Ordinal Optimization for Optimal Orientation Problems in 3D Printing

Can Luo; Gang Xiong; Zhishuai Li; Zhen Shen; Li Wan; Meng Chu Zhou; Fei Yue Wang

doi:10.1016/j.ifacol.2021.04.086

Ordinal Optimization for Optimal Orientation Problems in 3D Printing

Can Luo, Gang Xiong, Zhishuai Li, Zhen Shen, Li Wan, Meng Chu Zhou, Fei Yue Wang

Research output: Contribution to journal › Conference article › peer-review

2 Scopus citations

Abstract

Compared with a traditional manufacturing process, 3D printing has advantages of performance and cost in personalized customization and has been applied in many fields. The problem of 3D model orientation optimization is a crucial one in practice. In this paper, based on the mathematical relationship between model orientation and printing time, surface quality, and supporting area, the model orientation problem is transformed into a multi-objective optimization problem with goal of minimizing printing time, surface quality, and supporting area. Ordinal Optimization (OO) is not only applicable to problems with random factors, but also to solve complex deterministic problems. The model orientation is a complex deterministic problem. We solve it with OO in this paper and use linear weighting to convert the multi-objective optimization problem into single-objective one. Finally, we compare the experimental results of solving 3D model orientation problems solved by OO and Genetic Algorithm (GA). The results show that OO requires less calculation time than GA while achieving comparable performance.

Original language	English (US)
Pages (from-to)	97-102
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	53
Issue number	5
DOIs	https://doi.org/10.1016/j.ifacol.2021.04.086
State	Published - 2020
Externally published	Yes
Event	3rd IFAC Workshop on Cyber-Physical and Human Systems, CPHS 2020 - Beijing, China Duration: Dec 3 2020 → Dec 5 2020

All Science Journal Classification (ASJC) codes

Control and Systems Engineering

Keywords

3D Printing
Digital Manufacturing
Genetic Algorithm
Intelligent Optimization
Machine Learning
Ordinal Optimization
Orientation Optimization

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10.1016/j.ifacol.2021.04.086

Cite this

@article{2bade6c1afc34e24882b0b6f56be383d,

title = "Ordinal Optimization for Optimal Orientation Problems in 3D Printing",

abstract = "Compared with a traditional manufacturing process, 3D printing has advantages of performance and cost in personalized customization and has been applied in many fields. The problem of 3D model orientation optimization is a crucial one in practice. In this paper, based on the mathematical relationship between model orientation and printing time, surface quality, and supporting area, the model orientation problem is transformed into a multi-objective optimization problem with goal of minimizing printing time, surface quality, and supporting area. Ordinal Optimization (OO) is not only applicable to problems with random factors, but also to solve complex deterministic problems. The model orientation is a complex deterministic problem. We solve it with OO in this paper and use linear weighting to convert the multi-objective optimization problem into single-objective one. Finally, we compare the experimental results of solving 3D model orientation problems solved by OO and Genetic Algorithm (GA). The results show that OO requires less calculation time than GA while achieving comparable performance.",

keywords = "3D Printing, Digital Manufacturing, Genetic Algorithm, Intelligent Optimization, Machine Learning, Ordinal Optimization, Orientation Optimization",

author = "Can Luo and Gang Xiong and Zhishuai Li and Zhen Shen and Li Wan and Zhou, {Meng Chu} and Wang, {Fei Yue}",

note = "Funding Information: Ordinal Optimization, Orientation Optimization, 3D Printing. Ordinal Optimization, Orientation Optimization, 3DD PPrraiinndttjiiunnsgt.ed support cannot be guaranteed unfortunately. In other 1. INTRODUCTION adjusted support cannot be guaranteed unfortunately. In other adjusted support cannot be guaranteed unfortunately. In other Modern 3Dprinting11 t..eIIcNTNhTnoRRlODUCTIOogDyU oCriTgIinONOaNted in the 1980s, and adcojumuspstedtleedtessduu.ppppoorrt t cacannnnoot t bbe e gguuararananteedteed uunnffoorrtutunnatelyately.. IInn ootthherer 1. INTRODUCTION words, some problems may arise after the printing is Modern 3Dprinting technology originatedinthe1980s,and wcoomrdps,letedso.me problems may arise after the printing is Mforodearrnnlo 3Dngprtiminteinthg tisectechhnolnoogy orlogyigihadnatebdeeinntcahelled1980s{"}Rap,andid wcoomrdps,letedso.me problems may arise after the printing is MMoodedern rn 3D3D prpriintntiinng tg teecchhnolnoloogy orgy oriigiginnaatteedd iinn tthhee 11980s980s,, aandnd ccoTohmmerppelleted eatreed ..two technical methods for the orientation of 3D fPorrodtoaetrynlop i3nnDggptimr(iRnetPin)th{"}g. istec3techhDn onloPogrloiyng toyinrigghiadnaistebdeeain ntncahoelledv1e9l 80{"}Rapds,igaintiaddl completed. ffoorr aa lolonngg timtimee ththisis techtechnnoolologgyy hhadad bbeeeenn cacalledlled {"}Rap{"}Rapiidd mhoerdels:e are ontwoe istecha hneical urismtic methoethdsofdorththate oevrienalutatioates snoevfer3D al foarnuafalcotnugrintgimteechthnioslotgeychthnaotl ohgays bheaedn abdeoepntecdalinledind{"}uRsatrpiiadl There are two technical methods for the orientation of 3D Promantoutyfacptuinrging(RtechP){"}n.olo3gD y thPat rinhas tinbgeenisadoa ptednoivnel indduigstrital ial Tlhteerrnea tairvee towroientetacthionnicsala nmdestheloedcstsftohre thbesot roiennetautniodner osfo3mDe manufacturing technology thatt haass been adopted in industriiaall models: one is a heuristic method that evaluates several and consumer settings (Belikovetsky et al., 2018; Shen et al., m0a1n9u;f Zachtauorinetg atle.,c2h0n1o9lo)g. y that has been adopted in industrial alternativee orientations and selects thee best one underr some and consumer settings (Belikovetsky et al., 2018; Shen et al., alnterinnafitnivitee onriuemntbaetironosfanpdosseiblelec tsdtihrectbieosnts ,onevaulnudaeter ss oamnde 2019T0h1e9 o; ; rZZiehhnaoatoatet eiot nal.alo.,,f22300D11 99m))..odels is critical in 3D printing. When ceoeprrttaintiaminizfafeasctc ttoohrsresm.. TTthhoe es ooethtlheceretr tisihseana nopootppimtimtimalizatioi zoartiieonnntaootnnioeentht.hTat ath coceo gnnossidiadlee orrssf 2019; Zhao et al., 2019). an infinite number of possible directions, evaluaatteess and The orientationof3D models iscritical in3D printing.When ananptimininiffzinineite nist et henmuummtobberesreleoocfft tpphooess ssoibipbtle dliem adliri roecercitioteinotnnasst,,ionevev.aluaTluhates aet egso aanal noddf Thee orientation of 3DD modeellss is critical in 3D printing. Whenn optimizes them to selectt thee optimaall orientation. Thee goal of The orientation of 3D models is critical in 3D printing. When optimizes them to select the optimal orientation. The goal of adding support automatically in 3D printing, its shape, density the former is to approachh aa human decision-making process. adding support automatically in 3D printing, its shape, density the former is to approach a human decision-making process. anandd specific location ddirirecectlytly afafffecectt pprrinintintingg qquualityality aandnd IItsts adadvvanantagtagee isis ffast ast asstt cacalculculatiolationn ssppeeeedd,, whwhile thile thee ddisisadadvvaanntagtage e e onfdmosdpeelcihfaics al ogcraetaiot ninfdluireencctely onaftfheects uprpinotritnogf3qDua plirtiyntianngd, totshaadnvdalneta3gDeiosbfjaesctt sc awlcituhlactoiomnpslpeexetdo,pwohloilgei etsh eanddisagdevoamnetatrgice amount of materials used (Zhang et al., 2018). The orientation is that the quality of the solution may not be the best, and fails ofmodelhasa greatt influence onthesupportof3DD printing,, toto hhananddlele 3D3D oobbjects jects jeeccttss withwith cocommpplexlex totoppoolologgies ies ieess anandd ggeeoommetetrricic because it directly affects the amount of support and printing shapes. In recent years, research on model orientation based on becausee iitt directly affects thee amountt of supportt and printing shapeess.. In recentt years, research on modeell orientation based on because it directly affects the amount of support and printing shapes. In recent years, research on model orientation based on effect. Now, most 3D software needs to manually set the optimization algorithms becomes popular and has achievedd hfefuercits.ticNso. wA,ftemroasdtdi3nDg thsoefstuwpaproe rtnmeeoddsulteotomgaennuearlaltyesuept ptohret , orientation of a system model requires more calculations. orientation. It gives a recommended orientation based on some encouraging results (Zhao et al., 2006; Byun et al., 2006). The heuristics.. Afteradding thesupportmoduletogeneratesupport, oorrienientatiotationn ooff aa sysyststeemm mmooddel eell rreqequuirires mes moorre ee cacalculculatiolationnss.. heuristics. After adding the support module to generate support, orientation of a system model requires more calculations. the orientation often needs to bee manually adjusted to generatee Theree is currently no softwaree to solvee this problem. Basically, the orientation often needs to be manually adjusted to generate There is currently no software to solve this problem. Basically, as littllee support as possible. For aa complex model, much iitt is adjusted manually, or somee simpllee rulleess are used to assistt as little support as possible. For a complex model, much it is adjusted manually, or some simple rules are used to assist mThanis wuaaorllk w woarsksupisproreqteudirin edpa.rTt byheNefatfieconatlofNasturucah ml Scieanncuae Floundation of peopllee in making decisions. Ordinaall Optimization (OO) has manual workisrequired.Theeffectofsuch manual thpree oobpaefleb fiecilnityt om wahkfilneeng resdqueurciniirsiginognanos.nlOyexradce ifnellenawl cOtopmtsipomuluitzitionagtinorenswitho(OurOce)hshigfaohsr Chiisnawuonrkd ewraGsrsaunptspo6r1te7d73in3 8p2a,rtUb1y90N9a2t0io4n,a6l1N7a7t3u3r8al1,S6ci1e8n7c2e3F6o5u;nCdAatSionK eoyf thee effect of ensuring an excellent solution with high This work was supported in part by National Natural Science Foundation of probability while requiring only a few computing resources for TChhiisnawunork wderaGsrsaupntspor6177ted338in pa2,rtUby1909Na204tiona, 617l Na733tur81al,S6ci18en723ce F65;ounCdaAtSionK eyof probability while requiring only a few computing resources for TrehocijnheancotulonofdgetyhreTGCarlaheninnttsesP6er1oA7je7cc3at3d8e(Zm2,hyeU no1 f9SS0hc9ei2ne0n);4c,eS;6cD1ie7on7nt3igf3igc8u1aI,n6s{\textquoteright}st1r8uIn7mn2eo3nv6ta5tD;ioCenvAeTlSaolpKeinnetgys probability while requiring only a few computing resources for China under Grants 61773382, U1909204, 61773381, 61872365; CAS Key ssooOlvlv iniwnggascoc oommrigppilexlneaxllppyrroopbbrlemloepmoss..ed to solve problems with random Treocjhencot loo(fGgtyahneTgC alXheinnotensPger)o;AjFeccoatsdhe(aZmnhy e Snoc fiSeShncecinen);acneS;dc DieTonentcigfhigncuoaIlnos{\textquoteright}gstyruI nmInnenonovtvataDitoieonvneT laoTlpeiannmtgs solving complex problems. Technology Talent Project (Zhen Shen); Scientific Instrument Developing Project (o(2fG0ta1hn8egITC X1h0iino0en1sg4e)2;A).FcCoaosdhreramensy p SoocnfideSincncigenaacuneth;do DrT:oenZcghhgenunoa lSnoh{\textquoteright}gseynI n.InnnoovvataitoionnT aTleanmts OaOct owrsa,sb ourti fguinrtahlelyr rpersoepaorcshedshtowsos ltvhea tp irto cbalenmbse wapipthlicraanbdleo mto Project ((2G0a1n8gIT X10io0n1g4)2;).FCooshrraens pSocnideinncgeaaunthdo rT:eZchhenno lSohgeyn .Innovation Team OO was originally proposed to solve problems with random Project (2018IT100142). Corresponding author: Zhen Shen. factors, but further research shows that it can be applicable to Project (2018IT100142). Corresponding author: Zhen Shen. factors, but further research shows that it can be applicable to 2405-8963 Copyright {\textcopyright} 2020 The Authors. This is an open access article under the CC BY-NC-ND license. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2021.04.086 Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.. All rights reserved.; 3rd IFAC Workshop on Cyber-Physical and Human Systems, CPHS 2020 ; Conference date: 03-12-2020 Through 05-12-2020",

year = "2020",

doi = "10.1016/j.ifacol.2021.04.086",

language = "English (US)",

volume = "53",

pages = "97--102",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "IFAC Secretariat",

number = "5",

}

TY - JOUR

T1 - Ordinal Optimization for Optimal Orientation Problems in 3D Printing

AU - Luo, Can

AU - Xiong, Gang

AU - Li, Zhishuai

AU - Shen, Zhen

AU - Wan, Li

AU - Zhou, Meng Chu

AU - Wang, Fei Yue

N1 - Funding Information: Ordinal Optimization, Orientation Optimization, 3D Printing. Ordinal Optimization, Orientation Optimization, 3DD PPrraiinndttjiiunnsgt.ed support cannot be guaranteed unfortunately. In other 1. INTRODUCTION adjusted support cannot be guaranteed unfortunately. In other adjusted support cannot be guaranteed unfortunately. In other Modern 3Dprinting11 t..eIIcNTNhTnoRRlODUCTIOogDyU oCriTgIinONOaNted in the 1980s, and adcojumuspstedtleedtessduu.ppppoorrt t cacannnnoot t bbe e gguuararananteedteed uunnffoorrtutunnatelyately.. IInn ootthherer 1. INTRODUCTION words, some problems may arise after the printing is Modern 3Dprinting technology originatedinthe1980s,and wcoomrdps,letedso.me problems may arise after the printing is Mforodearrnnlo 3Dngprtiminteinthg tisectechhnolnoogy orlogyigihadnatebdeeinntcahelled1980s"Rap,andid wcoomrdps,letedso.me problems may arise after the printing is MMoodedern rn 3D3D prpriintntiinng tg teecchhnolnoloogy orgy oriigiginnaatteedd iinn tthhee 11980s980s,, aandnd ccoTohmmerppelleted eatreed ..two technical methods for the orientation of 3D fPorrodtoaetrynlop i3nnDggptimr(iRnetPin)th"g. istec3techhDn onloPogrloiyng toyinrigghiadnaistebdeeain ntncahoelledv1e9l 80"Rapds,igaintiaddl completed. ffoorr aa lolonngg timtimee ththisis techtechnnoolologgyy hhadad bbeeeenn cacalledlled "Rap"Rapiidd mhoerdels:e are ontwoe istecha hneical urismtic methoethdsofdorththate oevrienalutatioates snoevfer3D al foarnuafalcotnugrintgimteechthnioslotgeychthnaotl ohgays bheaedn abdeoepntecdalinledind"uRsatrpiiadl There are two technical methods for the orientation of 3D Promantoutyfacptuinrging(RtechP)"n.olo3gD y thPat rinhas tinbgeenisadoa ptednoivnel indduigstrital ial Tlhteerrnea tairvee towroientetacthionnicsala nmdestheloedcstsftohre thbesot roiennetautniodner osfo3mDe manufacturing technology thatt haass been adopted in industriiaall models: one is a heuristic method that evaluates several and consumer settings (Belikovetsky et al., 2018; Shen et al., m0a1n9u;f Zachtauorinetg atle.,c2h0n1o9lo)g. y that has been adopted in industrial alternativee orientations and selects thee best one underr some and consumer settings (Belikovetsky et al., 2018; Shen et al., alnterinnafitnivitee onriuemntbaetironosfanpdosseiblelec tsdtihrectbieosnts ,onevaulnudaeter ss oamnde 2019T0h1e9 o; ; rZZiehhnaoatoatet eiot nal.alo.,,f22300D11 99m))..odels is critical in 3D printing. When ceoeprrttaintiaminizfafeasctc ttoohrsresm.. TTthhoe es ooethtlheceretr tisihseana nopootppimtimtimalizatioi zoartiieonnntaootnnioeentht.hTat ath coceo gnnossidiadlee orrssf 2019; Zhao et al., 2019). an infinite number of possible directions, evaluaatteess and The orientationof3D models iscritical in3D printing.When ananptimininiffzinineite nist et henmuummtobberesreleoocfft tpphooess ssoibipbtle dliem adliri roecercitioteinotnnasst,,ionevev.aluaTluhates aet egso aanal noddf Thee orientation of 3DD modeellss is critical in 3D printing. Whenn optimizes them to selectt thee optimaall orientation. Thee goal of The orientation of 3D models is critical in 3D printing. When optimizes them to select the optimal orientation. The goal of adding support automatically in 3D printing, its shape, density the former is to approachh aa human decision-making process. adding support automatically in 3D printing, its shape, density the former is to approach a human decision-making process. anandd specific location ddirirecectlytly afafffecectt pprrinintintingg qquualityality aandnd IItsts adadvvanantagtagee isis ffast ast asstt cacalculculatiolationn ssppeeeedd,, whwhile thile thee ddisisadadvvaanntagtage e e onfdmosdpeelcihfaics al ogcraetaiot ninfdluireencctely onaftfheects uprpinotritnogf3qDua plirtiyntianngd, totshaadnvdalneta3gDeiosbfjaesctt sc awlcituhlactoiomnpslpeexetdo,pwohloilgei etsh eanddisagdevoamnetatrgice amount of materials used (Zhang et al., 2018). The orientation is that the quality of the solution may not be the best, and fails ofmodelhasa greatt influence onthesupportof3DD printing,, toto hhananddlele 3D3D oobbjects jects jeeccttss withwith cocommpplexlex totoppoolologgies ies ieess anandd ggeeoommetetrricic because it directly affects the amount of support and printing shapes. In recent years, research on model orientation based on becausee iitt directly affects thee amountt of supportt and printing shapeess.. In recentt years, research on modeell orientation based on because it directly affects the amount of support and printing shapes. In recent years, research on model orientation based on effect. Now, most 3D software needs to manually set the optimization algorithms becomes popular and has achievedd hfefuercits.ticNso. wA,ftemroasdtdi3nDg thsoefstuwpaproe rtnmeeoddsulteotomgaennuearlaltyesuept ptohret , orientation of a system model requires more calculations. orientation. It gives a recommended orientation based on some encouraging results (Zhao et al., 2006; Byun et al., 2006). The heuristics.. Afteradding thesupportmoduletogeneratesupport, oorrienientatiotationn ooff aa sysyststeemm mmooddel eell rreqequuirires mes moorre ee cacalculculatiolationnss.. heuristics. After adding the support module to generate support, orientation of a system model requires more calculations. the orientation often needs to bee manually adjusted to generatee Theree is currently no softwaree to solvee this problem. Basically, the orientation often needs to be manually adjusted to generate There is currently no software to solve this problem. Basically, as littllee support as possible. For aa complex model, much iitt is adjusted manually, or somee simpllee rulleess are used to assistt as little support as possible. For a complex model, much it is adjusted manually, or some simple rules are used to assist mThanis wuaaorllk w woarsksupisproreqteudirin edpa.rTt byheNefatfieconatlofNasturucah ml Scieanncuae Floundation of peopllee in making decisions. Ordinaall Optimization (OO) has manual workisrequired.Theeffectofsuch manual thpree oobpaefleb fiecilnityt om wahkfilneeng resdqueurciniirsiginognanos.nlOyexradce ifnellenawl cOtopmtsipomuluitzitionagtinorenswitho(OurOce)hshigfaohsr Chiisnawuonrkd ewraGsrsaunptspo6r1te7d73in3 8p2a,rtUb1y90N9a2t0io4n,a6l1N7a7t3u3r8al1,S6ci1e8n7c2e3F6o5u;nCdAatSionK eoyf thee effect of ensuring an excellent solution with high This work was supported in part by National Natural Science Foundation of probability while requiring only a few computing resources for TChhiisnawunork wderaGsrsaupntspor6177ted338in pa2,rtUby1909Na204tiona, 617l Na733tur81al,S6ci18en723ce F65;ounCdaAtSionK eyof probability while requiring only a few computing resources for TrehocijnheancotulonofdgetyhreTGCarlaheninnttsesP6er1oA7je7cc3at3d8e(Zm2,hyeU no1 f9SS0hc9ei2ne0n);4c,eS;6cD1ie7on7nt3igf3igc8u1aI,n6s’st1r8uIn7mn2eo3nv6ta5tD;ioCenvAeTlSaolpKeinnetgys probability while requiring only a few computing resources for China under Grants 61773382, U1909204, 61773381, 61872365; CAS Key ssooOlvlv iniwnggascoc oommrigppilexlneaxllppyrroopbbrlemloepmoss..ed to solve problems with random Treocjhencot loo(fGgtyahneTgC alXheinnotensPger)o;AjFeccoatsdhe(aZmnhy e Snoc fiSeShncecinen);acneS;dc DieTonentcigfhigncuoaIlnos’gstyruI nmInnenonovtvataDitoieonvneT laoTlpeiannmtgs solving complex problems. Technology Talent Project (Zhen Shen); Scientific Instrument Developing Project (o(2fG0ta1hn8egITC X1h0iino0en1sg4e)2;A).FcCoaosdhreramensy p SoocnfideSincncigenaacuneth;do DrT:oenZcghhgenunoa lSnoh’gseynI n.InnnoovvataitoionnT aTleanmts OaOct owrsa,sb ourti fguinrtahlelyr rpersoepaorcshedshtowsos ltvhea tp irto cbalenmbse wapipthlicraanbdleo mto Project ((2G0a1n8gIT X10io0n1g4)2;).FCooshrraens pSocnideinncgeaaunthdo rT:eZchhenno lSohgeyn .Innovation Team OO was originally proposed to solve problems with random Project (2018IT100142). Corresponding author: Zhen Shen. factors, but further research shows that it can be applicable to Project (2018IT100142). Corresponding author: Zhen Shen. factors, but further research shows that it can be applicable to 2405-8963 Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2021.04.086 Publisher Copyright: © 2020 Elsevier B.V.. All rights reserved.

PY - 2020

Y1 - 2020

N2 - Compared with a traditional manufacturing process, 3D printing has advantages of performance and cost in personalized customization and has been applied in many fields. The problem of 3D model orientation optimization is a crucial one in practice. In this paper, based on the mathematical relationship between model orientation and printing time, surface quality, and supporting area, the model orientation problem is transformed into a multi-objective optimization problem with goal of minimizing printing time, surface quality, and supporting area. Ordinal Optimization (OO) is not only applicable to problems with random factors, but also to solve complex deterministic problems. The model orientation is a complex deterministic problem. We solve it with OO in this paper and use linear weighting to convert the multi-objective optimization problem into single-objective one. Finally, we compare the experimental results of solving 3D model orientation problems solved by OO and Genetic Algorithm (GA). The results show that OO requires less calculation time than GA while achieving comparable performance.

AB - Compared with a traditional manufacturing process, 3D printing has advantages of performance and cost in personalized customization and has been applied in many fields. The problem of 3D model orientation optimization is a crucial one in practice. In this paper, based on the mathematical relationship between model orientation and printing time, surface quality, and supporting area, the model orientation problem is transformed into a multi-objective optimization problem with goal of minimizing printing time, surface quality, and supporting area. Ordinal Optimization (OO) is not only applicable to problems with random factors, but also to solve complex deterministic problems. The model orientation is a complex deterministic problem. We solve it with OO in this paper and use linear weighting to convert the multi-objective optimization problem into single-objective one. Finally, we compare the experimental results of solving 3D model orientation problems solved by OO and Genetic Algorithm (GA). The results show that OO requires less calculation time than GA while achieving comparable performance.

KW - 3D Printing

KW - Digital Manufacturing

KW - Genetic Algorithm

KW - Intelligent Optimization

KW - Machine Learning

KW - Ordinal Optimization

KW - Orientation Optimization

UR - http://www.scopus.com/inward/record.url?scp=85107868361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85107868361&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2021.04.086

DO - 10.1016/j.ifacol.2021.04.086

M3 - Conference article

AN - SCOPUS:85107868361

SN - 2405-8963

VL - 53

SP - 97

EP - 102

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 5

T2 - 3rd IFAC Workshop on Cyber-Physical and Human Systems, CPHS 2020

Y2 - 3 December 2020 through 5 December 2020

ER -

Ordinal Optimization for Optimal Orientation Problems in 3D Printing

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