{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T10:28:08Z","timestamp":1769855288697,"version":"3.49.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s00500-014-1570-8","type":"journal-article","created":{"date-parts":[[2014,12,31]],"date-time":"2014-12-31T11:49:14Z","timestamp":1420026554000},"page":"1105-1111","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["An improved $${\\alpha }$$ \u03b1 -dominance strategy for many-objective optimization problems"],"prefix":"10.1007","volume":"20","author":[{"given":"Cai","family":"Dai","sequence":"first","affiliation":[]},{"given":"Yuping","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Lijuan","family":"Hu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,1,1]]},"reference":[{"key":"1570_CR1","doi-asserted-by":"crossref","unstructured":"Auger A, Bader J, Brockhoff D, Zitzler E (2009) Theory of the hypervolume indicator: optimal $$\\mu $$ \u03bc -distributions and the choice of the reference point. In: Proceedings of the foundations of genetic algorithm, vol X, pp 87\u2013102","DOI":"10.1145\/1527125.1527138"},{"key":"1570_CR2","doi-asserted-by":"crossref","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":"1570_CR3","unstructured":"Bentley PJ, Wakefield JP (1997) Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms. World Conf Soft Comput Des Manuf. 231\u2013240"},{"issue":"3","key":"1570_CR4","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1016\/j.ejor.2006.08.008","volume":"180","author":"N Beume","year":"2007","unstructured":"Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 180(3):1653\u20131669","journal-title":"Eur J Oper Res"},{"issue":"5","key":"1570_CR5","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1109\/TEVC.2009.2015575","volume":"13","author":"N Beume","year":"2009","unstructured":"Beume N, Fonseca C, L\u00f3pez-Ib\u00e1\u00f1e M, Paquete L, Vahrenhold J (2009) On the complexity of computing the hypervolume indicator. IEEE Trans Evol Comput 13(5):1075\u20131082","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1570_CR6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10710-005-6164-x","volume":"6","author":"CA Coello Coello","year":"2005","unstructured":"Coello Coello CA, Cruz Cort\u00e9s N (2005) Solving multiobjective optimization problems using an artificial immune system. Genet Program Evol Mach 6(2):163\u2013190","journal-title":"Genet Program Evol Mach"},{"key":"1570_CR7","doi-asserted-by":"crossref","unstructured":"Coello Coello CA, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multiobjective problems. Kluwer, New York","DOI":"10.1007\/978-1-4757-5184-0"},{"key":"1570_CR8","volume-title":"Evolutionary algorithms for solving multi-objective problems (genetic and evolutionary computation)","author":"CA Coello Coello","year":"2006","unstructured":"Coello Coello CA, Lamont GB, Van Veldhuizen DA (2006) Evolutionary algorithms for solving multi-objective problems (genetic and evolutionary computation). Springer-Verlag, New York"},{"key":"1570_CR9","volume-title":"Multiobjective optimization using evolutionary algorithms","author":"K Deb","year":"2001","unstructured":"Deb K (2001) Multiobjective optimization using evolutionary algorithms. Wiley, New York"},{"issue":"2","key":"1570_CR10","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb K, Agrawal S, Pratap A, 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"},{"key":"1570_CR11","doi-asserted-by":"crossref","unstructured":"Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Congress on evolutionary computation (CEC 2002), pp 825\u2013830","DOI":"10.1109\/CEC.2002.1007032"},{"key":"1570_CR12","doi-asserted-by":"crossref","unstructured":"Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization, pp 105\u2013145. Springer, London","DOI":"10.1007\/1-84628-137-7_6"},{"issue":"1","key":"1570_CR13","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TEVC.2006.876362","volume":"11","author":"F Pierro di","year":"2007","unstructured":"di Pierro F, Khu S-T, Savi\u2019c 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"},{"issue":"3","key":"1570_CR14","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1109\/TSMCA.2004.824873","volume":"34","author":"M Farina","year":"2004","unstructured":"Farina M, Amato P (2004) A fuzzy definition of \u201coptimality\u201d for many-criteria optimization problems. IEEE Trans Syst Man Cybern Part A Syst Hum 34(3):315\u2013326","journal-title":"IEEE Trans Syst Man Cybern Part A Syst Hum"},{"key":"1570_CR15","doi-asserted-by":"crossref","unstructured":"Friedrich T, Horoba C, Neumann F (2009) Multiplicative approximations and the hypervolume indicator. In: Proceedings of the 2009 genetic and evolutionary computation conference, pp 571\u2013578","DOI":"10.1145\/1569901.1569981"},{"key":"1570_CR16","doi-asserted-by":"crossref","unstructured":"Hughes EJ (2005) Evolutionary many-objective optimization: many once or one many? In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 222\u2013227","DOI":"10.1109\/CEC.2005.1554688"},{"key":"1570_CR17","doi-asserted-by":"crossref","unstructured":"Hughes EJ (2007) MSOPS-II: a general-purpose many-objective optimizer. In: Proceedings of the 2007 IEEE congress on evolutionary computation, pp 3944\u20133951","DOI":"10.1109\/CEC.2007.4424985"},{"key":"1570_CR18","doi-asserted-by":"crossref","unstructured":"Ishibuchi H, Nojima Y (2007) Optimization, of scalarizing functions through evolutionary multiobjective optimization. In: Lecture notes in computer science, vol 4403. Evolutionary multi-criterion optimization, EMO, pp 51\u201365. Springer, Berlin","DOI":"10.1007\/978-3-540-70928-2_8"},{"key":"1570_CR19","doi-asserted-by":"crossref","unstructured":"Ishibuchi H, Sakane Y, Tsukamoto N, Nojima Y (2009) Evolutionary many-objective optimization by NSGA-II and MOEA\/D with large populations. In: Proceedings of 2009 IEEE international conference on systems, man, and cybernetics, pp 1820\u20131825","DOI":"10.1109\/ICSMC.2009.5346628"},{"key":"1570_CR20","doi-asserted-by":"crossref","unstructured":"Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. IEEE Congr Evol Comput 2419\u20132426","DOI":"10.1109\/GEFS.2008.4484566"},{"key":"1570_CR21","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.artint.2013.08.001","volume":"204","author":"Bringmann Karl","year":"2013","unstructured":"Karl Bringmann, Tobias Friedrich, Christian Igel, Thomas Vo\u00df (2013) Speeding up many-objective optimization by Monte Carlo approximations. Artif Intell 204:22\u201329","journal-title":"Artif Intell"},{"key":"1570_CR22","doi-asserted-by":"crossref","unstructured":"Kokolo I, Hajime K, Shigenobu K (2001) Failure of pareto-based MOEAs: does nondominated really mean near to optimal? Proc Congr Evol Comput 2:957\u2013962","DOI":"10.1109\/CEC.2001.934293"},{"issue":"16","key":"1570_CR23","doi-asserted-by":"crossref","first-page":"2799","DOI":"10.1016\/j.neucom.2010.06.022","volume":"73","author":"I Kokshenev","year":"2010","unstructured":"Kokshenev I, Braga AP (2010) An efficient multi-objective learning algorithm for RBF neural network. Neurocomputing 73(16):2799\u20132808","journal-title":"Neurocomputing"},{"key":"1570_CR24","unstructured":"Le K, Landa-Silva D (2007) Obtaining better non-dominated sets using volume dominance. In: 2007 IEEE congress on evolutionary computation, pp 3119\u20133126"},{"key":"1570_CR25","doi-asserted-by":"crossref","unstructured":"Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA\/D and NSGA-II. IEEE Trans Evol Comput 13(2):284\u2013302","DOI":"10.1109\/TEVC.2008.925798"},{"key":"1570_CR26","first-page":"66","volume":"2009","author":"A Nebro","year":"2009","unstructured":"Nebro A, Durillo J, Garcia-Nieto J, Coello CAC, Luna F, Alba E (2009) SMPSO: a new PSO-based metaheuristic for multi-objective optimization. IEEE Sympos Comput Intell Multicriteria Decis Mak 2009:66\u201373","journal-title":"IEEE Sympos Comput Intell Multicriteria Decis Mak"},{"key":"1570_CR27","volume-title":"Principles and procedures of statistics: a biometrical approach","author":"S Robert","year":"1997","unstructured":"Robert S, Torrie J, Dickey D (1997) Principles and procedures of statistics: a biometrical approach. McGraw-Hill, New York"},{"key":"1570_CR28","doi-asserted-by":"crossref","unstructured":"Sato H, Aguirre HE, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of mOEAs. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T (eds) EMO 2007. LNCS, vol 4403, pp 5\u201320. Springer, Heidelberg","DOI":"10.1007\/978-3-540-70928-2_5"},{"issue":"4","key":"1570_CR29","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TEVC.2011.2161872","volume":"16","author":"O Schutze","year":"2012","unstructured":"Schutze O, Esquivel X, Lara A, Coello Coello CA (2012) Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization. IEEE Trans Evol Comput 16(4):504\u2013522","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"1570_CR30","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1109\/4235.974840","volume":"5","author":"KC Tan","year":"2001","unstructured":"Tan KC, Lee TH, Khor EF (2001) Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Trans Evol Comput 5(6):565\u2013588","journal-title":"IEEE Trans Evol Comput"},{"key":"1570_CR31","unstructured":"Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. dissertation, Department ofElectrical and Computer Engineering, Graduate School Engineering, Air Force Institute ofTechnology, Wright-Patterson AFB, OH"},{"key":"1570_CR32","doi-asserted-by":"crossref","unstructured":"Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation-, and indicator-based methods in manyobjective optimization. In: Lecture notes in computer science, vol 4403. Evolutionary multi-criterion optimization\u2014EMO, pp 742\u2013756. Springer, Berlin","DOI":"10.1007\/978-3-540-70928-2_56"},{"issue":"6","key":"1570_CR33","doi-asserted-by":"crossref","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":"1570_CR34","doi-asserted-by":"crossref","unstructured":"Zitzler E, K\u00fcnzli S (2004) Indicator-based selection in multiobjective search. In: Lecture notes in computer science, vol 3242. Parallel problem solving from nature\u2014PPSN VIII, pp 832\u2013842. Springer, Berlin","DOI":"10.1007\/978-3-540-30217-9_84"},{"issue":"5","key":"1570_CR35","doi-asserted-by":"crossref","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 Part B Cybern 38(5):1402\u20131412","journal-title":"IEEE Trans Syst Man Cybern Part B Cybern"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-014-1570-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-014-1570-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-014-1570-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T19:05:56Z","timestamp":1747335956000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-014-1570-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,1]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["1570"],"URL":"https:\/\/doi.org\/10.1007\/s00500-014-1570-8","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,1]]}}}