Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming

•Exploits the objective function structure of a multiple objective linear program.•Shows methods for decomposing the criterion cone.•Allows for the computation of all efficient extreme points by distributed processing.•Computational experiments show typical time savings running from 40 to 70%. This...

Full description

Saved in:
Bibliographic Details
Published in:European journal of operational research Vol. 277; no. 2; pp. 653 - 666
Main Authors: Piercy, Craig A., Steuer, Ralph E.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2019
Subjects:
ISSN:0377-2217, 1872-6860
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract •Exploits the objective function structure of a multiple objective linear program.•Shows methods for decomposing the criterion cone.•Allows for the computation of all efficient extreme points by distributed processing.•Computational experiments show typical time savings running from 40 to 70%. This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multiple objective linear program (MOLP) with three objectives. The approach is particularly useful when working with such MOLPs possessing large numbers of efficient extreme points. By subdividing the criterion cone into sub-cones, the paper shows how the task of computing all efficient extreme points can be broken down into parts so that the parts can be solved concurrently, thus allowing all efficient extreme points to be computed in much reduced elapsed time. The paper investigates several schemes for conducting this task and reports on a volume of computational experience.
AbstractList •Exploits the objective function structure of a multiple objective linear program.•Shows methods for decomposing the criterion cone.•Allows for the computation of all efficient extreme points by distributed processing.•Computational experiments show typical time savings running from 40 to 70%. This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multiple objective linear program (MOLP) with three objectives. The approach is particularly useful when working with such MOLPs possessing large numbers of efficient extreme points. By subdividing the criterion cone into sub-cones, the paper shows how the task of computing all efficient extreme points can be broken down into parts so that the parts can be solved concurrently, thus allowing all efficient extreme points to be computed in much reduced elapsed time. The paper investigates several schemes for conducting this task and reports on a volume of computational experience.
Author Steuer, Ralph E.
Piercy, Craig A.
Author_xml – sequence: 1
  givenname: Craig A.
  surname: Piercy
  fullname: Piercy, Craig A.
– sequence: 2
  givenname: Ralph E.
  surname: Steuer
  fullname: Steuer, Ralph E.
  email: rsteuer@uga.edu
BookMark eNp9kM9KxDAQh4Os4O7qC3jKC7QmaZuk4EUW_8GCIHoO2XS6prZNSdNV396U9eRhLzMMzDfD71uhRe96QOiakpQSym-aFBrnU0ZomRKWkpydoSWVgiVccrJAS5IJkTBGxQVajWNDCKEFLZZoeoVqMrbf4y_dtolpnfnEwXaAa-dx-ABsXDdMQQfreuxqHLcw1LU1FvqA4Tt4iMuDs30Yse1xN7XBDi1gt2vABHsA3NoetMeDd3uvuy4-u0TntW5HuPrra_T-cP-2eUq2L4_Pm7ttYjJehERKzgUzopKU8R2RMsuhohBrHIUglQDCdYxW7ApqKg1lkZuyNBVhDEQusjWSx7vGu3H0UCtjj1GC17ZVlKhZn2rUrE_N-hRhKuqLKPuHDt522v-chm6PEMRQBwtejbMnA5X1UYaqnD2F_wLxjo3z
CitedBy_id crossref_primary_10_1007_s12351_021_00664_z
Cites_doi 10.1007/BF00120667
10.1007/s10107-016-1061-z
10.1007/BF02207641
10.1057/jors.1977.147
10.1287/mnsc.1070.0838
10.1007/BF00941298
10.1007/s10898-015-0301-8
10.1007/s00186-008-0220-2
10.1023/A:1004605810296
10.1016/j.ejor.2013.08.001
10.1016/S0377-2217(01)00153-9
10.1023/A:1013875600711
10.1016/0895-7177(89)90369-5
10.1002/cae.21601
10.1016/0022-247X(87)90065-5
10.1016/j.ejor.2005.02.072
10.1007/BF01580111
10.1111/j.1475-3995.2012.00851.x
10.1007/s00186-007-0194-5
10.1007/BF01588968
10.1007/BF02023100
10.1007/s10898-011-9709-y
10.1016/j.ejor.2010.02.041
10.1016/j.ejor.2003.09.014
10.1016/j.ejor.2016.02.039
ContentType Journal Article
Copyright 2019
Copyright_xml – notice: 2019
DBID AAYXX
CITATION
DOI 10.1016/j.ejor.2019.02.042
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
Business
EISSN 1872-6860
EndPage 666
ExternalDocumentID 10_1016_j_ejor_2019_02_042
S0377221719301900
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
4.4
457
4G.
5GY
5VS
6OB
7-5
71M
8P~
9JN
9JO
AAAKF
AABNK
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AARIN
AAXUO
AAYFN
ABAOU
ABBOA
ABFNM
ABFRF
ABJNI
ABMAC
ABUCO
ABYKQ
ACAZW
ACDAQ
ACGFO
ACGFS
ACIWK
ACNCT
ACRLP
ACZNC
ADBBV
ADEZE
ADGUI
AEBSH
AEFWE
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
APLSM
ARUGR
AXJTR
BKOJK
BKOMP
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FIRID
FNPLU
FYGXN
G-Q
GBLVA
GBOLZ
HAMUX
IHE
J1W
KOM
LY1
M41
MHUIS
MO0
MS~
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
RIG
ROL
RPZ
RXW
SCC
SDF
SDG
SDP
SDS
SES
SPC
SPCBC
SSB
SSD
SSV
SSW
SSZ
T5K
TAE
TN5
U5U
XPP
ZMT
~02
~G-
1OL
29G
41~
9DU
AAAKG
AAQXK
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ABXDB
ACLOT
ACNNM
ACRPL
ACVFH
ADCNI
ADIYS
ADJOM
ADMUD
ADNMO
ADXHL
AEIPS
AEUPX
AFFNX
AFJKZ
AFPUW
AGQPQ
AI.
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
ASPBG
AVWKF
AZFZN
CITATION
EFKBS
FEDTE
FGOYB
HVGLF
HZ~
R2-
SEW
VH1
WUQ
~HD
ID FETCH-LOGICAL-c365t-886672c7d8126b08834ed1e34e26b770d7e06a0375b51cdae954c99cd022e7473
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000466254800019&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0377-2217
IngestDate Tue Nov 18 22:18:45 EST 2025
Sat Nov 29 07:18:16 EST 2025
Fri Feb 23 02:17:45 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Efficient extreme points
Distributed processing
Nondominated vertices
Criterion cones
Multiple objective programming
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c365t-886672c7d8126b08834ed1e34e26b770d7e06a0375b51cdae954c99cd022e7473
PageCount 14
ParticipantIDs crossref_citationtrail_10_1016_j_ejor_2019_02_042
crossref_primary_10_1016_j_ejor_2019_02_042
elsevier_sciencedirect_doi_10_1016_j_ejor_2019_02_042
PublicationCentury 2000
PublicationDate 2019-09-01
PublicationDateYYYYMMDD 2019-09-01
PublicationDate_xml – month: 09
  year: 2019
  text: 2019-09-01
  day: 01
PublicationDecade 2010
PublicationTitle European journal of operational research
PublicationYear 2019
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Ehrgott, Löhne, Shao (bib0014) 2012; 52
Ecker, Song (bib0013) 1994; 83
Benson, Sun (bib0006) 2000; 105
Shao, Ehrgott (bib0024) 2008; 68
Armand, Malivert (bib0004) 1991; 70
Kirlik, Sayin (bib0019) 2014; 232
Wallenius, Dyer, Fishburn, Steuer, Zionts, Deb (bib0028) 2008; 54
Hwang, Masud (bib0017) 1979; L164
Benson (bib0005) 1991; 1
Isermann (bib0018) 1977; 28
Ehrgott, Shao (bib0015) 2008; 68
Steuer (bib0025) 2017
Evans, Steuer (bib0016) 1973; 5
Rudloff, Ulus, Vanderbei (bib0023) 2017; 163
Miettinen, Podkopaev, Ruiz, Luque (bib0022) 2015; 4
Chaabane, Brahmi, Ramdan (bib0008) 2012; 19
Steuer, Piercy (bib0027) 2005; 162
Yamamoto (bib0029) 2002; 22
Zeleny (bib0030) 1974
Abbas, Chaabane (bib0001) 2006; 174
Steuer (bib0026) 1986
Miettinen, Eskelainen, Ruiz, Luque (bib0021) 2010; 206
Dauer (bib0011) 1993; 46–47
Löhne, Weissing (bib0020) 2017; 260
Alves, Antunes, Climaco (bib0002) 2015; 23
Climaco, Antunes (bib0009) 1989; 12
Ecker, Kouada (bib0012) 1978; 14
Antunes, Alves, Climaco (bib0003) 2016
Benson, Sun (bib0007) 2002; 139
Dauer (bib0010) 1987; 126
Steuer (10.1016/j.ejor.2019.02.042_sbref0025) 2017
Isermann (10.1016/j.ejor.2019.02.042_bib0018) 1977; 28
Kirlik (10.1016/j.ejor.2019.02.042_bib0019) 2014; 232
Löhne (10.1016/j.ejor.2019.02.042_bib0020) 2017; 260
Ecker (10.1016/j.ejor.2019.02.042_bib0013) 1994; 83
Ecker (10.1016/j.ejor.2019.02.042_bib0012) 1978; 14
Miettinen (10.1016/j.ejor.2019.02.042_bib0021) 2010; 206
Antunes (10.1016/j.ejor.2019.02.042_bib0003) 2016
Dauer (10.1016/j.ejor.2019.02.042_bib0010) 1987; 126
Dauer (10.1016/j.ejor.2019.02.042_bib0011) 1993; 46–47
Evans (10.1016/j.ejor.2019.02.042_bib0016) 1973; 5
Benson (10.1016/j.ejor.2019.02.042_bib0006) 2000; 105
Ehrgott (10.1016/j.ejor.2019.02.042_bib0014) 2012; 52
Chaabane (10.1016/j.ejor.2019.02.042_bib0008) 2012; 19
Shao (10.1016/j.ejor.2019.02.042_bib0024) 2008; 68
Zeleny (10.1016/j.ejor.2019.02.042_bib0030) 1974
Miettinen (10.1016/j.ejor.2019.02.042_bib0022) 2015; 4
Armand (10.1016/j.ejor.2019.02.042_bib0004) 1991; 70
Rudloff (10.1016/j.ejor.2019.02.042_bib0023) 2017; 163
Alves (10.1016/j.ejor.2019.02.042_bib0002) 2015; 23
Hwang (10.1016/j.ejor.2019.02.042_bib0017) 1979; L164
Steuer (10.1016/j.ejor.2019.02.042_bib0027) 2005; 162
Climaco (10.1016/j.ejor.2019.02.042_bib0009) 1989; 12
Yamamoto (10.1016/j.ejor.2019.02.042_bib0029) 2002; 22
Ehrgott (10.1016/j.ejor.2019.02.042_bib0015) 2008; 68
Steuer (10.1016/j.ejor.2019.02.042_bib0026) 1986
Abbas (10.1016/j.ejor.2019.02.042_bib0001) 2006; 174
Benson (10.1016/j.ejor.2019.02.042_bib0007) 2002; 139
Benson (10.1016/j.ejor.2019.02.042_bib0005) 1991; 1
Wallenius (10.1016/j.ejor.2019.02.042_bib0028) 2008; 54
References_xml – volume: 139
  start-page: 26
  year: 2002
  end-page: 41
  ident: bib0007
  article-title: A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program
  publication-title: European Journal of Operational Research
– volume: 19
  start-page: 531
  year: 2012
  end-page: 545
  ident: bib0008
  article-title: The augmented weighted Tchebychev norm for optimizing a linear function over an integer efficient set of a multicriteria linear program
  publication-title: International Transactions in Operations Research
– volume: 14
  start-page: 249
  year: 1978
  end-page: 261
  ident: bib0012
  article-title: Finding all efficient extreme points for multiple objective linear programs
  publication-title: Mathematical Programming
– year: 2017
  ident: bib0025
  article-title: ADBASE: A self-contained multiple objective linear programming solver for all efficient extreme points and unbounded efficient edges
– volume: 206
  start-page: 426
  year: 2010
  end-page: 434
  ident: bib0021
  article-title: Nautilus method: an interactive technique in multiobjective optimization based on the nadir point
  publication-title: European Journal of Operational Research
– volume: 12
  start-page: 1299
  year: 1989
  end-page: 1309
  ident: bib0009
  article-title: Implementation of a user friendly software package – a guided tour of TRIMAP
  publication-title: Mathematical and Computer Modelling
– volume: 28
  start-page: 711
  year: 1977
  end-page: 725
  ident: bib0018
  article-title: The enumeration of the set of all efficient solutions for a linear multiple objective program
  publication-title: Operational Research Quarterly
– volume: 1
  start-page: 83
  year: 1991
  end-page: 104
  ident: bib0005
  article-title: An all-linear programming relaxation algorithm for optimizing over the efficient set
  publication-title: Journal of Global Optimization
– volume: L164
  year: 1979
  ident: bib0017
  publication-title: Multiple objective decision making – methods and applications: A state-of-the-art survey
– volume: 260
  start-page: 807
  year: 2017
  end-page: 813
  ident: bib0020
  article-title: The vector linear program solver Bensolve – notes on theoretical background
  publication-title: European Journal of Operational Research
– year: 1986
  ident: bib0026
  article-title: Multiple criteria optimization: Theory, computation, and application
– volume: 126
  start-page: 579
  year: 1987
  end-page: 593
  ident: bib0010
  article-title: Analysis of the objective space in multiple objective programming
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 105
  start-page: 17
  year: 2000
  end-page: 36
  ident: bib0006
  article-title: Outcome space partition of the weight set in multiobjective linear programming
  publication-title: Journal of Optimization Theory and Applications
– year: 1974
  ident: bib0030
  article-title: Linear multi-objective programming
– volume: 174
  start-page: 1140
  year: 2006
  end-page: 1161
  ident: bib0001
  article-title: Optimizing a linear function over an integer efficient set
  publication-title: European Journal of Operational Research
– volume: 52
  start-page: 757
  year: 2012
  end-page: 778
  ident: bib0014
  article-title: A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming
  publication-title: Journal of Global Optimization
– volume: 68
  start-page: 257
  year: 2008
  end-page: 276
  ident: bib0015
  article-title: Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning
  publication-title: Mathematical Methods of Operational Research
– volume: 83
  start-page: 541
  year: 1994
  end-page: 563
  ident: bib0013
  article-title: Optimizing a linear function over the efficient set
  publication-title: Journal of Optimization Theory and Applications
– volume: 5
  start-page: 54
  year: 1973
  end-page: 72
  ident: bib0016
  article-title: A revised simplex method for multiple objective programs
  publication-title: Mathematical Programming
– volume: 23
  start-page: 314
  year: 2015
  end-page: 326
  ident: bib0002
  article-title: Interactive MOLP explorer – a graphical-based computational tool for teaching and decision support in multi-objective linear programming models
  publication-title: Computer Applications of Engineering Education
– volume: 162
  start-page: 484
  year: 2005
  end-page: 496
  ident: bib0027
  article-title: A regression study of the number of efficient extreme points in multiple objective linear programming
  publication-title: European Journal of Operational Research
– volume: 232
  start-page: 479
  year: 2014
  end-page: 488
  ident: bib0019
  article-title: A new algorithm for generating all nondominated solutions for multiobjective discrete optimization problems
  publication-title: European Journal of Operational Research
– volume: 4
  start-page: 633
  year: 2015
  end-page: 652
  ident: bib0022
  article-title: A new preference handling technique for interactive multiobjective optimization without trading-off
  publication-title: Journal of Global Optimization
– volume: 68
  start-page: 469
  year: 2008
  end-page: 492
  ident: bib0024
  article-title: Approximating the nondominated set of an MOLP by approximately solving its dual problem
  publication-title: Mathematical Methods of Operations Research
– volume: 46–47
  start-page: 279
  year: 1993
  end-page: 292
  ident: bib0011
  article-title: On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program
  publication-title: Annals of Operations Research
– volume: 54
  start-page: 1336
  year: 2008
  end-page: 1349
  ident: bib0028
  article-title: Multiple criteria decision making, multiattribute utility analysis: Recent accomplishments and what lies ahead
  publication-title: Management Science
– volume: 22
  start-page: 285
  year: 2002
  end-page: 317
  ident: bib0029
  article-title: Optimization over the efficient set: overview
  publication-title: Journal of Global Optimization
– year: 2016
  ident: bib0003
  article-title: Multiobjective linear and integer programming
– volume: 70
  start-page: 467
  year: 1991
  end-page: 489
  ident: bib0004
  article-title: Determination of the efficient set in multiobjective linear programming
  publication-title: Journal of Optimization Theory and Applications
– volume: 163
  start-page: 213
  year: 2017
  end-page: 242
  ident: bib0023
  article-title: A parametric simplex algorithm for linear vector optimization problems
  publication-title: Mathematical Programming
– volume: 1
  start-page: 83
  issue: 1
  year: 1991
  ident: 10.1016/j.ejor.2019.02.042_bib0005
  article-title: An all-linear programming relaxation algorithm for optimizing over the efficient set
  publication-title: Journal of Global Optimization
  doi: 10.1007/BF00120667
– volume: 163
  start-page: 213
  issue: 1–2
  year: 2017
  ident: 10.1016/j.ejor.2019.02.042_bib0023
  article-title: A parametric simplex algorithm for linear vector optimization problems
  publication-title: Mathematical Programming
  doi: 10.1007/s10107-016-1061-z
– volume: 83
  start-page: 541
  issue: 3
  year: 1994
  ident: 10.1016/j.ejor.2019.02.042_bib0013
  article-title: Optimizing a linear function over the efficient set
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF02207641
– volume: 28
  start-page: 711
  issue: 3
  year: 1977
  ident: 10.1016/j.ejor.2019.02.042_bib0018
  article-title: The enumeration of the set of all efficient solutions for a linear multiple objective program
  publication-title: Operational Research Quarterly
  doi: 10.1057/jors.1977.147
– volume: 54
  start-page: 1336
  issue: 7
  year: 2008
  ident: 10.1016/j.ejor.2019.02.042_bib0028
  article-title: Multiple criteria decision making, multiattribute utility analysis: Recent accomplishments and what lies ahead
  publication-title: Management Science
  doi: 10.1287/mnsc.1070.0838
– volume: 70
  start-page: 467
  issue: 3
  year: 1991
  ident: 10.1016/j.ejor.2019.02.042_bib0004
  article-title: Determination of the efficient set in multiobjective linear programming
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF00941298
– volume: 4
  start-page: 633
  issue: 63
  year: 2015
  ident: 10.1016/j.ejor.2019.02.042_bib0022
  article-title: A new preference handling technique for interactive multiobjective optimization without trading-off
  publication-title: Journal of Global Optimization
  doi: 10.1007/s10898-015-0301-8
– volume: 68
  start-page: 257
  issue: 2
  year: 2008
  ident: 10.1016/j.ejor.2019.02.042_bib0015
  article-title: Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning
  publication-title: Mathematical Methods of Operational Research
  doi: 10.1007/s00186-008-0220-2
– year: 1974
  ident: 10.1016/j.ejor.2019.02.042_bib0030
– volume: 105
  start-page: 17
  issue: 1
  year: 2000
  ident: 10.1016/j.ejor.2019.02.042_bib0006
  article-title: Outcome space partition of the weight set in multiobjective linear programming
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1023/A:1004605810296
– volume: 232
  start-page: 479
  issue: 3
  year: 2014
  ident: 10.1016/j.ejor.2019.02.042_bib0019
  article-title: A new algorithm for generating all nondominated solutions for multiobjective discrete optimization problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2013.08.001
– year: 1986
  ident: 10.1016/j.ejor.2019.02.042_bib0026
– volume: 139
  start-page: 26
  issue: 1
  year: 2002
  ident: 10.1016/j.ejor.2019.02.042_bib0007
  article-title: A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program
  publication-title: European Journal of Operational Research
  doi: 10.1016/S0377-2217(01)00153-9
– volume: 22
  start-page: 285
  issue: 1
  year: 2002
  ident: 10.1016/j.ejor.2019.02.042_bib0029
  article-title: Optimization over the efficient set: overview
  publication-title: Journal of Global Optimization
  doi: 10.1023/A:1013875600711
– volume: 12
  start-page: 1299
  issue: 10–11
  year: 1989
  ident: 10.1016/j.ejor.2019.02.042_bib0009
  article-title: Implementation of a user friendly software package – a guided tour of TRIMAP
  publication-title: Mathematical and Computer Modelling
  doi: 10.1016/0895-7177(89)90369-5
– volume: 23
  start-page: 314
  issue: 2
  year: 2015
  ident: 10.1016/j.ejor.2019.02.042_bib0002
  article-title: Interactive MOLP explorer – a graphical-based computational tool for teaching and decision support in multi-objective linear programming models
  publication-title: Computer Applications of Engineering Education
  doi: 10.1002/cae.21601
– volume: 126
  start-page: 579
  issue: 2
  year: 1987
  ident: 10.1016/j.ejor.2019.02.042_bib0010
  article-title: Analysis of the objective space in multiple objective programming
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1016/0022-247X(87)90065-5
– volume: 174
  start-page: 1140
  issue: 3
  year: 2006
  ident: 10.1016/j.ejor.2019.02.042_bib0001
  article-title: Optimizing a linear function over an integer efficient set
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2005.02.072
– volume: L164
  year: 1979
  ident: 10.1016/j.ejor.2019.02.042_bib0017
– volume: 5
  start-page: 54
  issue: 1
  year: 1973
  ident: 10.1016/j.ejor.2019.02.042_bib0016
  article-title: A revised simplex method for multiple objective programs
  publication-title: Mathematical Programming
  doi: 10.1007/BF01580111
– year: 2017
  ident: 10.1016/j.ejor.2019.02.042_sbref0025
– volume: 19
  start-page: 531
  issue: 4
  year: 2012
  ident: 10.1016/j.ejor.2019.02.042_bib0008
  article-title: The augmented weighted Tchebychev norm for optimizing a linear function over an integer efficient set of a multicriteria linear program
  publication-title: International Transactions in Operations Research
  doi: 10.1111/j.1475-3995.2012.00851.x
– volume: 68
  start-page: 469
  issue: 3
  year: 2008
  ident: 10.1016/j.ejor.2019.02.042_bib0024
  article-title: Approximating the nondominated set of an MOLP by approximately solving its dual problem
  publication-title: Mathematical Methods of Operations Research
  doi: 10.1007/s00186-007-0194-5
– year: 2016
  ident: 10.1016/j.ejor.2019.02.042_bib0003
– volume: 14
  start-page: 249
  issue: 1
  year: 1978
  ident: 10.1016/j.ejor.2019.02.042_bib0012
  article-title: Finding all efficient extreme points for multiple objective linear programs
  publication-title: Mathematical Programming
  doi: 10.1007/BF01588968
– volume: 46–47
  start-page: 279
  issue: 2
  year: 1993
  ident: 10.1016/j.ejor.2019.02.042_bib0011
  article-title: On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program
  publication-title: Annals of Operations Research
  doi: 10.1007/BF02023100
– volume: 52
  start-page: 757
  issue: 4
  year: 2012
  ident: 10.1016/j.ejor.2019.02.042_bib0014
  article-title: A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming
  publication-title: Journal of Global Optimization
  doi: 10.1007/s10898-011-9709-y
– volume: 206
  start-page: 426
  issue: 2
  year: 2010
  ident: 10.1016/j.ejor.2019.02.042_bib0021
  article-title: Nautilus method: an interactive technique in multiobjective optimization based on the nadir point
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2010.02.041
– volume: 162
  start-page: 484
  issue: 2
  year: 2005
  ident: 10.1016/j.ejor.2019.02.042_bib0027
  article-title: A regression study of the number of efficient extreme points in multiple objective linear programming
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2003.09.014
– volume: 260
  start-page: 807
  issue: 3
  year: 2017
  ident: 10.1016/j.ejor.2019.02.042_bib0020
  article-title: The vector linear program solver Bensolve – notes on theoretical background
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2016.02.039
SSID ssj0001515
Score 2.3105638
Snippet •Exploits the objective function structure of a multiple objective linear program.•Shows methods for decomposing the criterion cone.•Allows for the computation...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 653
SubjectTerms Criterion cones
Distributed processing
Efficient extreme points
Multiple objective programming
Nondominated vertices
Title Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming
URI https://dx.doi.org/10.1016/j.ejor.2019.02.042
Volume 277
WOSCitedRecordID wos000466254800019&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: 1872-6860
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001515
  issn: 0377-2217
  databaseCode: AIEXJ
  dateStart: 19950105
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEF6FFCE48AigFgraAzfLUWx3X8cIBVFUVRUqUm6Wd71GDsGOQlL1Z_QnM-t9xC2logculrOyN4_5svPteOYbhD4oySUFWhArXhDYoFQ05gLOZCU0B49OsqLTmT1hp6d8Phdng8GVr4W5WLKm4ZeXYvVfTQ1jYGxTOnsPc4dJYQDOwehwBLPD8Z8M_9WIsXYh1mK5jBU4qx9dB_mQUKi6Rg6BKppn07oTkjBpAbBWm4hhtGprkyBTN7uUw1Yu7OoYGWpqJLJtbtdP7_1uC_A7sgsDax92dPpCIQ59Bp5Z2RzgdVF_j6bjEPbZ6K3rzWxqgqPZuB-kSHZZWKE4i7E4TW2Zpl94U9fApe5tgO0ySq2AsPPI1PZl-WOxt3GHxVgvWqPsmohOfdWKdV1X1r7h8UIeok9xW-RmjtzMkU_SHOZ4gPZSRgQfor3p8Wz-JXh3QwC7J1PuC7lCLJszePOT3E52egTm_Dl66nYeeGoR8wINdDNCj3zhwwg98w0-sFvvR-hJT63yJdp6ZOEdsrBBFgZkYUAW7iELtxWGq3BAFnbIwhZZuG6wRxYOyMIWWbiHrFfo26fZ-cfPsevaEauMkk3MOaUsVawE6kglOLHsSJeJhiO8ZGxSMj2hhWm9LEmiykILcqSEUCWwSQ2b2-w1GjZto_cR1jKbyFQpXQHRJCWRVVmAv-CwhU9YWdEDlPifN1dO0t50VlnmfzfsAYrCPSsr6HLn1cRbLXeU1FLNHEB4x31v7vUub9Hj3Z_mEA03661-hx6qi039a_3eIfA3uyyyQg
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=Reducing+wall-clock+time+for+the+computation+of+all+efficient+extreme+points+in+multiple+objective+linear+programming&rft.jtitle=European+journal+of+operational+research&rft.au=Piercy%2C+Craig+A.&rft.au=Steuer%2C+Ralph+E.&rft.date=2019-09-01&rft.issn=0377-2217&rft.volume=277&rft.issue=2&rft.spage=653&rft.epage=666&rft_id=info:doi/10.1016%2Fj.ejor.2019.02.042&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ejor_2019_02_042
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-2217&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-2217&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-2217&client=summon