{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T07:01:00Z","timestamp":1772262060326,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T00:00:00Z","timestamp":1447718400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Basic Research Program (973 Program) of China","award":["2013CB329402"],"award-info":[{"award-number":["2013CB329402"]}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/J017515\/1"],"award-info":[{"award-number":["EP\/J017515\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Cheung Kong Scholars and Innovative Research Team in University","award":["IRT1170"],"award-info":[{"award-number":["IRT1170"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61329302"],"award-info":[{"award-number":["61329302"]}],"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":["91438103 and 91438201"],"award-info":[{"award-number":["91438103 and 91438201"]}],"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":[[2017,5]]},"DOI":"10.1007\/s00500-015-1940-x","type":"journal-article","created":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T04:11:35Z","timestamp":1447733495000},"page":"2283-2295","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Nadir point estimation for many-objective optimization problems based on emphasized critical regions"],"prefix":"10.1007","volume":"21","author":[{"given":"Handing","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,11,17]]},"reference":[{"issue":"6","key":"1940_CR1","doi-asserted-by":"crossref","first-page":"7222","DOI":"10.1016\/j.eswa.2010.12.061","volume":"36","author":"M Amiri","year":"2010","unstructured":"Amiri M, Ekhtiari M, Yazdani M (2010) Nadir compromise programming: a model for optimization of multi-objective portfolio problem. Expert Syst Appl 36(6):7222\u20137226","journal-title":"Expert Syst Appl"},{"key":"1940_CR2","doi-asserted-by":"publisher","unstructured":"Bechikh S, Ben Said L, Ghedira K (2010) Estimating nadir point in multi-objective optimization using mobile reference points. In: Evolutionary computation (CEC), 2010 IEEE congress on, IEEE Press, pp 1\u20139","DOI":"10.1109\/CEC.2010.5586203"},{"issue":"5","key":"1940_CR3","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1109\/TEVC.2010.2041060","volume":"14","author":"L Ben Said","year":"2010","unstructured":"Ben Said L, Bechikh S, Gh\u00e9dira K (2010) The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Trans Evol Comput 14(5):801\u2013818","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"1940_CR4","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/BF01584098","volume":"1","author":"R Benayoun","year":"1971","unstructured":"Benayoun R, De Montgolfier J, Tergny J, Laritchev O (1971) Linear programming with multiple objective functions: step method (STEM). Math Program 1(1):366\u2013375","journal-title":"Math Program"},{"key":"1940_CR5","doi-asserted-by":"publisher","unstructured":"Branke J, Kau\u00dfler T, Smidt C, Schmeck H (2000) A multi-population approach to dynamic optimization problems. In: Evolutionary design and manufacture. Springer, pp 299\u2013307","DOI":"10.1007\/978-1-4471-0519-0_24"},{"key":"1940_CR6","doi-asserted-by":"publisher","unstructured":"Branke J, Deb K, Dierolf H, Osswald M (2004) Finding knees in multi-objective optimization. In: Parallel problem solving from nature-PPSN VIII. Springer, pp 722\u2013731","DOI":"10.1007\/978-3-540-30217-9_73"},{"key":"1940_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88908-3","volume-title":"Multiobjective optimization: interactive and evolutionary approaches","author":"J Branke","year":"2008","unstructured":"Branke J, Deb K, Miettinen K (2008) Multiobjective optimization: interactive and evolutionary approaches. Springer, New York"},{"issue":"9","key":"1940_CR8","doi-asserted-by":"publisher","first-page":"1851","DOI":"10.1109\/TCYB.2014.2360923","volume":"45","author":"N Chen","year":"2015","unstructured":"Chen N, Chen WN, Gong YJ, Zhan ZH, Zhang J, Li Y, Tan YS (2015) An evolutionary algorithm with double-level archives for multiobjective optimization. IEEE Trans Cybern 45(9):1851\u20131863","journal-title":"IEEE Trans Cybern"},{"issue":"4","key":"1940_CR9","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1109\/TSMCB.2012.2228480","volume":"43","author":"J Dai","year":"2013","unstructured":"Dai J, Wang W, Xu Q (2013) An uncertainty measure for incomplete decision tables and its applications. IEEE Trans Cybern 43(4):1277\u20131289","journal-title":"IEEE Trans Cybern"},{"issue":"4","key":"1940_CR10","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":"1940_CR11","doi-asserted-by":"publisher","unstructured":"Deb K, Kumar A (2007) Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2007). ACM Press, pp 781\u2013788","DOI":"10.1145\/1276958.1277116"},{"key":"1940_CR12","unstructured":"Deb K, Miettinen K (2009) A review of nadir point estimation procedures using evolutionary approaches: a tale of dimensionality reduction. In: Proceedings of the multiple criterion decision making (MCDM-2008) conference. Springer, pp 1\u201314"},{"issue":"2","key":"1940_CR13","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 (2002a) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182\u2013197","journal-title":"IEEE Trans Evol Comput"},{"key":"1940_CR14","doi-asserted-by":"publisher","unstructured":"Deb K, Thiele L, Laumanns M, Zitzler E (2002b) Scalable multi-objective optimization test problems. In: Evolutionary computation (CEC), 2002 IEEE congress on, vol 1. IEEE Press, pp 825\u2013830","DOI":"10.1109\/CEC.2002.1007032"},{"key":"1940_CR15","doi-asserted-by":"publisher","unstructured":"Deb K, Chaudhuri S, Miettinen K (2006) Towards estimating nadir objective vector using evolutionary approaches. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2006). ACM Press, pp 643\u2013650","DOI":"10.1145\/1143997.1144113"},{"key":"1940_CR16","doi-asserted-by":"publisher","unstructured":"Deb K, Miettinen K, Sharma D (2009) A hybrid integrated multi-objective optimization procedure for estimating nadir point. In: Evolutionary multi-criterion optimization. Springer, pp 569\u2013583","DOI":"10.1007\/978-3-642-01020-0_44"},{"issue":"6","key":"1940_CR17","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1109\/TEVC.2010.2041667","volume":"14","author":"K Deb","year":"2010","unstructured":"Deb K, Miettinen K, Chaudhuri S (2010) Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Trans Evol Comput 14(6):821\u2013841","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"1940_CR18","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","volume":"1","author":"J Derrac","year":"2011","unstructured":"Derrac J, Garc\u00eda S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3\u201318","journal-title":"Swarm Evol Comput"},{"issue":"1","key":"1940_CR19","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0167-188X(86)90030-3","volume":"10","author":"M Dessouky","year":"1986","unstructured":"Dessouky M, Ghiassi M, Davis W (1986) Estimates of the minimum nondominated criterion values in multiple-criteria decision-making. Eng Costs Prod Econ 10(1):95\u2013104","journal-title":"Eng Costs Prod Econ"},{"issue":"1","key":"1940_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/S0377-2217(02)00595-7","volume":"151","author":"M Ehrgott","year":"2003","unstructured":"Ehrgott M, Tenfelde-Podehl D (2003) Computation of ideal and nadir values and implications for their use in MCDM methods. Eur J Oper Res 151(1):119\u2013139","journal-title":"Eur J Oper Res"},{"issue":"5","key":"1940_CR21","doi-asserted-by":"publisher","first-page":"4000","DOI":"10.1016\/j.eswa.2009.11.016","volume":"37","author":"Z Fan","year":"2010","unstructured":"Fan Z, Liu Y (2010) A method for group decision-making based on multi-granularity uncertain linguistic information. Expert Syst Appl 37(5):4000\u20134008","journal-title":"Expert Syst Appl"},{"issue":"1","key":"1940_CR22","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/TCYB.2014.2320910","volume":"45","author":"Y He","year":"2015","unstructured":"He Y, He Z, Chen H (2015) Intuitionistic fuzzy interaction bonferroni means and its application to multiple attribute decision making. IEEE Trans Cybern 45(1):116\u2013128","journal-title":"IEEE Trans Cybern"},{"issue":"9","key":"1940_CR23","doi-asserted-by":"publisher","first-page":"10882","DOI":"10.1016\/j.eswa.2011.02.123","volume":"38","author":"S Hsu","year":"2011","unstructured":"Hsu S, Wang T (2011) Solving multi-criteria decision making with incomplete linguistic preference relations. Expert Syst Appl 38(9):10882\u201310888","journal-title":"Expert Syst Appl"},{"issue":"5","key":"1940_CR24","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1109\/TEVC.2005.861417","volume":"10","author":"S Huband","year":"2006","unstructured":"Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477\u2013506","journal-title":"IEEE Trans Evol Comput"},{"key":"1940_CR25","doi-asserted-by":"publisher","unstructured":"Hughes E (2005) Evolutionary many-objective optimisation: many once or one many? In: Evolutionary computation (CEC), 2005 IEEE congress on, vol 1. IEEE Press, pp 222\u2013227","DOI":"10.1109\/CEC.2005.1554688"},{"key":"1940_CR26","doi-asserted-by":"publisher","unstructured":"Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: Evolutionary computation (CEC), 2008 IEEE congress on. IEEE Press, pp 2419\u20132426","DOI":"10.1109\/CEC.2008.4631121"},{"key":"1940_CR27","doi-asserted-by":"publisher","unstructured":"Ishibuchi H, Masuda H, Tanigaki Y, Nojima Y (2014) Review of coevolutionary developments of evolutionary multi-objective and many-objective algorithms and test problems. In: Computational intelligence in multi-criteria decision-making (MCDM), 2014 IEEE symposium on. IEEE, pp 178\u2013184","DOI":"10.1109\/MCDM.2014.7007205"},{"issue":"12","key":"1940_CR28","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.1109\/TCYB.2014.2307319","volume":"44","author":"S Jiang","year":"2014","unstructured":"Jiang S, Ong YS, Zhang J, Feng L (2014) Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans Cybern 44(12):2391\u20132404","journal-title":"IEEE Trans Cybern"},{"issue":"6","key":"1940_CR29","doi-asserted-by":"publisher","first-page":"1845","DOI":"10.1109\/TSMCB.2012.2231860","volume":"43","author":"L Ke","year":"2013","unstructured":"Ke L, Zhang Q, Battiti R (2013) MOEA\/D-ACO: a multiobjective evolutionary algorithm using decomposition and antcolony. IEEE Trans Cybern 43(6):1845\u20131859","journal-title":"IEEE Trans Cybern"},{"key":"1940_CR30","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1007\/3-540-36970-8_27","volume-title":"Evolutionary multi-criterion optimization. Lecture notes in computer science","author":"V Khare","year":"2003","unstructured":"Khare V, Yao X, Deb K (2003) Performance scaling of multi-objective evolutionary algorithms. In: Fonseca C, Fleming P, Zitzler E, Thiele L, Deb K (eds) Evolutionary multi-criterion optimization. Lecture notes in computer science, vol 2632. Springer, Berlin, pp 376\u2013390"},{"issue":"1","key":"1940_CR31","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1287\/opre.1070.0425","volume":"56","author":"K Klamroth","year":"2008","unstructured":"Klamroth K, Miettinen K (2008) Integrating approximation and interactive decision making in multicriteria optimization. Oper Res 56(1):222\u2013234","journal-title":"Oper Res"},{"issue":"5","key":"1940_CR32","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1287\/opre.45.5.751","volume":"45","author":"P Korhonen","year":"1997","unstructured":"Korhonen P, Salo S, Steuer R (1997) A heuristic for estimating nadir criterion values in multiple objective linear programming. Oper Res 45(5):751\u2013757","journal-title":"Oper Res"},{"key":"1940_CR33","doi-asserted-by":"publisher","unstructured":"Li K, Kwong S, Zhang Q, Deb K (2015) Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans Cybern 45(10):2076\u20132088","DOI":"10.1109\/TCYB.2014.2365354"},{"key":"1940_CR34","doi-asserted-by":"publisher","unstructured":"Ma X, liu f, Qi Y, Wang X, Li L, Jiao L, Yin M, Gong M (2015) A multiobjective evolutionary algorithm based on decision variable analyses for multi-objective optimization problems with large scale variables. IEEE Trans Evolut Comput PP(99):1\u20131. doi: 10.1109\/TEVC.2015.2455812","DOI":"10.1109\/TEVC.2015.2455812"},{"issue":"2","key":"1940_CR35","first-page":"15","volume":"3","author":"B Metev","year":"2003","unstructured":"Metev B, Vassilev V (2003) A method for nadir point estimation in MOLP problems. Cybern Inf Technol 3(2):15\u201324","journal-title":"Cybern Inf Technol"},{"key":"1940_CR36","volume-title":"Nonlinear multiobjective optimization","author":"K Miettinen","year":"1999","unstructured":"Miettinen K (1999) Nonlinear multiobjective optimization. Springer, New York"},{"issue":"2","key":"1940_CR37","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1016\/j.ejor.2010.02.041","volume":"206","author":"K Miettinen","year":"2010","unstructured":"Miettinen K, Eskelinen P, Ruiz F, Luque M (2010) NAUTILUS method: an interactive technique in multiobjective optimization based on the nadir point. Eur J Oper Res 206(2):426\u2013434","journal-title":"Eur J Oper Res"},{"key":"1940_CR38","doi-asserted-by":"publisher","unstructured":"Praditwong K, Yao X (2006) A new multi-objective evolutionary optimisation algorithm: the two-archive algorithm. In: Computational intelligence and security, 2006 international conference on, vol 1. IEEE Press, pp 286\u2013291","DOI":"10.1109\/ICCIAS.2006.294139"},{"key":"1940_CR39","doi-asserted-by":"publisher","unstructured":"Praditwong K, Yao X (2007) How well do multi-objective evolutionary algorithms scale to large problems. In: Evolutionary computation (CEC), 2007 IEEE congress on. IEEE Press, pp 3959\u20133966","DOI":"10.1109\/CEC.2007.4424987"},{"key":"1940_CR40","doi-asserted-by":"publisher","unstructured":"Purshouse R, Fleming P (2003) Evolutionary many-objective optimisation: an exploratory analysis. In: Evolutionary computation (CEC), 2003 IEEE congress on, vol 3. IEEE Press, pp 2066\u20132073","DOI":"10.1109\/CEC.2003.1299927"},{"key":"1940_CR41","first-page":"16","volume":"3","author":"M Szczepanski","year":"2003","unstructured":"Szczepanski M, Wierzbicki A (2003) Application of multiple criteria evolutionary algorithms to vector optimisation, decision support and reference point approaches. J Telecommun Inf Technol 3:16\u201333","journal-title":"J Telecommun Inf Technol"},{"issue":"3","key":"1940_CR42","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1162\/evco.2009.17.3.411","volume":"17","author":"L Thiele","year":"2009","unstructured":"Thiele L, Miettinen K, Korhonen P, Molina J (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411\u2013436","journal-title":"Evol Comput"},{"issue":"4","key":"1940_CR43","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1109\/TEVC.2014.2350987","volume":"19","author":"H Wang","year":"2015","unstructured":"Wang H, Jiao L, Yao X (2015) Two\\_Arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19(4):524\u2013541","journal-title":"IEEE Trans Evol Comput"},{"key":"1940_CR44","doi-asserted-by":"publisher","unstructured":"Yuan Y, Xu H, Wang B, Yao X (2015a) A new dominance relation based evolutionary algorithm for many-objective optimization. doi: 10.1109\/TEVC.2015.2420112","DOI":"10.1109\/TEVC.2015.2420112"},{"key":"1940_CR45","doi-asserted-by":"publisher","unstructured":"Yuan Y, Xu H, Wang B, Zhang B, Yao X (2015b) Balancing convergence and diversity in decomposition-based many-objective optimizers. doi: 10.1109\/TEVC.2015.2443001","DOI":"10.1109\/TEVC.2015.2443001"},{"key":"1940_CR46","doi-asserted-by":"publisher","unstructured":"Zitzler E, K\u00fcnzli S (2004) Indicator-based selection in multiobjective search. In: Parallel problem solving from nature-PPSN VIII. Springer, pp 832\u2013842","DOI":"10.1007\/978-3-540-30217-9_84"},{"issue":"4","key":"1940_CR47","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1109\/4235.797969","volume":"3","author":"E Zitzler","year":"1999","unstructured":"Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257\u2013271","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1940_CR48","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1162\/106365600568202","volume":"8","author":"E Zitzler","year":"2000","unstructured":"Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173\u2013195","journal-title":"Evol Comput"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1940-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-015-1940-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1940-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1940-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T12:11:16Z","timestamp":1567339876000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-015-1940-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,17]]},"references-count":48,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["1940"],"URL":"https:\/\/doi.org\/10.1007\/s00500-015-1940-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,17]]}}}