{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T03:03:02Z","timestamp":1763348582785,"version":"3.40.3"},"publisher-location":"Cham","reference-count":44,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031252624"},{"type":"electronic","value":"9783031252631"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-25263-1_4","type":"book-chapter","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T14:02:22Z","timestamp":1690552942000},"page":"81-111","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Many-Criteria Dominance Relations"],"prefix":"10.1007","author":[{"given":"Andre H.","family":"Deutz","sequence":"first","affiliation":[]},{"given":"Michael","family":"Emmerich","sequence":"additional","affiliation":[]},{"given":"Yali","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,7,29]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"L.\u00a0Batista, F.\u00a0Campelo, F.G. Guimaraes, J.A. Ram\u00edrez, Pareto cone $$\\varepsilon $$-dominance: improving convergence and diversity in multiobjective evolutionary algorithms, in Evolutionary Multi-Criterion Optimization (EMO) (Springer, 2011), pp. 76\u201390","DOI":"10.1007\/978-3-642-19893-9_6"},{"key":"4_CR2","doi-asserted-by":"crossref","unstructured":"P.\u00a0Bentley, J.\u00a0Wakefield, Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms, in Soft computing in engineering design and manufacturing (Springer, 1998), pp. 231\u2013240","DOI":"10.1007\/978-1-4471-0427-8_25"},{"key":"4_CR3","unstructured":"D.\u00a0Bertsekas, A. Nedic, A. Ozdaglar, Convex Analysis and Optimization, vol.\u00a01 (Athena Scientific, 2003)"},{"issue":"2","key":"4_CR4","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1080\/02331938008842650","volume":"11","author":"J Borwein","year":"1980","unstructured":"J. Borwein, The geometry of Pareto efficiency over cones. Mathematische Operationsforschung und Statistik. Series Optimization 11(2), 235\u2013248 (1980)","journal-title":"Mathematische Operationsforschung und Statistik. Series Optimization"},{"key":"4_CR5","doi-asserted-by":"crossref","unstructured":"J.\u00a0Branke, K.\u00a0Deb, H.\u00a0Dierolf, M.\u00a0Osswald, Finding knees in multi-objective optimization, in Parallel Problem Solving from Nature (PPSN) (Springer, 2004), pp. 722\u2013731","DOI":"10.1007\/978-3-540-30217-9_73"},{"issue":"5\u20136","key":"4_CR6","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1002\/mcda.1502","volume":"20","author":"D Brockhoff","year":"2013","unstructured":"D. Brockhoff, J. Bader, L. Thiele, E. Zitzler, Directed multiobjective optimization based on the weighted hypervolume indicator. J. Multi-Criteria Decis. Anal. 20(5\u20136), 291\u2013317 (2013)","journal-title":"J. Multi-Criteria Decis. Anal."},{"issue":"3","key":"4_CR7","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1137\/070697720","volume":"40","author":"C Daskalakis","year":"2011","unstructured":"C. Daskalakis, R.M. Karp, E. Mossel, S.J. Riesenfeld, E. Verbin, Sorting and selection in posets. SIAM J. Comput. 40(3), 597\u2013622 (2011)","journal-title":"SIAM J. Comput."},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"K.\u00a0Deb, Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions, in Advances in evolutionary computing (Springer, 2003), pp. 263\u2013292","DOI":"10.1007\/978-3-642-18965-4_10"},{"issue":"4","key":"4_CR9","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1162\/106365605774666895","volume":"13","author":"K Deb","year":"2005","unstructured":"K. Deb, M. Mohan, S. Mishra, Evaluating the domination based multi-objective evolutionary algorithm for a quick computation of pareto-optimal solutions. Evol. Comput. 13(4), 501\u2013525 (2005)","journal-title":"Evol. Comput."},{"key":"4_CR10","doi-asserted-by":"crossref","unstructured":"K.\u00a0Deb, J.\u00a0Sundar, Reference point based multi-objective optimization using evolutionary algorithms, in Genetic and Evolutionary Computation Conference (GECCO) (ACM Press, 2006), pp. 635\u2013642","DOI":"10.1145\/1143997.1144112"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"N.\u00a0Drechsler, R.\u00a0Drechsler, B.\u00a0Becker, Multi-objective optimisation based on relation favour, in Evolutionary Multi-criterion Optimization (EMO) (Springer, 2001), pp. 154\u2013166","DOI":"10.1007\/3-540-44719-9_11"},{"key":"4_CR12","unstructured":"M.\u00a0Ehrgott, Multicriteria Optimization, 2nd edn (Springer, 2005)"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"G.\u00a0Eichfelder, Variable Ordering Structures in Vector Optimization (Springer, 2014)","DOI":"10.1007\/978-3-642-54283-1"},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1016\/j.protcy.2014.10.001","volume":"16","author":"MTM Emmerich","year":"2014","unstructured":"M.T.M. Emmerich, A. Deutz, I. Yevseyeva, On reference point free weighted hypervolume indicators based on desirability functions and their probabilistic interpretation. Proc. Technol. 16, 532\u2013541 (2014)","journal-title":"Proc. Technol."},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"M.T.M. Emmerich, A.H. Deutz, J.\u00a0Kruisselbrink, P.K. Shukla, Cone-based hypervolume indicators: Construction, properties, and efficient computation, in Evolutionary Multi-criterion Optimization (EMO) (Springer, 2013), pp. 111\u2013127","DOI":"10.1007\/978-3-642-37140-0_12"},{"key":"4_CR16","doi-asserted-by":"crossref","unstructured":"M.\u00a0Farina, P.\u00a0Amato, Fuzzy optimality and evolutionary multiobjective optimization, in Evolutionary Multi-criterion Optimization (EMO) (Springer, 2003), pp. 58\u201372","DOI":"10.1007\/3-540-36970-8_5"},{"key":"4_CR17","doi-asserted-by":"crossref","unstructured":"K.\u00a0Fukuda, A.\u00a0Prodon, Double description method revisited, in Combinatorics and Computer Science, vol. 11210 (Springer, 1995), pp. 91\u2013111","DOI":"10.1007\/3-540-61576-8_77"},{"key":"4_CR18","doi-asserted-by":"crossref","unstructured":"K.\u00a0Ikeda, H.\u00a0Kita, S.\u00a0Kobayashi, Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal? in Congress on Evolutionary Computation (CEC) (IEEE Press, 2001), pp. 957\u2013962","DOI":"10.1109\/CEC.2001.934293"},{"key":"4_CR19","doi-asserted-by":"crossref","unstructured":"H.\u00a0Ishibuchi, N.\u00a0Tsukamoto, Y.\u00a0Nojima, Evolutionary many-objective optimization, in International Workshop on Genetic and Evolving Systems (GEFS) (IEEE Press, 2008), pp. 47\u201352","DOI":"10.1109\/GEFS.2008.4484566"},{"key":"4_CR20","doi-asserted-by":"crossref","unstructured":"I.\u00a0Kaliszewski, Quantitative Pareto Analysis by Cone Separation Technique (Kluwer Academic Press, 1994)","DOI":"10.1007\/978-1-4615-2772-5"},{"issue":"4","key":"4_CR21","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1109\/TEVC.2009.2033586","volume":"14","author":"I Karahan","year":"2010","unstructured":"I. Karahan, M. K\u00f6ksalan, A territory defining multiobjective evolutionary algorithms and preference incorporation. IEEE Trans. Evol. Comput. 14(4), 636\u2013664 (2010)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"4_CR22","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1145\/321906.321910","volume":"22","author":"H Kung","year":"1975","unstructured":"H. Kung, F. Luccio, F. Preparata, On finding the maxima of a set of vectors. J. ACM 22(4), 469\u2013476 (1975)","journal-title":"J. ACM"},{"issue":"3","key":"4_CR23","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1162\/106365602760234108","volume":"10","author":"M Laumanns","year":"2002","unstructured":"M. Laumanns, L. Thiele, K. Deb, E. Zitzler, Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263\u2013282 (2002)","journal-title":"Evol. Comput."},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"K.\u00a0Le, D.\u00a0Landa-Silva, Obtaining better non-dominated sets using volume dominance, in Congress on Evolutionary Computation (CEC) (IEEE Press, 2007), pp. 3119\u20133126","DOI":"10.1109\/CEC.2007.4424870"},{"key":"4_CR25","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.swevo.2018.02.006","volume":"40","author":"L Li","year":"2018","unstructured":"L. Li, Y. Wang, H. Trautmann, N. Jing, M.T.M. Emmerich, Multiobjective evolutionary algorithms based on target region preferences. Swarm Evol. Comput. 40, 196\u2013215 (2018)","journal-title":"Swarm Evol. Comput."},{"key":"4_CR26","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1016\/j.ins.2018.12.078","volume":"509","author":"Y Liu","year":"2020","unstructured":"Y. Liu, N. Zhu, K. Li, M. Li, J. Zheng, K. Li, An angle dominance criterion for evolutionary many-objective optimization. Inf. Sci. 509, 376\u2013399 (2020)","journal-title":"Inf. Sci."},{"key":"4_CR27","doi-asserted-by":"crossref","unstructured":"K.\u00a0Maneeratana, K.\u00a0Boonlong, N.\u00a0Chaiyaratana, Compressed-objective genetic algorithm, in Parallel Problem Solving from Nature (PPSN) (Springer, 2006), pp. 473\u2013482","DOI":"10.1007\/11844297_48"},{"key":"4_CR28","doi-asserted-by":"crossref","unstructured":"K.\u00a0Miettinen, Nonlinear Multiobjective Optimization (Kluwer Academic Publishers, 1999)","DOI":"10.1007\/978-1-4615-5563-6"},{"issue":"4","key":"4_CR29","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s001860000109","volume":"53","author":"K Miettinen","year":"2001","unstructured":"K. Miettinen, M. M\u00e4kel\u00e4, On cone characterizations of weak, proper and Pareto optimality in multiobjective optimization. Math. Methods Oper. Res. 53(4), 233\u2013245 (2001)","journal-title":"Math. Methods Oper. Res."},{"issue":"7","key":"4_CR30","doi-asserted-by":"publisher","first-page":"2733","DOI":"10.1007\/s00500-015-1674-9","volume":"20","author":"K Narukawa","year":"2016","unstructured":"K. Narukawa, Y. Setoguchi, Y. Tanigaki, M. Olhofer, B. Sendhoff, H. Ishibuchi, Preference representation using Gaussian functions on a hyperplane in evolutionary multi-objective optimization. Soft. Comput. 20(7), 2733\u20132757 (2016)","journal-title":"Soft. Comput."},{"key":"4_CR31","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1002\/(SICI)1099-1360(199711)6:6<355::AID-MCDA174>3.0.CO;2-O","volume":"6","author":"V Noghin","year":"1997","unstructured":"V. Noghin, Relative importance of criteria: a quantitative approach. J. Multi-criteria Decis. Anal. 6, 355\u2013363 (1997)","journal-title":"J. Multi-criteria Decis. Anal."},{"key":"4_CR32","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2197\/ipsjdc.3.703","volume":"3","author":"H Sato","year":"2007","unstructured":"H. Sato, H. Aguirre, K. Tanaka, Controlling dominance area of solutions in multiobjective evolutionary algorithms and performance analysis on multiobjective 0\/1 knapsack problems. IPSJ Digit. Cour. 3, 703\u2013718 (2007)","journal-title":"IPSJ Digit. Cour."},{"key":"4_CR33","doi-asserted-by":"crossref","unstructured":"D.\u00a0K. Saxena, S.\u00a0Mittal, S.\u00a0Kapoor, K.\u00a0Deb, A Localized High Fidelity Dominance based Many-Objective Evolutionary Algorithm. Technical report, Michigan State University (2021)","DOI":"10.1109\/TEVC.2022.3188064"},{"issue":"3","key":"4_CR34","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/s101070050128","volume":"87","author":"S Say\u0131n","year":"2000","unstructured":"S. Say\u0131n, Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Math. Program. 87(3), 543\u2013560 (2000)","journal-title":"Math. Program."},{"key":"4_CR35","doi-asserted-by":"publisher","first-page":"6299","DOI":"10.1088\/0031-9155\/54\/20\/018","volume":"54","author":"J Serna","year":"2009","unstructured":"J. Serna, M. Monz, K.-H. K\u00fcfer, C. Thieke, Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning. Phys. Med. Biol. 54, 6299\u20136311 (2009)","journal-title":"Phys. Med. Biol."},{"key":"4_CR36","doi-asserted-by":"crossref","unstructured":"P.\u00a0Shukla, C.\u00a0Hirsch, H.\u00a0Schmeck, In search of equitable solutions using multi-objective evolutionary algorithms, in Parallel Problem Solving from Nature (PPSN) (Springer, 2010), pp. 687\u2013696","DOI":"10.1007\/978-3-642-15844-5_69"},{"issue":"1","key":"4_CR37","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/03052150802347926","volume":"41","author":"H Trautmann","year":"2009","unstructured":"H. Trautmann, J. Mehnen, Preference-based Pareto optimization in certain and noisy environments. Eng. Optim. 41(1), 23\u201338 (2009)","journal-title":"Eng. Optim."},{"key":"4_CR38","doi-asserted-by":"crossref","unstructured":"Y.\u00a0Wang, A.\u00a0Deutz, T.\u00a0B\u00e4ck, M.\u00a0Emmerich, Improving many-objective evolutionary algorithms by means of edge-rotated cones, in Parallel Problem Solving from Nature (PPSN) (Springer, 2008), pp. 313\u2013326","DOI":"10.1007\/978-3-030-58115-2_22"},{"issue":"2","key":"4_CR39","first-page":"153","volume":"1","author":"MM Wiecek","year":"2007","unstructured":"M.M. Wiecek, Advances in cone-based preference modeling for decision making with multiple criteria. Decis. Mak. Manufact. Ser. 1(2), 153\u2013173 (2007)","journal-title":"Decis. Mak. Manufact. Ser."},{"issue":"5","key":"4_CR40","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1109\/TEVC.2012.2227145","volume":"17","author":"S Yang","year":"2013","unstructured":"S. Yang, M. Li, X. Liu, J. Zheng, A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 17(5), 721\u2013736 (2013)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"4_CR41","doi-asserted-by":"crossref","unstructured":"I.\u00a0Yevseyeva, A.P. Guerreiro, M.T.M. Emmerich, C.M. Fonseca, A portfolio optimization approach to selection in multiobjective evolutionary algorithms, in Parallel Problem Solving from Nature (PPSN) (Springer, 2014), pp. 672\u2013681","DOI":"10.1007\/978-3-319-10762-2_66"},{"key":"4_CR42","doi-asserted-by":"crossref","unstructured":"P.\u00a0Yu, G.\u00a0Leitmann, Nondominated decisions and cone convexity in dynamic multicriteria decision problems, in Multicriteria Decision Making and Differential Games (Springer, 1976), pp. 61\u201372","DOI":"10.1007\/978-1-4615-8768-2_2"},{"key":"4_CR43","doi-asserted-by":"crossref","unstructured":"E.\u00a0Zitzler, L.\u00a0Thiele, J.\u00a0Bader, SPAM: set preference algorithm for multiobjective optimization, in Parallel Problem Solving from Nature (PPSN) (Springer, 2008), pp. 847\u2013858","DOI":"10.1007\/978-3-540-87700-4_84"},{"issue":"2","key":"4_CR44","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","volume":"7","author":"E Zitzler","year":"2003","unstructured":"E. Zitzler, L. Thiele, M. Laumanns, C.M. Fonseca, V. Grunert da Fonseca, Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117\u2013132 (2003)","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Natural Computing Series","Many-Criteria Optimization and Decision Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-25263-1_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T07:23:27Z","timestamp":1729841007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-25263-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031252624","9783031252631"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-25263-1_4","relation":{},"ISSN":["1619-7127","2627-6461"],"issn-type":[{"type":"print","value":"1619-7127"},{"type":"electronic","value":"2627-6461"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"29 July 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}