Multi-objective design optimization using hybrid search algorithms with interval uncertainty for thin-walled structures

Thin-walled structures have been widely used in vehicle components due to their lightweight characteristics. To design structural parameters that are more in line with actual requirements, it is often necessary to consider the influence of uncertainty in design parameters. An effective multi-objecti...

Full description

Saved in:
Bibliographic Details
Published in:Thin-walled structures Vol. 175; p. 109218
Main Authors: Xu, Xiang, Xu, Gaoxiang, Chen, Jiawei, Liu, Zhe, Chen, Xinbo, Zhang, Yong, Fang, Jianguang, Gao, Yunkai
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2022
Subjects:
ISSN:0263-8231, 1879-3223
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Thin-walled structures have been widely used in vehicle components due to their lightweight characteristics. To design structural parameters that are more in line with actual requirements, it is often necessary to consider the influence of uncertainty in design parameters. An effective multi-objective design optimization method using hybrid search algorithms under interval uncertainty (MDOHSA) is proposed in this study. The MDOHSA mainly consists of the modified gray​ wolf optimization (mGWO) and the pattern search (PS) algorithms. The mGWO algorithm is applied to derive a new solution set and the PS algorithm is used to quickly search the lower and upper bounds of interval responses in MDOHSA. The non-dominated strategy considering uncertainty is designed by the possibility degree of interval value. The mGWO is designed by improving the initialization population and the updating mechanism. Some standard test functions are implemented to analyze the proposed method, and the result shows that the mGWO algorithm is superior to the other analogous algorithms. In this study, the car subframe, the hexagonal fractal structure, and the bracket of an intelligent sanitation vehicle are optimized by MDOHSA. The above results show that the optimization method proposed in this study is effective. The feasible solution of the multi-objective design optimization method can be selected according to the interval deviation degree of design variables and performance requirements. This study develops an effective multi-objective design optimization method for thin-walled structures under interval uncertainty and can continue to be used for the uncertain optimization of other engineering problems. •An effective multi-objective optimization method using hybrid search algorithms under interval uncertainty is proposed.•The modified grey wolf optimization is designed by improving the initialization population and the updating mechanism.•Thin-walled structures considering modal, dynamic crushing, and static loading are taken as optimization examples.
AbstractList Thin-walled structures have been widely used in vehicle components due to their lightweight characteristics. To design structural parameters that are more in line with actual requirements, it is often necessary to consider the influence of uncertainty in design parameters. An effective multi-objective design optimization method using hybrid search algorithms under interval uncertainty (MDOHSA) is proposed in this study. The MDOHSA mainly consists of the modified gray​ wolf optimization (mGWO) and the pattern search (PS) algorithms. The mGWO algorithm is applied to derive a new solution set and the PS algorithm is used to quickly search the lower and upper bounds of interval responses in MDOHSA. The non-dominated strategy considering uncertainty is designed by the possibility degree of interval value. The mGWO is designed by improving the initialization population and the updating mechanism. Some standard test functions are implemented to analyze the proposed method, and the result shows that the mGWO algorithm is superior to the other analogous algorithms. In this study, the car subframe, the hexagonal fractal structure, and the bracket of an intelligent sanitation vehicle are optimized by MDOHSA. The above results show that the optimization method proposed in this study is effective. The feasible solution of the multi-objective design optimization method can be selected according to the interval deviation degree of design variables and performance requirements. This study develops an effective multi-objective design optimization method for thin-walled structures under interval uncertainty and can continue to be used for the uncertain optimization of other engineering problems. •An effective multi-objective optimization method using hybrid search algorithms under interval uncertainty is proposed.•The modified grey wolf optimization is designed by improving the initialization population and the updating mechanism.•Thin-walled structures considering modal, dynamic crushing, and static loading are taken as optimization examples.
ArticleNumber 109218
Author Chen, Xinbo
Liu, Zhe
Chen, Jiawei
Gao, Yunkai
Fang, Jianguang
Xu, Gaoxiang
Xu, Xiang
Zhang, Yong
Author_xml – sequence: 1
  givenname: Xiang
  surname: Xu
  fullname: Xu, Xiang
  email: xiangxu@tongji.edu.cn
  organization: School of Automotive Studies, Tongji University, Shanghai 201804, China
– sequence: 2
  givenname: Gaoxiang
  surname: Xu
  fullname: Xu, Gaoxiang
  organization: School of Automotive Studies, Tongji University, Shanghai 201804, China
– sequence: 3
  givenname: Jiawei
  surname: Chen
  fullname: Chen, Jiawei
  organization: School of Mechanical Engineering, Tongji University, Shanghai 201804, China
– sequence: 4
  givenname: Zhe
  surname: Liu
  fullname: Liu, Zhe
  organization: School of Automotive Studies, Tongji University, Shanghai 201804, China
– sequence: 5
  givenname: Xinbo
  surname: Chen
  fullname: Chen, Xinbo
  email: chenxinbo@tongji.edu.cn
  organization: School of Automotive Studies, Tongji University, Shanghai 201804, China
– sequence: 6
  givenname: Yong
  surname: Zhang
  fullname: Zhang, Yong
  organization: College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China
– sequence: 7
  givenname: Jianguang
  surname: Fang
  fullname: Fang, Jianguang
  organization: School of Civil and Environmental Engineering, University of Technology Sydney, Sydney, NSW 2007, Australia
– sequence: 8
  givenname: Yunkai
  surname: Gao
  fullname: Gao, Yunkai
  organization: School of Automotive Studies, Tongji University, Shanghai 201804, China
BookMark eNp9kMtOwzAQRS1UJErhA9j5B1L8SOtErFDFSypiA2vLcabtRKlT2U6j8vW4lBWLrq6uRmc0c67JyHUOCLnjbMoZn9830ziEqWBCpF4KXlyQMS9UmUkh5IiMmZjLrBCSX5HrEBrGuOJlPibDe99GzLqqARtxD7SGgGtHu13ELX6biJ2jfUC3pptD5bGmAYy3G2radecxbraBDikough-b1raOws-mtQPdNV5GjfossG0LSQ2-t7G3kO4IZcr0wa4_csJ-Xp--ly8ZsuPl7fF4zKzolQxq1U6U8GcGzkzJedMVErmUhnBZrmq2RzKythZnoZWWJHPwIiVrEsJVVFDZeWEqNNe67sQPKy0xfj7VfQGW82ZPvrTjU7-9NGfPvlLJP9H7jxujT-cZR5ODKSX9gheB4uQhNTok19dd3iG_gEJMo7c
CitedBy_id crossref_primary_10_1016_j_ast_2025_110965
crossref_primary_10_1016_j_tws_2024_111655
crossref_primary_10_1016_j_tws_2024_111603
crossref_primary_10_3390_axioms11120714
crossref_primary_10_1177_09544070221141506
crossref_primary_10_1016_j_engstruct_2022_115380
crossref_primary_10_3390_math13183018
crossref_primary_10_1016_j_jobe_2024_111317
crossref_primary_10_3390_mca27030049
Cites_doi 10.1016/j.tws.2021.108257
10.1016/j.tws.2015.04.031
10.1016/j.asoc.2021.107454
10.1631/jzus.A1300311
10.1162/106365600568202
10.1016/j.future.2017.02.048
10.1016/j.eswa.2018.12.003
10.1007/s00158-021-02911-5
10.1080/0305215X.2014.982632
10.1016/j.cma.2019.03.048
10.1016/j.asoc.2018.11.043
10.1016/j.cma.2018.07.015
10.1016/j.knosys.2021.107796
10.1016/j.tws.2020.107248
10.1016/j.ast.2019.01.032
10.1002/(SICI)1099-1360(199801)7:1<34::AID-MCDA161>3.0.CO;2-6
10.1007/s00158-016-1579-y
10.1007/s00500-019-03804-y
10.1016/j.apm.2019.10.019
10.1016/S0377-2217(99)00319-7
10.1002/nme.6751
10.1162/evco.1994.2.3.221
10.1109/4235.797969
10.1016/j.jspi.2004.02.014
10.1016/j.tws.2015.07.002
10.1137/S1052623400374495
10.1007/s00158-021-03065-0
10.1016/j.apm.2017.03.053
10.1016/j.tws.2018.12.033
10.1016/j.ress.2004.01.011
10.1016/j.asoc.2019.106003
10.1016/j.ejor.2007.03.031
10.1016/j.tws.2020.107410
10.1109/4235.996017
10.1016/j.asoc.2015.01.020
10.1016/j.apm.2013.11.027
10.1016/j.ijsolstr.2006.01.012
10.1016/j.compstruc.2012.12.028
10.1016/j.tws.2015.05.014
10.1016/j.tws.2020.106921
10.1016/j.advengsoft.2019.02.003
10.1016/j.apm.2018.12.025
10.1016/j.eswa.2015.10.039
10.1016/j.tws.2021.108087
10.1016/j.swevo.2011.08.001
10.1016/j.ress.2014.10.007
10.1016/j.istruc.2020.12.024
10.1016/j.compstruct.2018.03.099
10.1016/j.apm.2015.11.038
10.1016/j.advengsoft.2013.12.007
10.1016/j.cja.2019.11.002
10.1016/j.tws.2016.09.003
10.1016/j.ijnonlinmec.2014.08.005
10.1016/j.tws.2021.107545
10.1016/j.tws.2018.07.007
10.1016/j.apm.2014.10.015
10.1007/s00366-020-01077-w
10.1142/S0219876220500085
10.1016/j.tws.2017.09.028
10.1016/j.eswa.2017.06.009
ContentType Journal Article
Copyright 2022 Elsevier Ltd
Copyright_xml – notice: 2022 Elsevier Ltd
DBID AAYXX
CITATION
DOI 10.1016/j.tws.2022.109218
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1879-3223
ExternalDocumentID 10_1016_j_tws_2022_109218
S0263823122001835
GroupedDBID --K
--M
.~1
0R~
123
1B1
1~.
1~5
29Q
4.4
457
4G.
5VS
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABFNM
ABJNI
ABMAC
ABTAH
ABXDB
ABYKQ
ACDAQ
ACGFS
ACNNM
ACRLP
ADBBV
ADEZE
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HVGLF
HZ~
IHE
J1W
JJJVA
KOM
LY7
M41
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SDF
SDG
SES
SET
SEW
SPC
SPCBC
SST
SSZ
T5K
WH7
WUQ
XPP
ZMT
ZY4
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ID FETCH-LOGICAL-c297t-d77197e61a35a91102b73437a20547d06e9bac545a9c2c245ea2f3d93eb8debc3
ISICitedReferencesCount 13
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000792947100005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0263-8231
IngestDate Sat Nov 29 07:22:44 EST 2025
Tue Nov 18 22:24:58 EST 2025
Fri Feb 23 02:40:17 EST 2024
IsPeerReviewed true
IsScholarly true
Keywords Thin-walled structures
Uncertainty
Multi-objective optimization
Vehicle structures
Design optimization
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c297t-d77197e61a35a91102b73437a20547d06e9bac545a9c2c245ea2f3d93eb8debc3
ParticipantIDs crossref_citationtrail_10_1016_j_tws_2022_109218
crossref_primary_10_1016_j_tws_2022_109218
elsevier_sciencedirect_doi_10_1016_j_tws_2022_109218
PublicationCentury 2000
PublicationDate June 2022
2022-06-00
PublicationDateYYYYMMDD 2022-06-01
PublicationDate_xml – month: 06
  year: 2022
  text: June 2022
PublicationDecade 2020
PublicationTitle Thin-walled structures
PublicationYear 2022
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Fang, Gao, Sun, Xu, Li (b3) 2015; 135
Liu, Qiu (b27) 2021; 64
Jin, Chen, Sudjianto (b55) 2005; 134
Lv, Gu, He, Zhou, Liu (b1) 2015; 94
Yu, Gu, Qian, Jiang, Wang, Yu (b38) 2021; 161
Xu, Zhang, Wang, Jiang, Wang (b66) 2018; 194
Wang (b16) 2019; 351
Lu, Gao, Pan, Li, Zheng (b42) 2019; 75
C.A.C. Coello and M.S. Lechuga (Eds.), MOPSO: a proposal for multiple objective particle swarm optimization, in: Proceedings of the 2002 Congress on Evolutionary Computation CEC’02 (Cat No02TH8600); 2002 12-17 2002.
Song, Sun, Li (b46) 2016; 109
Zitzler, Deb, Thiele (b60) 2000; 8
Bae, Grandhi, Canfield (b14) 2004; 86
Xiong, Wang, Liu, Shi (b21) 2019; 86
Xu, Zhang, Chen, Liu, Xu, Gao (b67) 2019; 161–162
Li, Luo, Rong, Zhang (b31) 2013; 119
Fang, Gao, Sun, Qiu, Li (b48) 2015; 95
Su, Li, Qian, Mahadevan, Deng (b15) 2019; 23
Miao, Wan (b35) 2020; 17
Lei, Lv, Fang, Pang, Li, Sun (b2) 2021; 167
Qiu, Jin, Liu, Fu, Chen, Kim (b6) 2021; 162
Li, Bai, Gao, Shi, Wang, Ye, Gu, Xu, Liu (b17) 2021; 29
Bigdeli, Nouri (b37) 2019; 137
(b57) 2005
Li, Lu (b13) 2014; 38
Xu, Zhang, Wu, Dong (b47) 2018; 131
Jiang, Han, Liu, Liu (b53) 2008; 188
Liu, Wang, Gu, Li (b22) 2022; 237
Srinivas, Deb (b50) 1994; 2
Zapotecas-Martínez, García-Nájera, López-Jaimes (b39) 2019; 120
Dolan, Lewis, Torczon (b44) 2003; 14
Qiu, Zhu (b26) 2021; 122
Mirjalili, Saremi, Mirjalili, d. S. Coelho (b58) 2016; 47
Akbari, Hedayatzadeh, Ziarati, Hassanizadeh (b64) 2012; 2
Lei, Lv, Fang, Li, Sun (b4) 2021; 167
Meng, Hao, Li, Wang, Zhang (b23) 2015; 94
Zheng, Da, Li, Xiao, Gao (b28) 2020; 78
Wang, Qiu, Xu, Li (b11) 2017; 47
Heris (b63) 2015
Cheng, Duan, Liu, Li, Feng, Chen (b34) 2014; 15
Zhao, Yue, Liu, Gao, Zhang (b8) 2015; 39
Sengupta, Pal (b49) 2000; 127
Sun, Li, Fang, Li (b5) 2021; 161
Zhang, Xu, Sun, Lai, Li (b10) 2018; 122
Wang, Tian, Zhu, Cai (b19) 2020; 33
Fang, Sun, Qiu, Kim, Li (b7) 2017; 55
Sahu, Panda, Padhan (b59) 2015; 29
Wang, Zhang, Zhou, Ouyang (b45) 2021; 167
(b56) 2006
Zitzler, Thiele (b61) 1999; 3
Czyzżak, Jaszkiewicz (b62) 1998; 7
Feng, Zhang, Tian, Lv, Tian, Jia (b32) 2018; 86
Mirjalili, Mirjalili, Lewis (b54) 2014; 69
(b52) 2005
Xu, Chen, Liu, Zhang, Xu, Fang, Gao (b24) 2021
Wang, Yang, Li, Xu (b29) 2021; 108
(b43) 2016
Fang, Gao, Sun, Zhang, Li (b9) 2014; 67
Qiu, Wang, Chen (b25) 2006; 43
Jiang, Xie, Zhang, Han (b33) 2015; 47
Deb, Pratap, Agarwal, Meyarivan (b51) 2002; 6
Wang, Matthies (b18) 2018; 341
Fu, Liu, Xiao (b30) 2019; 69
Wang, Liu, Liu (b20) 2019; 131
Wansasueb, Pholdee, Panagant, Bureerat (b65) 2022; 38
Dey, Mukhopadhyay, Khodaparast, Adhikari (b12) 2016; 40
Yang, Yang, Wang, Jin, Li (b40) 2020; 87
Nuaekaew, Artrit, Pholdee, Bureerat (b41) 2017; 87
Yang (10.1016/j.tws.2022.109218_b40) 2020; 87
Su (10.1016/j.tws.2022.109218_b15) 2019; 23
Jin (10.1016/j.tws.2022.109218_b55) 2005; 134
Liu (10.1016/j.tws.2022.109218_b22) 2022; 237
Xiong (10.1016/j.tws.2022.109218_b21) 2019; 86
Zhang (10.1016/j.tws.2022.109218_b10) 2018; 122
Xu (10.1016/j.tws.2022.109218_b47) 2018; 131
Bigdeli (10.1016/j.tws.2022.109218_b37) 2019; 137
Srinivas (10.1016/j.tws.2022.109218_b50) 1994; 2
Li (10.1016/j.tws.2022.109218_b13) 2014; 38
Fu (10.1016/j.tws.2022.109218_b30) 2019; 69
Nuaekaew (10.1016/j.tws.2022.109218_b41) 2017; 87
Heris (10.1016/j.tws.2022.109218_b63) 2015
Sun (10.1016/j.tws.2022.109218_b5) 2021; 161
Xu (10.1016/j.tws.2022.109218_b66) 2018; 194
Wang (10.1016/j.tws.2022.109218_b20) 2019; 131
Wang (10.1016/j.tws.2022.109218_b18) 2018; 341
Qiu (10.1016/j.tws.2022.109218_b6) 2021; 162
Cheng (10.1016/j.tws.2022.109218_b34) 2014; 15
Dolan (10.1016/j.tws.2022.109218_b44) 2003; 14
Xu (10.1016/j.tws.2022.109218_b67) 2019; 161–162
Deb (10.1016/j.tws.2022.109218_b51) 2002; 6
Jiang (10.1016/j.tws.2022.109218_b53) 2008; 188
Lei (10.1016/j.tws.2022.109218_b2) 2021; 167
Song (10.1016/j.tws.2022.109218_b46) 2016; 109
Fang (10.1016/j.tws.2022.109218_b48) 2015; 95
Akbari (10.1016/j.tws.2022.109218_b64) 2012; 2
Fang (10.1016/j.tws.2022.109218_b9) 2014; 67
Xu (10.1016/j.tws.2022.109218_b24) 2021
(10.1016/j.tws.2022.109218_b52) 2005
Wang (10.1016/j.tws.2022.109218_b11) 2017; 47
Wang (10.1016/j.tws.2022.109218_b19) 2020; 33
Sengupta (10.1016/j.tws.2022.109218_b49) 2000; 127
Wansasueb (10.1016/j.tws.2022.109218_b65) 2022; 38
(10.1016/j.tws.2022.109218_b43) 2016
Wang (10.1016/j.tws.2022.109218_b45) 2021; 167
Qiu (10.1016/j.tws.2022.109218_b26) 2021; 122
Zitzler (10.1016/j.tws.2022.109218_b61) 1999; 3
Wang (10.1016/j.tws.2022.109218_b16) 2019; 351
(10.1016/j.tws.2022.109218_b56) 2006
Lei (10.1016/j.tws.2022.109218_b4) 2021; 167
Miao (10.1016/j.tws.2022.109218_b35) 2020; 17
Zhao (10.1016/j.tws.2022.109218_b8) 2015; 39
Lv (10.1016/j.tws.2022.109218_b1) 2015; 94
Wang (10.1016/j.tws.2022.109218_b29) 2021; 108
Qiu (10.1016/j.tws.2022.109218_b25) 2006; 43
Dey (10.1016/j.tws.2022.109218_b12) 2016; 40
Feng (10.1016/j.tws.2022.109218_b32) 2018; 86
Czyzżak (10.1016/j.tws.2022.109218_b62) 1998; 7
Mirjalili (10.1016/j.tws.2022.109218_b58) 2016; 47
Li (10.1016/j.tws.2022.109218_b31) 2013; 119
Bae (10.1016/j.tws.2022.109218_b14) 2004; 86
Zapotecas-Martínez (10.1016/j.tws.2022.109218_b39) 2019; 120
Li (10.1016/j.tws.2022.109218_b17) 2021; 29
10.1016/j.tws.2022.109218_b36
Fang (10.1016/j.tws.2022.109218_b7) 2017; 55
Fang (10.1016/j.tws.2022.109218_b3) 2015; 135
Liu (10.1016/j.tws.2022.109218_b27) 2021; 64
Lu (10.1016/j.tws.2022.109218_b42) 2019; 75
Zitzler (10.1016/j.tws.2022.109218_b60) 2000; 8
Jiang (10.1016/j.tws.2022.109218_b33) 2015; 47
Meng (10.1016/j.tws.2022.109218_b23) 2015; 94
Mirjalili (10.1016/j.tws.2022.109218_b54) 2014; 69
Yu (10.1016/j.tws.2022.109218_b38) 2021; 161
(10.1016/j.tws.2022.109218_b57) 2005
Sahu (10.1016/j.tws.2022.109218_b59) 2015; 29
Zheng (10.1016/j.tws.2022.109218_b28) 2020; 78
References_xml – volume: 161
  year: 2021
  ident: b5
  article-title: On lower confidence bound improvement matrix-based approaches for multiobjective Bayesian optimization and its applications to thin-walled structures
  publication-title: Thin-Walled Struct.
– volume: 122
  start-page: 4922
  year: 2021
  end-page: 4943
  ident: b26
  article-title: A Newton iteration-based interval analysis method for nonlinear structural systems with uncertain-but-bounded parameters
  publication-title: Internat. J. Numer. Methods Engrg.
– volume: 14
  start-page: 567
  year: 2003
  end-page: 583
  ident: b44
  article-title: On the local convergence of pattern search
  publication-title: SIAM J. Optim.
– volume: 94
  start-page: 500
  year: 2015
  end-page: 511
  ident: b1
  article-title: Reliability design optimization of vehicle front-end structure for pedestrian lower extremity protection under multiple impact cases
  publication-title: Thin-Walled Struct.
– volume: 237
  year: 2022
  ident: b22
  article-title: Artificial neural network (ANN) - Bayesian probability framework (BPF) based method of dynamic force reconstruction under multi-source uncertainties
  publication-title: Knowl.-Based Syst.
– volume: 167
  year: 2021
  ident: b45
  article-title: Implementation of a novel six sigma multi-objective robustness optimization method based on the improved response surface model for bumper system design
  publication-title: Thin-Walled Struct.
– volume: 40
  start-page: 4412
  year: 2016
  end-page: 4428
  ident: b12
  article-title: Fuzzy uncertainty propagation in composites using Gram–Schmidt polynomial chaos expansion
  publication-title: Appl. Math. Model.
– volume: 7
  start-page: 34
  year: 1998
  end-page: 47
  ident: b62
  article-title: Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization
  publication-title: J. Multi-Criteria Decis. Anal.
– volume: 120
  start-page: 357
  year: 2019
  end-page: 371
  ident: b39
  article-title: Multi-objective grey wolf optimizer based on decomposition
  publication-title: Expert Syst. Appl.
– volume: 15
  start-page: 774
  year: 2014
  end-page: 788
  ident: b34
  article-title: Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II
  publication-title: J. Zhejiang Univ. Sci. A
– volume: 109
  start-page: 132
  year: 2016
  end-page: 142
  ident: b46
  article-title: Sensitivity analysis and reliability based design optimization for high-strength steel tailor welded thin-walled structures under crashworthiness
  publication-title: Thin-Walled Struct.
– volume: 55
  start-page: 1091
  year: 2017
  end-page: 1119
  ident: b7
  article-title: On design optimization for structural crashworthiness and its state of the art
  publication-title: Struct. Multidiscip. Optim.
– volume: 87
  year: 2020
  ident: b40
  article-title: An enhanced multi-objective grey wolf optimizer for service composition in cloud manufacturing
  publication-title: Appl. Soft Comput.
– volume: 47
  start-page: 106
  year: 2016
  end-page: 119
  ident: b58
  article-title: Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization
  publication-title: Expert Syst. Appl.
– volume: 33
  start-page: 1454
  year: 2020
  end-page: 1467
  ident: b19
  article-title: Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle
  publication-title: Chin. J. Aeronaut.
– volume: 161
  year: 2021
  ident: b38
  article-title: Application of tailor rolled blanks in optimum design of pure electric vehicle crashworthiness and lightweight
  publication-title: Thin-Walled Struct.
– volume: 341
  start-page: 640
  year: 2018
  end-page: 657
  ident: b18
  article-title: Evidence theory-based reliability optimization design using polynomial chaos expansion
  publication-title: Comput. Methods Appl. Mech. Engrg.
– volume: 122
  start-page: 193
  year: 2018
  end-page: 207
  ident: b10
  article-title: Nondeterministic optimization of tapered sandwich column for crashworthiness
  publication-title: Thin-Walled Struct.
– year: 2021
  ident: b24
  article-title: A feasible identification method of uncertainty responses for vehicle structures
  publication-title: Struct. Multidiscip. Optim.
– volume: 167
  year: 2021
  ident: b2
  article-title: Injury biomechanics-based nondeterministic optimization of front-end structures for safety in pedestrian–vehicle impact
  publication-title: Thin-Walled Struct.
– year: 2006
  ident: b56
  article-title: Opposition-based differential evolution algorithms
  publication-title: 2006 IEEE International Conference on Evolutionary Computation
– volume: 86
  start-page: 1242
  year: 2018
  end-page: 1250
  ident: b32
  article-title: Data-driven accurate design of variable blank holder force in sheet forming under interval uncertainty using sequential approximate multi-objective optimization
  publication-title: Future Gener. Comput. Syst.
– volume: 188
  start-page: 1
  year: 2008
  end-page: 13
  ident: b53
  article-title: A nonlinear interval number programming method for uncertain optimization problems
  publication-title: European J. Oper. Res.
– volume: 23
  start-page: 9793
  year: 2019
  end-page: 9799
  ident: b15
  article-title: A new rule to combine dependent bodies of evidence
  publication-title: Soft Comput.
– volume: 127
  start-page: 28
  year: 2000
  end-page: 43
  ident: b49
  article-title: On comparing interval numbers
  publication-title: European J. Oper. Res.
– volume: 2
  start-page: 39
  year: 2012
  end-page: 52
  ident: b64
  article-title: A multi-objective artificial bee colony algorithm
  publication-title: Swarm Evol. Comput.
– volume: 194
  start-page: 36
  year: 2018
  end-page: 48
  ident: b66
  article-title: Crashworthiness design of novel hierarchical hexagonal columns
  publication-title: Compos. Struct.
– volume: 137
  start-page: 1
  year: 2019
  end-page: 18
  ident: b37
  article-title: A crushing analysis and multi-objective optimization of thin-walled five-cell structures
  publication-title: Thin-Walled Struct.
– year: 2005
  ident: b52
  article-title: An optimization algorithm for imprecise multi-objective problem functions
  publication-title: 2005 IEEE Congress on Evolutionary Computation
– volume: 39
  start-page: 1853
  year: 2015
  end-page: 1866
  ident: b8
  article-title: An efficient reliability method combining adaptive importance sampling and kriging metamodel
  publication-title: Appl. Math. Model.
– volume: 78
  start-page: 627
  year: 2020
  end-page: 647
  ident: b28
  article-title: Robust topology optimization for multi-material structures under interval uncertainty
  publication-title: Appl. Math. Model.
– volume: 134
  start-page: 268
  year: 2005
  end-page: 287
  ident: b55
  article-title: An efficient algorithm for constructing optimal design of computer experiments
  publication-title: J. Statist. Plann. Inference
– volume: 167
  year: 2021
  ident: b4
  article-title: Nondeterministic multi-objective and multi-case discrete optimization of functionally-graded front-bumper structures for pedestrian protection
  publication-title: Thin-Walled Struct.
– volume: 43
  start-page: 6574
  year: 2006
  end-page: 6593
  ident: b25
  article-title: Exact bounds for the static response set of structures with uncertain-but-bounded parameters
  publication-title: Int. J. Solids Struct.
– volume: 8
  start-page: 173
  year: 2000
  end-page: 195
  ident: b60
  article-title: Comparison of multiobjective evolutionary algorithms: Empirical results
  publication-title: Evol. Comput.
– volume: 94
  start-page: 325
  year: 2015
  end-page: 333
  ident: b23
  article-title: Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint
  publication-title: Thin-Walled Struct.
– volume: 162
  year: 2021
  ident: b6
  article-title: Hybrid multi-objective robust design optimization of a truck cab considering fatigue life
  publication-title: Thin-Walled Struct.
– volume: 161–162
  year: 2019
  ident: b67
  article-title: Crushing behaviors of hierarchical sandwich-walled columns
  publication-title: Int. J. Mech. Sci.
– volume: 29
  start-page: 1111
  year: 2021
  end-page: 1118
  ident: b17
  article-title: Reliability-based design optimization for the lattice boom of crawler crane
  publication-title: Structures
– volume: 87
  start-page: 79
  year: 2017
  end-page: 89
  ident: b41
  article-title: Optimal reactive power dispatch problem using a two-archive multi-objective grey wolf optimizer
  publication-title: Expert Syst. Appl.
– volume: 3
  start-page: 257
  year: 1999
  end-page: 271
  ident: b61
  article-title: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach
  publication-title: IEEE Trans. Evol. Comput.
– volume: 119
  start-page: 68
  year: 2013
  end-page: 84
  ident: b31
  article-title: Interval multi-objective optimisation of structures using adaptive kriging approximations
  publication-title: Comput. Struct.
– volume: 75
  start-page: 728
  year: 2019
  end-page: 749
  ident: b42
  article-title: A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution
  publication-title: Appl. Soft Comput.
– volume: 38
  start-page: 3124
  year: 2014
  end-page: 3135
  ident: b13
  article-title: Interval optimization based line sampling method for fuzzy and random reliability analysis
  publication-title: Appl. Math. Model.
– volume: 67
  start-page: 120
  year: 2014
  end-page: 132
  ident: b9
  article-title: Crashworthiness design of foam-filled bitubal structures with uncertainty
  publication-title: Int. J. Non-Linear Mech.
– volume: 47
  start-page: 1637
  year: 2015
  end-page: 1650
  ident: b33
  article-title: A new interval optimization method considering tolerance design
  publication-title: Eng. Optim.
– volume: 131
  start-page: 286
  year: 2018
  end-page: 296
  ident: b47
  article-title: Multi-response optimization design of tailor-welded blank (TWB) thin-walled structures using Taguchi-based gray relational analysis
  publication-title: Thin-Walled Struct.
– volume: 2
  start-page: 221
  year: 1994
  end-page: 248
  ident: b50
  article-title: Muiltiobjective optimization using nondominated sorting in genetic algorithms
  publication-title: Evol. Comput.
– volume: 6
  start-page: 182
  year: 2002
  end-page: 197
  ident: b51
  article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II
  publication-title: IEEE Trans. Evol. Comput.
– reference: C.A.C. Coello and M.S. Lechuga (Eds.), MOPSO: a proposal for multiple objective particle swarm optimization, in: Proceedings of the 2002 Congress on Evolutionary Computation CEC’02 (Cat No02TH8600); 2002 12-17 2002.
– volume: 131
  start-page: 77
  year: 2019
  end-page: 89
  ident: b20
  article-title: An inverse method for distributed dynamic load identification of structures with interval uncertainties
  publication-title: Adv. Eng. Softw.
– volume: 47
  start-page: 573
  year: 2017
  end-page: 586
  ident: b11
  article-title: Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters
  publication-title: Appl. Math. Model.
– volume: 38
  start-page: 695
  year: 2022
  end-page: 713
  ident: b65
  article-title: Multiobjective meta-heuristic with iterative parameter distribution estimation for aeroelastic design of an aircraft wing
  publication-title: Eng. Comput.
– volume: 69
  start-page: 441
  year: 2019
  end-page: 452
  ident: b30
  article-title: Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems
  publication-title: Appl. Math. Model.
– volume: 95
  start-page: 115
  year: 2015
  end-page: 126
  ident: b48
  article-title: On design of multi-cell tubes under axial and oblique impact loads
  publication-title: Thin-Walled Struct.
– volume: 29
  start-page: 310
  year: 2015
  end-page: 327
  ident: b59
  article-title: A novel hybrid gravitational search and pattern search algorithm for load frequency control of nonlinear power system
  publication-title: Appl. Soft Comput.
– volume: 351
  start-page: 281
  year: 2019
  end-page: 296
  ident: b16
  article-title: Evidence-theory-based uncertain parameter identification method for mechanical systems with imprecise information
  publication-title: Comput. Methods Appl. Mech. Engrg.
– volume: 135
  start-page: 1
  year: 2015
  end-page: 8
  ident: b3
  article-title: Multiobjective robust design optimization of fatigue life for a truck cab
  publication-title: Reliab. Eng. Syst. Saf.
– volume: 17
  year: 2020
  ident: b35
  article-title: Hull form optimization based on an NM+CFD integrated method for KCS
  publication-title: Int. J. Comput. Methods
– volume: 108
  year: 2021
  ident: b29
  article-title: An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion
  publication-title: Appl. Soft Comput.
– year: 2016
  ident: b43
  article-title: Multi-objective modified grey wolf optimizer for optimal power flow
  publication-title: 2016 Eighteenth International Middle East Power Systems Conference (MEPCON)
– year: 2005
  ident: b57
  article-title: Opposition-based learning: a new scheme for machine intelligence
  publication-title: Proceedings 2006 International Conference on Intelligence for Modelling, Control and Automation Jointly with International Conference on Intelligent Agents, Web Technologies and Internet Commerce, 28-30 2005
– volume: 86
  start-page: 572
  year: 2019
  end-page: 581
  ident: b21
  article-title: An iterative dimension-by-dimension method for structural interval response prediction with multidimensional uncertain variables
  publication-title: Aerosp. Sci. Technol.
– volume: 69
  start-page: 46
  year: 2014
  end-page: 61
  ident: b54
  article-title: Grey wolf optimizer
  publication-title: Adv. Eng. Softw.
– year: 2015
  ident: b63
  article-title: Multi-objective PSO in MATLAB
– volume: 64
  start-page: 1241
  year: 2021
  end-page: 1258
  ident: b27
  article-title: A subinterval dimension-wise method for robust topology optimization of structures with truss-like lattice material under unknown but bounded uncertainties
  publication-title: Struct. Multidiscip. Optim.
– volume: 86
  start-page: 215
  year: 2004
  end-page: 225
  ident: b14
  article-title: An approximation approach for uncertainty quantification using evidence theory
  publication-title: Reliab. Eng. Syst. Saf.
– volume: 167
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b45
  article-title: Implementation of a novel six sigma multi-objective robustness optimization method based on the improved response surface model for bumper system design
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2021.108257
– volume: 94
  start-page: 325
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b23
  article-title: Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2015.04.031
– volume: 108
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b29
  article-title: An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion
  publication-title: Appl. Soft Comput.
  doi: 10.1016/j.asoc.2021.107454
– volume: 15
  start-page: 774
  issue: 10
  year: 2014
  ident: 10.1016/j.tws.2022.109218_b34
  article-title: Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II
  publication-title: J. Zhejiang Univ. Sci. A
  doi: 10.1631/jzus.A1300311
– volume: 8
  start-page: 173
  issue: 2
  year: 2000
  ident: 10.1016/j.tws.2022.109218_b60
  article-title: Comparison of multiobjective evolutionary algorithms: Empirical results
  publication-title: Evol. Comput.
  doi: 10.1162/106365600568202
– volume: 86
  start-page: 1242
  year: 2018
  ident: 10.1016/j.tws.2022.109218_b32
  article-title: Data-driven accurate design of variable blank holder force in sheet forming under interval uncertainty using sequential approximate multi-objective optimization
  publication-title: Future Gener. Comput. Syst.
  doi: 10.1016/j.future.2017.02.048
– volume: 120
  start-page: 357
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b39
  article-title: Multi-objective grey wolf optimizer based on decomposition
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2018.12.003
– volume: 64
  start-page: 1241
  issue: 3
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b27
  article-title: A subinterval dimension-wise method for robust topology optimization of structures with truss-like lattice material under unknown but bounded uncertainties
  publication-title: Struct. Multidiscip. Optim.
  doi: 10.1007/s00158-021-02911-5
– volume: 47
  start-page: 1637
  issue: 12
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b33
  article-title: A new interval optimization method considering tolerance design
  publication-title: Eng. Optim.
  doi: 10.1080/0305215X.2014.982632
– volume: 351
  start-page: 281
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b16
  article-title: Evidence-theory-based uncertain parameter identification method for mechanical systems with imprecise information
  publication-title: Comput. Methods Appl. Mech. Engrg.
  doi: 10.1016/j.cma.2019.03.048
– volume: 75
  start-page: 728
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b42
  article-title: A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution
  publication-title: Appl. Soft Comput.
  doi: 10.1016/j.asoc.2018.11.043
– volume: 341
  start-page: 640
  year: 2018
  ident: 10.1016/j.tws.2022.109218_b18
  article-title: Evidence theory-based reliability optimization design using polynomial chaos expansion
  publication-title: Comput. Methods Appl. Mech. Engrg.
  doi: 10.1016/j.cma.2018.07.015
– volume: 237
  year: 2022
  ident: 10.1016/j.tws.2022.109218_b22
  article-title: Artificial neural network (ANN) - Bayesian probability framework (BPF) based method of dynamic force reconstruction under multi-source uncertainties
  publication-title: Knowl.-Based Syst.
  doi: 10.1016/j.knosys.2021.107796
– ident: 10.1016/j.tws.2022.109218_b36
– volume: 161
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b5
  article-title: On lower confidence bound improvement matrix-based approaches for multiobjective Bayesian optimization and its applications to thin-walled structures
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2020.107248
– volume: 86
  start-page: 572
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b21
  article-title: An iterative dimension-by-dimension method for structural interval response prediction with multidimensional uncertain variables
  publication-title: Aerosp. Sci. Technol.
  doi: 10.1016/j.ast.2019.01.032
– volume: 7
  start-page: 34
  issue: 1
  year: 1998
  ident: 10.1016/j.tws.2022.109218_b62
  article-title: Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization
  publication-title: J. Multi-Criteria Decis. Anal.
  doi: 10.1002/(SICI)1099-1360(199801)7:1<34::AID-MCDA161>3.0.CO;2-6
– volume: 55
  start-page: 1091
  issue: 3
  year: 2017
  ident: 10.1016/j.tws.2022.109218_b7
  article-title: On design optimization for structural crashworthiness and its state of the art
  publication-title: Struct. Multidiscip. Optim.
  doi: 10.1007/s00158-016-1579-y
– volume: 23
  start-page: 9793
  issue: 20
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b15
  article-title: A new rule to combine dependent bodies of evidence
  publication-title: Soft Comput.
  doi: 10.1007/s00500-019-03804-y
– volume: 78
  start-page: 627
  year: 2020
  ident: 10.1016/j.tws.2022.109218_b28
  article-title: Robust topology optimization for multi-material structures under interval uncertainty
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2019.10.019
– volume: 127
  start-page: 28
  issue: 1
  year: 2000
  ident: 10.1016/j.tws.2022.109218_b49
  article-title: On comparing interval numbers
  publication-title: European J. Oper. Res.
  doi: 10.1016/S0377-2217(99)00319-7
– volume: 122
  start-page: 4922
  issue: 18
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b26
  article-title: A Newton iteration-based interval analysis method for nonlinear structural systems with uncertain-but-bounded parameters
  publication-title: Internat. J. Numer. Methods Engrg.
  doi: 10.1002/nme.6751
– volume: 2
  start-page: 221
  issue: 3
  year: 1994
  ident: 10.1016/j.tws.2022.109218_b50
  article-title: Muiltiobjective optimization using nondominated sorting in genetic algorithms
  publication-title: Evol. Comput.
  doi: 10.1162/evco.1994.2.3.221
– volume: 3
  start-page: 257
  issue: 4
  year: 1999
  ident: 10.1016/j.tws.2022.109218_b61
  article-title: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach
  publication-title: IEEE Trans. Evol. Comput.
  doi: 10.1109/4235.797969
– volume: 134
  start-page: 268
  issue: 1
  year: 2005
  ident: 10.1016/j.tws.2022.109218_b55
  article-title: An efficient algorithm for constructing optimal design of computer experiments
  publication-title: J. Statist. Plann. Inference
  doi: 10.1016/j.jspi.2004.02.014
– year: 2016
  ident: 10.1016/j.tws.2022.109218_b43
  article-title: Multi-objective modified grey wolf optimizer for optimal power flow
– volume: 95
  start-page: 115
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b48
  article-title: On design of multi-cell tubes under axial and oblique impact loads
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2015.07.002
– volume: 14
  start-page: 567
  issue: 2
  year: 2003
  ident: 10.1016/j.tws.2022.109218_b44
  article-title: On the local convergence of pattern search
  publication-title: SIAM J. Optim.
  doi: 10.1137/S1052623400374495
– year: 2015
  ident: 10.1016/j.tws.2022.109218_b63
– year: 2021
  ident: 10.1016/j.tws.2022.109218_b24
  article-title: A feasible identification method of uncertainty responses for vehicle structures
  publication-title: Struct. Multidiscip. Optim.
  doi: 10.1007/s00158-021-03065-0
– year: 2005
  ident: 10.1016/j.tws.2022.109218_b57
  article-title: Opposition-based learning: a new scheme for machine intelligence
– volume: 47
  start-page: 573
  year: 2017
  ident: 10.1016/j.tws.2022.109218_b11
  article-title: Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2017.03.053
– volume: 137
  start-page: 1
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b37
  article-title: A crushing analysis and multi-objective optimization of thin-walled five-cell structures
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2018.12.033
– volume: 86
  start-page: 215
  issue: 3
  year: 2004
  ident: 10.1016/j.tws.2022.109218_b14
  article-title: An approximation approach for uncertainty quantification using evidence theory
  publication-title: Reliab. Eng. Syst. Saf.
  doi: 10.1016/j.ress.2004.01.011
– volume: 87
  year: 2020
  ident: 10.1016/j.tws.2022.109218_b40
  article-title: An enhanced multi-objective grey wolf optimizer for service composition in cloud manufacturing
  publication-title: Appl. Soft Comput.
  doi: 10.1016/j.asoc.2019.106003
– volume: 188
  start-page: 1
  issue: 1
  year: 2008
  ident: 10.1016/j.tws.2022.109218_b53
  article-title: A nonlinear interval number programming method for uncertain optimization problems
  publication-title: European J. Oper. Res.
  doi: 10.1016/j.ejor.2007.03.031
– volume: 161
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b38
  article-title: Application of tailor rolled blanks in optimum design of pure electric vehicle crashworthiness and lightweight
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2020.107410
– volume: 6
  start-page: 182
  issue: 2
  year: 2002
  ident: 10.1016/j.tws.2022.109218_b51
  article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II
  publication-title: IEEE Trans. Evol. Comput.
  doi: 10.1109/4235.996017
– volume: 29
  start-page: 310
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b59
  article-title: A novel hybrid gravitational search and pattern search algorithm for load frequency control of nonlinear power system
  publication-title: Appl. Soft Comput.
  doi: 10.1016/j.asoc.2015.01.020
– year: 2006
  ident: 10.1016/j.tws.2022.109218_b56
  article-title: Opposition-based differential evolution algorithms
– volume: 38
  start-page: 3124
  issue: 13
  year: 2014
  ident: 10.1016/j.tws.2022.109218_b13
  article-title: Interval optimization based line sampling method for fuzzy and random reliability analysis
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2013.11.027
– volume: 43
  start-page: 6574
  issue: 21
  year: 2006
  ident: 10.1016/j.tws.2022.109218_b25
  article-title: Exact bounds for the static response set of structures with uncertain-but-bounded parameters
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2006.01.012
– volume: 119
  start-page: 68
  year: 2013
  ident: 10.1016/j.tws.2022.109218_b31
  article-title: Interval multi-objective optimisation of structures using adaptive kriging approximations
  publication-title: Comput. Struct.
  doi: 10.1016/j.compstruc.2012.12.028
– volume: 94
  start-page: 500
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b1
  article-title: Reliability design optimization of vehicle front-end structure for pedestrian lower extremity protection under multiple impact cases
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2015.05.014
– volume: 167
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b4
  article-title: Nondeterministic multi-objective and multi-case discrete optimization of functionally-graded front-bumper structures for pedestrian protection
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2020.106921
– volume: 131
  start-page: 77
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b20
  article-title: An inverse method for distributed dynamic load identification of structures with interval uncertainties
  publication-title: Adv. Eng. Softw.
  doi: 10.1016/j.advengsoft.2019.02.003
– year: 2005
  ident: 10.1016/j.tws.2022.109218_b52
  article-title: An optimization algorithm for imprecise multi-objective problem functions
– volume: 69
  start-page: 441
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b30
  article-title: Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2018.12.025
– volume: 47
  start-page: 106
  year: 2016
  ident: 10.1016/j.tws.2022.109218_b58
  article-title: Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2015.10.039
– volume: 167
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b2
  article-title: Injury biomechanics-based nondeterministic optimization of front-end structures for safety in pedestrian–vehicle impact
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2021.108087
– volume: 2
  start-page: 39
  year: 2012
  ident: 10.1016/j.tws.2022.109218_b64
  article-title: A multi-objective artificial bee colony algorithm
  publication-title: Swarm Evol. Comput.
  doi: 10.1016/j.swevo.2011.08.001
– volume: 135
  start-page: 1
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b3
  article-title: Multiobjective robust design optimization of fatigue life for a truck cab
  publication-title: Reliab. Eng. Syst. Saf.
  doi: 10.1016/j.ress.2014.10.007
– volume: 29
  start-page: 1111
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b17
  article-title: Reliability-based design optimization for the lattice boom of crawler crane
  publication-title: Structures
  doi: 10.1016/j.istruc.2020.12.024
– volume: 194
  start-page: 36
  year: 2018
  ident: 10.1016/j.tws.2022.109218_b66
  article-title: Crashworthiness design of novel hierarchical hexagonal columns
  publication-title: Compos. Struct.
  doi: 10.1016/j.compstruct.2018.03.099
– volume: 40
  start-page: 4412
  issue: 7
  year: 2016
  ident: 10.1016/j.tws.2022.109218_b12
  article-title: Fuzzy uncertainty propagation in composites using Gram–Schmidt polynomial chaos expansion
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2015.11.038
– volume: 161–162
  year: 2019
  ident: 10.1016/j.tws.2022.109218_b67
  article-title: Crushing behaviors of hierarchical sandwich-walled columns
  publication-title: Int. J. Mech. Sci.
– volume: 69
  start-page: 46
  year: 2014
  ident: 10.1016/j.tws.2022.109218_b54
  article-title: Grey wolf optimizer
  publication-title: Adv. Eng. Softw.
  doi: 10.1016/j.advengsoft.2013.12.007
– volume: 33
  start-page: 1454
  issue: 5
  year: 2020
  ident: 10.1016/j.tws.2022.109218_b19
  article-title: Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle
  publication-title: Chin. J. Aeronaut.
  doi: 10.1016/j.cja.2019.11.002
– volume: 109
  start-page: 132
  year: 2016
  ident: 10.1016/j.tws.2022.109218_b46
  article-title: Sensitivity analysis and reliability based design optimization for high-strength steel tailor welded thin-walled structures under crashworthiness
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2016.09.003
– volume: 67
  start-page: 120
  year: 2014
  ident: 10.1016/j.tws.2022.109218_b9
  article-title: Crashworthiness design of foam-filled bitubal structures with uncertainty
  publication-title: Int. J. Non-Linear Mech.
  doi: 10.1016/j.ijnonlinmec.2014.08.005
– volume: 162
  year: 2021
  ident: 10.1016/j.tws.2022.109218_b6
  article-title: Hybrid multi-objective robust design optimization of a truck cab considering fatigue life
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2021.107545
– volume: 131
  start-page: 286
  year: 2018
  ident: 10.1016/j.tws.2022.109218_b47
  article-title: Multi-response optimization design of tailor-welded blank (TWB) thin-walled structures using Taguchi-based gray relational analysis
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2018.07.007
– volume: 39
  start-page: 1853
  issue: 7
  year: 2015
  ident: 10.1016/j.tws.2022.109218_b8
  article-title: An efficient reliability method combining adaptive importance sampling and kriging metamodel
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2014.10.015
– volume: 38
  start-page: 695
  issue: 1
  year: 2022
  ident: 10.1016/j.tws.2022.109218_b65
  article-title: Multiobjective meta-heuristic with iterative parameter distribution estimation for aeroelastic design of an aircraft wing
  publication-title: Eng. Comput.
  doi: 10.1007/s00366-020-01077-w
– volume: 17
  issue: 10
  year: 2020
  ident: 10.1016/j.tws.2022.109218_b35
  article-title: Hull form optimization based on an NM+CFD integrated method for KCS
  publication-title: Int. J. Comput. Methods
  doi: 10.1142/S0219876220500085
– volume: 122
  start-page: 193
  year: 2018
  ident: 10.1016/j.tws.2022.109218_b10
  article-title: Nondeterministic optimization of tapered sandwich column for crashworthiness
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2017.09.028
– volume: 87
  start-page: 79
  year: 2017
  ident: 10.1016/j.tws.2022.109218_b41
  article-title: Optimal reactive power dispatch problem using a two-archive multi-objective grey wolf optimizer
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2017.06.009
SSID ssj0017194
Score 2.4108212
Snippet Thin-walled structures have been widely used in vehicle components due to their lightweight characteristics. To design structural parameters that are more in...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 109218
SubjectTerms Design optimization
Multi-objective optimization
Thin-walled structures
Uncertainty
Vehicle structures
Title Multi-objective design optimization using hybrid search algorithms with interval uncertainty for thin-walled structures
URI https://dx.doi.org/10.1016/j.tws.2022.109218
Volume 175
WOSCitedRecordID wos000792947100005&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: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1879-3223
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0017194
  issn: 0263-8231
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELaWLQc4IJ6iFJAPnIiCUjtZ28eqKi-hCokiRVwiO3G6WW2TapvtLof-d8axnc0WigCJSxSN7Dia-TKejOeB0CvYY3iZSPiQqJJhHCcsVFLmYZJoqRIh47y0zSbY8TFPU_F5NLryuTCXc1bXfL0W5_9V1EADYZvU2b8Qd_9QIMA9CB2uIHa4_pHgu5TasFEzq8qCoovRCBrQDWcu6TJYdh6C6XeTrhU4x4ecnzaLqp2euYS3qouGBAnCzmfjBlxwZzut6nBlerAUgS0_u1y4SMSZx96NI0C26dLINQVcnm6T3slmPaQe-syRSq505amfqm7wt6keeizgZ7ePrLJuNJ9Ks4lbuugqwNLQnEnajclqY85ECBqHbqlr22nlJ9VvvRCzN-3KVGEnxBTKIk63b1fU_mLWMksRE1AGJugttENYIvgY7Rx8OEo_9sdQbL_rpNm_mz8W7wIEry30a8NmYKyc3Ef33F8GPrDoeIBGun6I7g5qTz5Cq2s4wRYneIgT3OEEW5xgixO8wQk2OMEeJ3iAEww4wQOc4A0KHqOvb49ODt-HrgtHmBPB2rBgwAWmJ_uSJhK2xogoRmPKJAFrnxXRRAslczDEpchJTmL4yElJC0G14oVWOX2CxnVT66cIU85iouVEy0jGpBSS80IJLkoVlzoq4l0UeRZmuStRbzqlzDMfizjLgOuZ4Xpmub6LXvdTzm19lt8Njr1cMmdgWsMxAxDdPO3Zv03bQ3c26H-OxsBo_QLdzi_b6mLx0kHtB3CoppU
linkProvider Elsevier
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=Multi-objective+design+optimization+using+hybrid+search+algorithms+with+interval+uncertainty+for+thin-walled+structures&rft.jtitle=Thin-walled+structures&rft.au=Xu%2C+Xiang&rft.au=Xu%2C+Gaoxiang&rft.au=Chen%2C+Jiawei&rft.au=Liu%2C+Zhe&rft.date=2022-06-01&rft.pub=Elsevier+Ltd&rft.issn=0263-8231&rft.eissn=1879-3223&rft.volume=175&rft_id=info:doi/10.1016%2Fj.tws.2022.109218&rft.externalDocID=S0263823122001835
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0263-8231&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0263-8231&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0263-8231&client=summon