Zhou","year":"2019","unstructured":"Zhou Y, Xiang Y, Chen Z, He J, Wang J (2019) A scalar projection and angle-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Cybern 49(6):2073\u20132084","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"10970_CR62","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1109\/TEVC.2015.2457245","volume":"20","author":"C Zhu","year":"2016","unstructured":"Zhu C, Xu L, Goodman ED (2016) Generalization of Pareto-optimality for many-objective evolutionary optimization. IEEE Trans Evol Comput 20(2):299\u2013315","journal-title":"IEEE Trans Evol Comput"},{"issue":"8","key":"10970_CR63","doi-asserted-by":"publisher","first-page":"7776","DOI":"10.1109\/TCYB.2021.3051078","volume":"52","author":"S Zhu","year":"2022","unstructured":"Zhu S, Xu L, Goodman ED, Lu Z (2022) A new many-objective evolutionary algorithm based on generalized pareto dominance. IEEE Trans Cybern 52(8):7776\u20137790","journal-title":"IEEE Trans Cybern"},{"issue":"1","key":"10970_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106192","volume":"90","author":"J Zou","year":"2020","unstructured":"Zou J, Yang Q, Yang S, Zheng J (2020) Ra-dominance: a new dominance relationship for preference-based evolutionary multiobjective optimization. Appl Soft Comput 90(1):106192","journal-title":"Appl Soft Comput"},{"issue":"5","key":"10970_CR65","doi-asserted-by":"publisher","first-page":"1402","DOI":"10.1109\/TSMCB.2008.926329","volume":"38","author":"X Zou","year":"2008","unstructured":"Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybern B Cybern 38(5):1402\u20131412","journal-title":"IEEE Trans Syst Man Cybern B Cybern"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10970-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-025-10970-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10970-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T09:04:46Z","timestamp":1772096686000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-025-10970-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,21]]},"references-count":65,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10970"],"URL":"https:\/\/doi.org\/10.1007\/s00500-025-10970-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,21]]},"assertion":[{"value":"5 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2026","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 there is no conflict of interest in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This paper 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"}}]}}