A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms
A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly d...
Uložené v:
| Vydané v: | IEEE transactions on evolutionary computation Ročník 25; číslo 6; s. 1028 - 1048 |
|---|---|
| Hlavní autori: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 1089-778X, 1941-0026 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori , many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range. |
|---|---|
| AbstractList | A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori , many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range. |
| Author | Wang, Handing Srinivasan, Dipti Ishibuchi, Hisao Nan, Yang He, Linjun Trivedi, Anupam |
| Author_xml | – sequence: 1 givenname: Linjun orcidid: 0000-0002-4255-2538 surname: He fullname: He, Linjun email: this.helj@gmail.com organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 2 givenname: Hisao orcidid: 0000-0001-9186-6472 surname: Ishibuchi fullname: Ishibuchi, Hisao email: hisao@sustech.edu.cn organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 3 givenname: Anupam orcidid: 0000-0002-3066-5578 surname: Trivedi fullname: Trivedi, Anupam email: eleatr@nus.edu.sg organization: Department of Electrical and Computer Engineering, National University of Singapore, Singapore – sequence: 4 givenname: Handing orcidid: 0000-0002-4805-3780 surname: Wang fullname: Wang, Handing email: hdwang@xidian.edu.cn organization: School of Artificial Intelligence, Xidian University, Xi'an, China – sequence: 5 givenname: Yang orcidid: 0000-0001-8396-294X surname: Nan fullname: Nan, Yang email: nany@mail.sustech.edu.cn organization: Department of Computer Science and Engineering, Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen, China – sequence: 6 givenname: Dipti orcidid: 0000-0003-4877-3478 surname: Srinivasan fullname: Srinivasan, Dipti email: dipti@nus.edu.sg organization: Department of Electrical and Computer Engineering, National University of Singapore, Singapore |
| BookMark | eNp9kT9PwzAQxS0EEm3hAyCWSMwpdpzE8VhV5Y8oMFAQm-U4Z-oqjYvtVCqfnoRWDAxM93R67-70uyE6bmwDCF0QPCYE8-vF7G06TnBCxhSzPCPpERoQnpIY4yQ_7jQueMxY8X6Kht6vMCZpRvgAPUyil9ZtYRdZHT1Zt5a1-ZLB2CZ6hLC0lY9MJ9u6a5UrUMFsIZptbd32Hul20aT-sM6E5dqfoRMtaw_nhzpCrzezxfQunj_f3k8n81jRjIe4KlNWQUWYSitVpKpkTCU8k5DIApSmJaW54gWRmkpQSmMGkoDUBSNZpbWmI3S1n7tx9rMFH8TKtq7pVookxylPCOW8c5G9SznrvQMtNs6su4sFwaJnJnpmomcmDsy6DPuTUSb80AhOmvrf5OU-aQDgd1P3AI5ZQr8B65F92w |
| CODEN | ITEVF5 |
| CitedBy_id | crossref_primary_10_1109_TEVC_2022_3192100 crossref_primary_10_1109_LWC_2025_3529082 crossref_primary_10_1016_j_ejor_2025_08_030 crossref_primary_10_1007_s40747_023_00969_w crossref_primary_10_1109_MCI_2025_3563425 crossref_primary_10_1109_TIM_2022_3169551 crossref_primary_10_1145_3610536 crossref_primary_10_3390_bdcc7040174 crossref_primary_10_1080_15376494_2022_2088907 crossref_primary_10_1109_TEVC_2022_3211643 crossref_primary_10_1016_j_csite_2024_105062 crossref_primary_10_1016_j_asoc_2024_111296 crossref_primary_10_1109_ACCESS_2021_3139137 crossref_primary_10_1016_j_apenergy_2025_126284 crossref_primary_10_1016_j_engappai_2023_106868 crossref_primary_10_1016_j_asoc_2023_110693 crossref_primary_10_1016_j_jclepro_2024_144051 crossref_primary_10_1016_j_compeleceng_2022_108285 crossref_primary_10_1016_j_ins_2024_121079 crossref_primary_10_1016_j_asoc_2024_111646 crossref_primary_10_1016_j_knosys_2024_112524 crossref_primary_10_1109_TAES_2025_3560609 crossref_primary_10_1016_j_ins_2025_122649 crossref_primary_10_1109_TII_2023_3316183 crossref_primary_10_1016_j_ifacol_2022_10_100 crossref_primary_10_1016_j_energy_2025_136505 crossref_primary_10_1109_TAI_2024_3443790 crossref_primary_10_1155_2024_2311998 crossref_primary_10_1016_j_ijpe_2023_109077 crossref_primary_10_1109_TCYB_2022_3226744 crossref_primary_10_1016_j_ijhydene_2024_05_167 crossref_primary_10_1109_TEVC_2022_3219062 crossref_primary_10_1109_TEVC_2022_3233364 crossref_primary_10_1016_j_autcon_2025_106284 crossref_primary_10_1109_TEVC_2023_3319009 crossref_primary_10_1080_0305215X_2025_2466119 crossref_primary_10_1109_TPWRS_2022_3200838 crossref_primary_10_1109_TSMC_2022_3201685 crossref_primary_10_1109_JIOT_2024_3481637 crossref_primary_10_1109_TEVC_2023_3287399 crossref_primary_10_1016_j_swevo_2023_101305 crossref_primary_10_1080_00207543_2025_2502106 crossref_primary_10_1109_TII_2021_3128405 crossref_primary_10_3390_ijgi12040152 crossref_primary_10_1007_s40747_021_00590_9 crossref_primary_10_1016_j_asoc_2022_109720 crossref_primary_10_1080_00207543_2023_2237122 crossref_primary_10_1016_j_scs_2023_105039 |
| Cites_doi | 10.1109/ACCESS.2020.2990567 10.1109/TEVC.2018.2866854 10.1109/TCYB.2014.2360923 10.1016/j.asoc.2017.03.041 10.1162/evco_a_00276 10.1109/TEVC.2003.810758 10.1109/TEVC.2019.2899030 10.1109/CEC.2019.8790342 10.1109/TEVC.2015.2420112 10.1109/TCYB.2014.2367526 10.1109/CEC.2002.1007032 10.1016/j.asoc.2017.04.002 10.1109/SSCI44817.2019.9002760 10.1109/TEVC.2019.2958921 10.1109/CEC.2002.1007013 10.1109/TEVC.2013.2281533 10.1109/TCYB.2020.2971638 10.1007/3-540-44719-9_11 10.1109/MCI.2019.2937612 10.1109/TEVC.2014.2339823 10.1109/ICEC.1994.349965 10.1007/978-3-319-99253-2_25 10.1109/TEVC.2015.2443001 10.1109/TEVC.2017.2744674 10.1109/TEVC.2013.2281534 10.1109/TCYB.2017.2737554 10.1145/3071178.3071264 10.1109/CEC.2001.934293 10.1007/s10898-014-0214-y 10.1109/TEVC.2018.2882166 10.1007/978-3-642-17144-4_3 10.1109/TCYB.2017.2762701 10.1007/978-3-642-37140-0_32 10.1109/TEVC.2016.2519378 10.1109/TEVC.2007.892759 10.1109/TEVC.2019.2894743 10.1109/TCYB.2017.2739185 10.1016/j.ejor.2005.06.019 10.1109/TEVC.2007.910138 10.1109/TCYB.2014.2365354 10.1109/SMC.2013.110 10.1109/ACCESS.2020.3022164 10.1016/j.ejor.2010.02.041 10.1109/TEVC.2019.2909271 10.1109/TEVC.2018.2871362 10.1109/TEVC.2020.2964705 10.1109/ACCESS.2017.2751071 10.1109/CEC.2010.5586185 10.1145/1143997.1144113 10.1109/TEVC.2014.2373386 10.1145/2908812.2908856 10.1016/j.asoc.2020.106316 10.1109/TEVC.2013.2281535 10.1016/j.swevo.2019.02.003 10.1109/CEC.2016.7744174 10.1109/TEVC.2017.2749619 10.1109/TEVC.2019.2913831 10.1007/978-3-030-12598-1_8 10.1109/SSCI.2016.7850222 10.1016/j.asoc.2017.11.029 10.1007/978-3-030-12598-1_19 10.1109/TSMC.2017.2654301 10.1109/TEVC.2015.2459718 10.1109/MCI.2017.2742868 10.1145/3205651.3205702 10.1109/TCYB.2018.2819360 10.1007/978-3-319-99253-2_20 10.1007/978-3-319-45823-6_53 10.1109/TCYB.2016.2638902 10.1162/evco_a_00226 10.1162/106365602760234108 10.1109/TEVC.2016.2611642 10.1109/TCYB.2013.2247594 10.1109/SMC.2016.7844861 10.1016/j.asoc.2017.08.036 10.1007/978-3-030-12598-1_16 10.1007/s10589-009-9241-x 10.1109/TEVC.2012.2227145 10.1007/s00500-015-1940-x 10.1109/TEVC.2014.2343791 10.1109/TEVC.2016.2592479 10.1016/j.artint.2015.06.007 10.1109/TEVC.2018.2865590 10.1109/CEC.2019.8789953 10.1007/s10732-015-9301-6 10.1007/978-3-319-45823-6_92 10.1109/TEVC.2018.2791283 10.1109/TEVC.2016.2587749 10.1109/TMAG.2013.2243123 10.1109/TEVC.2014.2378512 10.1109/ICIICII.2015.103 10.1016/j.asoc.2020.106078 10.1109/CEC.2017.7969302 10.1109/TEVC.2010.2093579 10.1007/978-3-030-12598-1_23 10.1007/s11721-017-0133-x 10.1109/CEC48606.2020.9185849 10.1145/3321707.3321839 10.1145/2739480.2754776 10.1109/TEVC.2018.2855411 10.1109/TCYB.2017.2737519 10.1109/TEVC.2018.2848254 10.1109/TEVC.2016.2587808 10.1007/978-3-540-88908-3_14 10.1109/TEVC.2005.861417 10.1016/j.apm.2017.10.015 10.1109/TEVC.2019.2909636 10.1109/TEVC.2010.2041667 10.1016/j.ejor.2006.08.008 10.1137/S1052623496307510 10.1162/EVCO_a_00009 10.1109/SSCI.2016.7850230 10.1145/3377930.3390166 10.1007/3-540-36970-8_34 10.1109/TEVC.2018.2844286 10.1109/4235.996017 10.1109/TEVC.2018.2836912 10.1109/TEVC.2018.2883094 10.1109/TEVC.2014.2350987 10.1007/s40747-017-0061-9 10.1007/s40747-017-0039-7 10.1016/j.swevo.2019.100592 10.2514/1.16875 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/TEVC.2021.3076514 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE/IET Electronic Library (IEL) (UW System Shared) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1941-0026 |
| EndPage | 1048 |
| ExternalDocumentID | 10_1109_TEVC_2021_3076514 9419072 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: Shenzhen Science and Technology Program grantid: KQTD2016112514355531 – fundername: Program for Guangdong Introducing Innovative and Enterpreneurial Teams grantid: 2017ZT07X386 – fundername: National Research Foundation Singapore under its AI Singapore Programme grantid: AISG-RP-2018-004 funderid: 10.13039/501100001381 – fundername: National Natural Science Foundation of China grantid: 61876075 funderid: 10.13039/501100001809 – fundername: Guangdong Provincial Key Laboratory grantid: 2020B121201001 |
| GroupedDBID | -~X .DC 0R~ 29I 4.4 5GY 5VS 6IF 6IK 6IL 6IN 97E AAJGR AARMG AASAJ AAWTH ABAZT ABJNI ABQJQ ABVLG ACGFO ACGFS ACIWK ADZIZ AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CHZPO CS3 EBS EJD HZ~ H~9 IEGSK IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P PQQKQ RIA RIE RIL RNS TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c359t-db47ded17c4dc84cb77c295ae2a8ecf3b336c981af3aeccf07ea1eaf8715dfff3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 60 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000724477500006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1089-778X |
| IngestDate | Sun Nov 30 04:56:17 EST 2025 Sat Nov 29 03:13:48 EST 2025 Tue Nov 18 21:43:01 EST 2025 Wed Aug 27 05:11:49 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c359t-db47ded17c4dc84cb77c295ae2a8ecf3b336c981af3aeccf07ea1eaf8715dfff3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-9186-6472 0000-0003-4877-3478 0000-0001-8396-294X 0000-0002-4805-3780 0000-0002-3066-5578 0000-0002-4255-2538 |
| PQID | 2604921399 |
| PQPubID | 85418 |
| PageCount | 21 |
| ParticipantIDs | proquest_journals_2604921399 ieee_primary_9419072 crossref_primary_10_1109_TEVC_2021_3076514 crossref_citationtrail_10_1109_TEVC_2021_3076514 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-12-01 |
| PublicationDateYYYYMMDD | 2021-12-01 |
| PublicationDate_xml | – month: 12 year: 2021 text: 2021-12-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on evolutionary computation |
| PublicationTitleAbbrev | TEVC |
| PublicationYear | 2021 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref57 ref56 ref59 ref58 ref53 ref52 ref55 ref54 ref51 ref50 ref46 ref45 ref48 ref47 ref42 ref41 steuer (ref113) 1986 ref44 ref43 ref49 ref8 ref7 ref9 knowles (ref123) 2002 ref4 ref6 ref5 ref100 ref101 ref40 ref35 ref34 ref37 ref31 ref30 ref33 ref32 ref39 ref38 he (ref36) 2019 ref24 ref23 cheng (ref116) 1997 ref26 ref25 ref20 zitzler (ref64) 2004; 3242 ref22 ref21 ref28 ref27 ref29 das (ref85) 1997 ref13 ref12 ref128 ref15 ref129 ref14 ref126 ref97 ref127 ref96 ref124 ref99 ref11 ref98 ref10 ref17 ref19 ref18 ref133 ref93 ref134 ref92 ref95 ref132 ref94 ref130 ref91 ref90 ref89 ref86 ref135 ref88 ref87 zitzler (ref125) 1999 zitzler (ref131) 2001 martínez (ref81) 2014; 8672 ref82 ref84 saxena (ref109) 2021 ref83 ref80 ref79 ref108 ref78 ref106 ref107 ref75 ref104 ref74 ref105 knowles (ref3) 2006 ref77 ref102 ref76 ref103 ref2 ref1 deb (ref16) 2009 ref71 ref111 ref70 ref112 ref73 ref72 ref110 ref68 ref119 ref67 ref117 ref69 ref118 ref115 ref63 ref66 ref65 ref114 ref60 ref122 ref62 ref120 ref61 ref121 |
| References_xml | – ident: ref23 doi: 10.1109/ACCESS.2020.2990567 – ident: ref52 doi: 10.1109/TEVC.2018.2866854 – ident: ref65 doi: 10.1109/TCYB.2014.2360923 – ident: ref96 doi: 10.1016/j.asoc.2017.03.041 – ident: ref50 doi: 10.1162/evco_a_00276 – ident: ref114 doi: 10.1109/TEVC.2003.810758 – ident: ref74 doi: 10.1109/TEVC.2019.2899030 – ident: ref112 doi: 10.1109/CEC.2019.8790342 – ident: ref26 doi: 10.1109/TEVC.2015.2420112 – ident: ref130 doi: 10.1109/TCYB.2014.2367526 – ident: ref11 doi: 10.1109/CEC.2002.1007032 – ident: ref58 doi: 10.1016/j.asoc.2017.04.002 – ident: ref60 doi: 10.1109/SSCI44817.2019.9002760 – ident: ref88 doi: 10.1109/TEVC.2019.2958921 – ident: ref126 doi: 10.1109/CEC.2002.1007013 – ident: ref110 doi: 10.1109/TEVC.2013.2281533 – ident: ref22 doi: 10.1109/TCYB.2020.2971638 – ident: ref127 doi: 10.1007/3-540-44719-9_11 – ident: ref63 doi: 10.1109/MCI.2019.2937612 – ident: ref87 doi: 10.1109/TEVC.2014.2339823 – ident: ref115 doi: 10.1109/ICEC.1994.349965 – ident: ref34 doi: 10.1007/978-3-319-99253-2_25 – ident: ref25 doi: 10.1109/TEVC.2015.2443001 – start-page: 1 year: 2009 ident: ref16 article-title: A review of nadir point estimation procedures using evolutionary approaches: A tale of dimensionality reduction publication-title: Proc Multiple Crit Decis Making Conf – year: 1997 ident: ref116 publication-title: Genetic Algorithms and Engineering Design – ident: ref51 doi: 10.1109/TEVC.2017.2744674 – ident: ref5 doi: 10.1109/TEVC.2013.2281534 – ident: ref69 doi: 10.1109/TCYB.2017.2737554 – ident: ref134 doi: 10.1145/3071178.3071264 – ident: ref41 doi: 10.1109/CEC.2001.934293 – ident: ref76 doi: 10.1007/s10898-014-0214-y – ident: ref93 doi: 10.1109/TEVC.2018.2882166 – ident: ref35 doi: 10.1007/978-3-642-17144-4_3 – ident: ref24 doi: 10.1109/TCYB.2017.2762701 – ident: ref94 doi: 10.1007/978-3-642-37140-0_32 – ident: ref67 doi: 10.1109/TEVC.2016.2519378 – ident: ref20 doi: 10.1109/TEVC.2007.892759 – ident: ref118 doi: 10.1109/TEVC.2019.2894743 – ident: ref68 doi: 10.1109/TCYB.2017.2739185 – ident: ref19 doi: 10.1016/j.ejor.2005.06.019 – year: 1999 ident: ref125 article-title: Evolutionary algorithms for multiobjective optimization: Methods and applications – ident: ref42 doi: 10.1109/TEVC.2007.910138 – ident: ref66 doi: 10.1109/TCYB.2014.2365354 – ident: ref122 doi: 10.1109/SMC.2013.110 – ident: ref117 doi: 10.1109/ACCESS.2020.3022164 – ident: ref15 doi: 10.1016/j.ejor.2010.02.041 – ident: ref133 doi: 10.1109/TEVC.2019.2909271 – ident: ref97 doi: 10.1109/TEVC.2018.2871362 – ident: ref75 doi: 10.1109/TEVC.2020.2964705 – ident: ref14 doi: 10.1109/ACCESS.2017.2751071 – ident: ref4 doi: 10.1109/CEC.2010.5586185 – ident: ref59 doi: 10.1145/1143997.1144113 – ident: ref38 doi: 10.1109/TEVC.2014.2373386 – ident: ref83 doi: 10.1145/2908812.2908856 – ident: ref121 doi: 10.1016/j.asoc.2020.106316 – ident: ref21 doi: 10.1109/TEVC.2013.2281535 – ident: ref10 doi: 10.1016/j.swevo.2019.02.003 – year: 2002 ident: ref123 article-title: Local-search and hybrid evolutionary algorithms for Pareto optimization – ident: ref37 doi: 10.1109/CEC.2016.7744174 – ident: ref72 doi: 10.1109/TEVC.2017.2749619 – ident: ref1 doi: 10.1109/TEVC.2019.2913831 – ident: ref84 doi: 10.1007/978-3-030-12598-1_8 – ident: ref80 doi: 10.1109/SSCI.2016.7850222 – ident: ref106 doi: 10.1016/j.asoc.2017.11.029 – ident: ref55 doi: 10.1007/978-3-030-12598-1_19 – ident: ref27 doi: 10.1109/TSMC.2017.2654301 – volume: 3242 start-page: 832 year: 2004 ident: ref64 article-title: Indicator-based selection in multiobjective search publication-title: Proc Int Conf Parallel Prob Solving Nat – ident: ref79 doi: 10.1109/TEVC.2015.2459718 – ident: ref99 doi: 10.1109/MCI.2017.2742868 – ident: ref111 doi: 10.1145/3205651.3205702 – year: 1997 ident: ref85 article-title: Nonlinear multicriteria optimization and robust optimality – ident: ref40 doi: 10.1109/TCYB.2018.2819360 – ident: ref71 doi: 10.1007/978-3-319-99253-2_20 – ident: ref82 doi: 10.1007/978-3-319-45823-6_53 – ident: ref33 doi: 10.1109/TCYB.2016.2638902 – ident: ref135 doi: 10.1162/evco_a_00226 – volume: 8672 start-page: 682 year: 2014 ident: ref81 article-title: Using a family of curves to approximate the Pareto front of a multi-objective optimization problem publication-title: Proc Int Conf Parallel Probl Solving Nat – year: 2001 ident: ref131 article-title: SPEA2: Improving the strength Pareto evolutionary algorithm – ident: ref48 doi: 10.1162/106365602760234108 – ident: ref28 doi: 10.1109/TEVC.2016.2611642 – start-page: 1834 year: 2019 ident: ref36 article-title: A study of the Naïve objective space normalization method in MOEA/D publication-title: Proc IEEE Symp Comput Intell – ident: ref100 doi: 10.1109/TCYB.2013.2247594 – ident: ref57 doi: 10.1109/SMC.2016.7844861 – ident: ref70 doi: 10.1016/j.asoc.2017.08.036 – ident: ref108 doi: 10.1007/978-3-030-12598-1_16 – ident: ref46 doi: 10.1007/s10589-009-9241-x – ident: ref31 doi: 10.1109/TEVC.2012.2227145 – ident: ref18 doi: 10.1007/s00500-015-1940-x – ident: ref103 doi: 10.1109/TEVC.2014.2343791 – ident: ref29 doi: 10.1109/TEVC.2016.2592479 – year: 2006 ident: ref3 article-title: A tutorial on the performance assessment of stochastic multiobjective optimizers – ident: ref43 doi: 10.1016/j.artint.2015.06.007 – ident: ref53 doi: 10.1109/TEVC.2018.2865590 – ident: ref2 doi: 10.1109/CEC.2019.8789953 – ident: ref107 doi: 10.1007/s10732-015-9301-6 – ident: ref95 doi: 10.1007/978-3-319-45823-6_92 – ident: ref92 doi: 10.1109/TEVC.2018.2791283 – ident: ref39 doi: 10.1109/TEVC.2016.2587749 – ident: ref102 doi: 10.1109/TMAG.2013.2243123 – ident: ref32 doi: 10.1109/TEVC.2014.2378512 – ident: ref56 doi: 10.1109/ICIICII.2015.103 – ident: ref6 doi: 10.1016/j.asoc.2020.106078 – year: 1986 ident: ref113 publication-title: Multiple Criteria Optimization Theory Computation and Application – ident: ref49 doi: 10.1109/CEC.2017.7969302 – ident: ref98 doi: 10.1109/TEVC.2010.2093579 – ident: ref73 doi: 10.1007/978-3-030-12598-1_23 – ident: ref105 doi: 10.1007/s11721-017-0133-x – ident: ref120 doi: 10.1109/CEC48606.2020.9185849 – ident: ref90 doi: 10.1145/3321707.3321839 – ident: ref104 doi: 10.1145/2739480.2754776 – ident: ref119 doi: 10.1109/TEVC.2018.2855411 – ident: ref101 doi: 10.1109/TCYB.2017.2737519 – ident: ref30 doi: 10.1109/TEVC.2018.2848254 – ident: ref62 doi: 10.1109/TEVC.2016.2587808 – ident: ref124 doi: 10.1007/978-3-540-88908-3_14 – ident: ref7 doi: 10.1109/TEVC.2005.861417 – ident: ref77 doi: 10.1016/j.apm.2017.10.015 – ident: ref91 doi: 10.1109/TEVC.2019.2909636 – ident: ref17 doi: 10.1109/TEVC.2010.2041667 – ident: ref128 doi: 10.1016/j.ejor.2006.08.008 – ident: ref86 doi: 10.1137/S1052623496307510 – ident: ref129 doi: 10.1162/EVCO_a_00009 – ident: ref47 doi: 10.1109/SSCI.2016.7850230 – ident: ref44 doi: 10.1145/3377930.3390166 – ident: ref13 doi: 10.1007/3-540-36970-8_34 – ident: ref45 doi: 10.1109/TEVC.2018.2844286 – ident: ref54 doi: 10.1109/4235.996017 – ident: ref8 doi: 10.1109/TEVC.2018.2836912 – ident: ref89 doi: 10.1109/TEVC.2018.2883094 – ident: ref61 doi: 10.1109/TEVC.2014.2350987 – ident: ref12 doi: 10.1007/s40747-017-0061-9 – ident: ref9 doi: 10.1007/s40747-017-0039-7 – ident: ref78 doi: 10.1016/j.swevo.2019.100592 – year: 2021 ident: ref109 article-title: A localized high fidelity dominance based many-objective evolutionary algorithm – ident: ref132 doi: 10.2514/1.16875 |
| SSID | ssj0014519 |
| Score | 2.5693843 |
| Snippet | A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1028 |
| SubjectTerms | Dominance resistant solution (DRS) Estimation Evolutionary algorithms Evolutionary computation evolutionary multiobjective optimization (EMO) Genetic algorithms ideal point Mopping Multiple objective analysis nadir point objective space normalization Optimization Pareto optimization Resistance Search problems |
| Title | A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms |
| URI | https://ieeexplore.ieee.org/document/9419072 https://www.proquest.com/docview/2604921399 |
| Volume | 25 |
| WOSCitedRecordID | wos000724477500006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0026 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014519 issn: 1089-778X databaseCode: RIE dateStart: 19970101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3LS8MwGP9Q8aAHp5vifJGDJ7Fb07RJcxyyIYhDcMpupc1DJ3OV7gH7703abCiK4C2HJJT8vme_F8Al1Sqj1Dg5WhLiWYPdi1WWelTggEmpma_8ctgE6_fj4ZA_bMD1uhZGKVUmn6mWXZaxfJmLuf1V1uahUV_MCNxNxmhVq7WOGNg2KVUyPTcWYzx0EUzs8_ag-3xjPMEAtwxB0wiH33RQOVTlhyQu1Uuv9r8P24c9Z0aiToX7AWyoSR1qqxENyHFsHXa_9BtswF0HPc6LhVqiXKO-tVbHrgwT3ZeTpKdoZJY2xzDP3ipRiLoLR51psUSd8UtejGav79NDeOp1Bze3npum4AkS8Zkns5BJJTEToRRxKDLGRMCjVAVprIQmGSFU8BinmqQGV-0zlWKVauNRRVJrTY5ga5JP1DGgAFMeGUYn5h6DrjA-iaBYUm5bz2QiaoK_et9EuFbjduLFOCldDp8nFpLEQpI4SJpwtT7yUfXZ-Gtzw2Kw3uievwlnKxATx4nTxPhrIQ-MnctPfj91Cjv27ipF5Qy2ZsVcncO2WMxG0-KiJLJPCfbQHQ |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3LS8MwGP8QFdSDb3E-c_AkVpumTZrjkImyOQSn7FbaPHQyV-kesP_epM2Gogjeckjakt_37PcCOKNaZZQaJ0dLQjxrsHuxylKPChwwKTXzlV8Om2Dtdtzt8ocFuJjXwiilyuQzdWmXZSxf5mJsf5Vd8dCoL2YE7lIUhoFfVWvNYwa2UUqVTs-NzRh3XQwT-_yq03i-Nr5ggC8NSdMIh9-0UDlW5YcsLhXMzcb_Pm0T1p0hieoV8luwoAbbsDEb0oAcz27D2peOgzvQrKPHcTFRU5Rr1Lb2at8VYqL7cpb0EPXM0mYZ5tlbJQxRY-LoMy2mqN5_yYve6PV9uAtPN43O9a3n5il4gkR85MksZFJJzEQoRRyKjDER8ChVQRoroUlGCBU8xqkmqUFW-0ylWKXa-FSR1FqTPVgc5AO1DyjAlEeG1Yl5jsFXGK9EUCwpt81nMhHVwJ_dbyJcs3E786KflE6HzxMLSWIhSRwkNTifH_moOm38tXnHYjDf6K6_BkczEBPHi8PEeGwhD4ylyw9-P3UKK7ed-1bSums3D2HVvqdKWDmCxVExVsewLCaj3rA4KQnuEwVy02Q |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Survey+of+Normalization+Methods+in+Multiobjective+Evolutionary+Algorithms&rft.jtitle=IEEE+transactions+on+evolutionary+computation&rft.au=He%2C+Linjun&rft.au=Ishibuchi%2C+Hisao&rft.au=Trivedi%2C+Anupam&rft.au=Wang%2C+Handing&rft.date=2021-12-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=1089-778X&rft.eissn=1941-0026&rft.volume=25&rft.issue=6&rft.spage=1028&rft_id=info:doi/10.1109%2FTEVC.2021.3076514&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-778X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-778X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-778X&client=summon |