A computational comparison of branch and bound and outer approximation algorithms for 0–1 mixed integer nonlinear programs

In this paper we compare the performance of two codes for convex 0–1 mixed integer nonlinear programs on a number of test problems. The first code uses a branch and bound algorithm. The second code is a commercially available implementation of an outer approximation algorithm. The comparison demonst...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Computers & operations research Ročník 24; číslo 8; s. 699 - 701
Hlavní autori: Borchers, Brian, Mitchell, John E.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Elsevier Ltd 01.08.1997
Elsevier Science
Pergamon Press Inc
Predmet:
Algorithms
Applied sciences
Approximation
Comparative analysis
Exact sciences and technology
Flows in networks. Combinatorial problems
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Portfolio theory
Studies
Approximation
Portfolio selection
Branch and bound method
Combinatorial problem
Mixed integer programming
Non linear programming
Comparative study
ISSN:0305-0548, 1873-765X, 0305-0548
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract In this paper we compare the performance of two codes for convex 0–1 mixed integer nonlinear programs on a number of test problems. The first code uses a branch and bound algorithm. The second code is a commercially available implementation of an outer approximation algorithm. The comparison demonstrates that both approaches are generally capable of solving the test problems. However, there are significant differences in the robustness of the two codes and their performance on different classes of problems.
AbstractList In this paper we compare the performance of two codes for convex 0–1 mixed integer nonlinear programs on a number of test problems. The first code uses a branch and bound algorithm. The second code is a commercially available implementation of an outer approximation algorithm. The comparison demonstrates that both approaches are generally capable of solving the test problems. However, there are significant differences in the robustness of the two codes and their performance on different classes of problems.
The performance of 2 codes for convex 0-1 mixed integer nonlinear programs are compared on a number of test problems. The first code uses a branch and bound algorithm. The 2nd code is a commercially available implementation of an outer approximation algorithm. The comparison demonstrates that both approaches are generally capable of solving the test problems. However, there are significant differences in the robustness of the 2 codes and their performance on different classes of problems.
Author Borchers, Brian
Mitchell, John E.
Author_xml – sequence: 1
  givenname: Brian
  surname: Borchers
  fullname: Borchers, Brian
  email: borchers@nmt.edu
  organization: Mathematics Department, New Mexico Tech, Socorro, NM 87801, U.S.A
– sequence: 2
  givenname: John E.
  surname: Mitchell
  fullname: Mitchell, John E.
  organization: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2755675$$DView record in Pascal Francis
BookMark eNqFkc9qHSEUxiWkkJu0j1CQkEWzmFbHUWfoooTQfxDooi10J2ccvTHM6I06IYEu8g55wz5JnXvTLLqJCz3C9zt6vu8Q7fvgDUKvKXlLCRXvvhNGeEV4077p5Ckpq67EHlrRVrJKCv5rH62eJAfoMKWrRSRrukK_z7AO02bOkF3wMG5vEF0KHgeL-wheX2LwA-7DXPalCnM2EcNmE8Otm7YghnEdosuXU8I2REz-3D9QPLlbM2Dns1kXoPx6dN5AxAVcR5jSS_TCwpjMq8fzCP389PHH-Zfq4tvnr-dnF5VmguWKS6hrIMK2Q2MpcDEA66C1hHbaDtyUQgsg1FDCaNM3krSk0dD3XW01Gxg7Qse7vuXh69mkrK7CHMu0SdGOt0yyui2ik0cRJA2jXSZ3SW1iGTHeqVpyLiQvsvc7mY4hpWis0m5nXo7gRkWJWkJR21DU4rjqpNqGokSh-X_0v_7PcR92nCk23TgTVdLOeG0GF43OagjumQ5_ATo_qN0
CODEN CMORAP
CitedBy_id crossref_primary_10_1016_S0305_0548_99_00074_X
crossref_primary_10_25142_aak_2011_043
crossref_primary_10_1080_00137910108967571
crossref_primary_10_1007_s11222_016_9658_x
crossref_primary_10_1007_s12293_016_0180_7
crossref_primary_10_1023_A_1011241421041
crossref_primary_10_1109_TCST_2014_2330997
crossref_primary_10_1109_TRO_2007_907488
crossref_primary_10_1007_s11075_024_01947_0
crossref_primary_10_1002_cem_1078
crossref_primary_10_1002_aic_11494
crossref_primary_10_1016_j_cie_2020_106742
crossref_primary_10_1080_0305215X_2016_1271881
crossref_primary_10_1023_A_1023239606028
crossref_primary_10_1287_ijoc_2021_1127
crossref_primary_10_1007_s10287_006_0038_4
crossref_primary_10_1080_01605682_2019_1581408
Cites_doi 10.1016/0098-1354(89)85008-2
10.1016/0305-0548(94)90024-8
10.1287/mnsc.15.2.B51
10.1007/BF02592064
10.1287/opre.18.3.454
10.1287/mnsc.31.12.1533
10.1287/opre.37.6.902
10.1016/0098-1354(90)87085-4
ContentType Journal Article
Copyright 1997
1997 INIST-CNRS
Copyright Pergamon Press Inc. Aug 1997
Copyright_xml – notice: 1997
– notice: 1997 INIST-CNRS
– notice: Copyright Pergamon Press Inc. Aug 1997
DBID AAYXX
CITATION
IQODW
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1016/S0305-0548(97)00002-6
DatabaseName CrossRef
Pascal-Francis
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
Business
Applied Sciences
EISSN 1873-765X
0305-0548
EndPage 701
ExternalDocumentID 13686975
2755675
10_1016_S0305_0548_97_00002_6
S0305054897000026
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
186
1B1
1OL
1RT
1~.
1~5
29F
4.4
457
4G.
5GY
5VS
6J9
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AABNK
AACTN
AAEDT
AAEDW
AAFJI
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
AAYFN
AAYOK
ABAOU
ABBOA
ABEFU
ABFNM
ABFRF
ABJNI
ABMAC
ABMMH
ABUCO
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFO
ACGFS
ACNCT
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADGUI
ADJOM
ADMUD
AEBSH
AEFWE
AEHXG
AEKER
AENEX
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AI.
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
AKYCK
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOMHK
AOUOD
APLSM
ARUGR
ASPBG
AVARZ
AVWKF
AXJTR
AZFZN
BKOJK
BKOMP
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-Q
G8K
GBLVA
GBOLZ
HAMUX
HVGLF
HZ~
H~9
IHE
J1W
KOM
LY1
M41
MHUIS
MO0
MS~
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
PQQKQ
PRBVW
Q38
R2-
RIG
ROL
RPZ
RXW
SDF
SDG
SDP
SDS
SES
SEW
SPC
SPCBC
SSB
SSD
SSO
SSV
SSW
SSZ
T5K
TAE
TN5
U5U
UAO
UPT
VH1
WUQ
XFK
XPP
ZMT
~02
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
AFXIZ
AGCQF
AGRNS
BNPGV
IQODW
SSH
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c363t-57a22a06f8d4f1a56da39a8f019cfd5ef01c6a01e10314b470804cabb92fc3d33
ISICitedReferencesCount 21
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1016_S0305_0548_97_00002_6&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0305-0548
IngestDate Fri Jul 25 03:28:10 EDT 2025
Mon Jul 21 09:16:01 EDT 2025
Tue Nov 18 22:32:12 EST 2025
Sat Nov 29 03:23:24 EST 2025
Fri Feb 23 02:33:36 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 8
Keywords Approximation
Portfolio selection
Branch and bound method
Combinatorial problem
Mixed integer programming
Non linear programming
Comparative study
Language English
License https://www.elsevier.com/tdm/userlicense/1.0
CC BY 4.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c363t-57a22a06f8d4f1a56da39a8f019cfd5ef01c6a01e10314b470804cabb92fc3d33
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
PQID 195837328
PQPubID 45870
PageCount 3
ParticipantIDs proquest_journals_195837328
pascalfrancis_primary_2755675
crossref_citationtrail_10_1016_S0305_0548_97_00002_6
crossref_primary_10_1016_S0305_0548_97_00002_6
elsevier_sciencedirect_doi_10_1016_S0305_0548_97_00002_6
PublicationCentury 1900
PublicationDate 1997-08-01
PublicationDateYYYYMMDD 1997-08-01
PublicationDate_xml – month: 08
  year: 1997
  text: 1997-08-01
  day: 01
PublicationDecade 1990
PublicationPlace Oxford
PublicationPlace_xml – name: Oxford
– name: New York
PublicationTitle Computers & operations research
PublicationYear 1997
Publisher Elsevier Ltd
Elsevier Science
Pergamon Press Inc
Publisher_xml – name: Elsevier Ltd
– name: Elsevier Science
– name: Pergamon Press Inc
References Brooke, Kendrick, Merraus (BIB11) 1988
Floudas (BIB1) 1995
Kocis, Grossman (BIB2) 1989; 13
Viswanathan, Grossman (BIB10) 1990; 14
Paules, Floudas (BIB3) 1989; 37
Mao, Wallingford (BIB5) 1968; 15
Duran, Grossman (BIB9) 1986; 36
GAMS (BIB12) 1993
Borchers, Mitchell (BIB6) 1994; 21
Gupta, Ravindran (BIB7) 1983; 20
Gupta, Ravindran (BIB8) 1985; 31
Bixby, Boyd, Indovina (BIB13) 1992; 25
Laughhunn (BIB4) 1970; 18
Duran (10.1016/S0305-0548(97)00002-6_BIB9) 1986; 36
Borchers (10.1016/S0305-0548(97)00002-6_BIB6) 1994; 21
Laughhunn (10.1016/S0305-0548(97)00002-6_BIB4) 1970; 18
Mao (10.1016/S0305-0548(97)00002-6_BIB5) 1968; 15
Gupta (10.1016/S0305-0548(97)00002-6_BIB7) 1983; 20
Bixby (10.1016/S0305-0548(97)00002-6_BIB13) 1992; 25
Floudas (10.1016/S0305-0548(97)00002-6_BIB1) 1995
GAMS (10.1016/S0305-0548(97)00002-6_BIB12) 1993
Paules (10.1016/S0305-0548(97)00002-6_BIB3) 1989; 37
Kocis (10.1016/S0305-0548(97)00002-6_BIB2) 1989; 13
Gupta (10.1016/S0305-0548(97)00002-6_BIB8) 1985; 31
Viswanathan (10.1016/S0305-0548(97)00002-6_BIB10) 1990; 14
Brooke (10.1016/S0305-0548(97)00002-6_BIB11) 1988
References_xml – volume: 15
  start-page: 51
  year: 1968
  end-page: 60
  ident: BIB5
  article-title: An extension of Lawler and Bell's method of discrete optimization with examples from capital budgeting
  publication-title: Management Science
– volume: 14
  start-page: 769
  year: 1990
  end-page: 782
  ident: BIB10
  article-title: A combined penalty function and outer approximation method for MINLP optimization
  publication-title: Computers and Chemical Engineering
– volume: 36
  start-page: 307
  year: 1986
  end-page: 339
  ident: BIB9
  article-title: An outer-approximation algorithm for a class of mixed-integer nonlinear programs
  publication-title: Mathematical Programming
– year: 1993
  ident: BIB12
  publication-title: GAMS—The Solver Manuals
– year: 1995
  ident: BIB1
  article-title: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications
– year: 1988
  ident: BIB11
  publication-title: GAMS: A User's Guide
– volume: 37
  start-page: 902
  year: 1989
  end-page: 915
  ident: BIB3
  article-title: APROS: algorithmic development methodology for discrete-continuous optimization problems
  publication-title: Operations Research
– volume: 21
  start-page: 359
  year: 1994
  end-page: 367
  ident: BIB6
  article-title: An improved branch and bound algorithm for mixed integer nonlinear programs
  publication-title: Computers and Operations Research
– volume: 13
  start-page: 307
  year: 1989
  end-page: 315
  ident: BIB2
  article-title: Computational experience with DICOPT solving MINLP problems in process systems engineering
  publication-title: Computers and Chemical Engineering
– volume: 25
  start-page: 16
  year: 1992
  ident: BIB13
  article-title: MIPLIB: a test set of mixed integer programming solutions
  publication-title: SIAM News
– volume: 18
  start-page: 454
  year: 1970
  end-page: 461
  ident: BIB4
  article-title: Quadratic binary programming with applications to capital-budgeting problems
  publication-title: Operations Research
– volume: 20
  start-page: 189
  year: 1983
  end-page: 206
  ident: BIB7
  article-title: Nonlinear integer programming algorithms: a survey
  publication-title: OPSEARCH
– volume: 31
  start-page: 1533
  year: 1985
  end-page: 1546
  ident: BIB8
  article-title: Branch and bound experiments in convex nonlinear integer programming
  publication-title: Management Science
– year: 1988
  ident: 10.1016/S0305-0548(97)00002-6_BIB11
– volume: 13
  start-page: 307
  year: 1989
  ident: 10.1016/S0305-0548(97)00002-6_BIB2
  article-title: Computational experience with DICOPT solving MINLP problems in process systems engineering
  publication-title: Computers and Chemical Engineering
  doi: 10.1016/0098-1354(89)85008-2
– volume: 25
  start-page: 16
  issue: 20
  year: 1992
  ident: 10.1016/S0305-0548(97)00002-6_BIB13
  article-title: MIPLIB: a test set of mixed integer programming solutions
  publication-title: SIAM News
– volume: 21
  start-page: 359
  issue: 4
  year: 1994
  ident: 10.1016/S0305-0548(97)00002-6_BIB6
  article-title: An improved branch and bound algorithm for mixed integer nonlinear programs
  publication-title: Computers and Operations Research
  doi: 10.1016/0305-0548(94)90024-8
– volume: 15
  start-page: 51
  issue: 2
  year: 1968
  ident: 10.1016/S0305-0548(97)00002-6_BIB5
  article-title: An extension of Lawler and Bell's method of discrete optimization with examples from capital budgeting
  publication-title: Management Science
  doi: 10.1287/mnsc.15.2.B51
– volume: 36
  start-page: 307
  year: 1986
  ident: 10.1016/S0305-0548(97)00002-6_BIB9
  article-title: An outer-approximation algorithm for a class of mixed-integer nonlinear programs
  publication-title: Mathematical Programming
  doi: 10.1007/BF02592064
– year: 1993
  ident: 10.1016/S0305-0548(97)00002-6_BIB12
– volume: 18
  start-page: 454
  issue: 3
  year: 1970
  ident: 10.1016/S0305-0548(97)00002-6_BIB4
  article-title: Quadratic binary programming with applications to capital-budgeting problems
  publication-title: Operations Research
  doi: 10.1287/opre.18.3.454
– volume: 31
  start-page: 1533
  issue: 12
  year: 1985
  ident: 10.1016/S0305-0548(97)00002-6_BIB8
  article-title: Branch and bound experiments in convex nonlinear integer programming
  publication-title: Management Science
  doi: 10.1287/mnsc.31.12.1533
– volume: 37
  start-page: 902
  issue: 6
  year: 1989
  ident: 10.1016/S0305-0548(97)00002-6_BIB3
  article-title: APROS: algorithmic development methodology for discrete-continuous optimization problems
  publication-title: Operations Research
  doi: 10.1287/opre.37.6.902
– volume: 20
  start-page: 189
  issue: 4
  year: 1983
  ident: 10.1016/S0305-0548(97)00002-6_BIB7
  article-title: Nonlinear integer programming algorithms: a survey
  publication-title: OPSEARCH
– year: 1995
  ident: 10.1016/S0305-0548(97)00002-6_BIB1
– volume: 14
  start-page: 769
  year: 1990
  ident: 10.1016/S0305-0548(97)00002-6_BIB10
  article-title: A combined penalty function and outer approximation method for MINLP optimization
  publication-title: Computers and Chemical Engineering
  doi: 10.1016/0098-1354(90)87085-4
SSID ssj0000721
Score 1.645195
Snippet In this paper we compare the performance of two codes for convex 0–1 mixed integer nonlinear programs on a number of test problems. The first code uses a...
The performance of 2 codes for convex 0-1 mixed integer nonlinear programs are compared on a number of test problems. The first code uses a branch and bound...
SourceID proquest
pascalfrancis
crossref
elsevier
SourceType Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 699
SubjectTerms Algorithms
Applied sciences
Approximation
Comparative analysis
Exact sciences and technology
Flows in networks. Combinatorial problems
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Portfolio theory
Studies
Title A computational comparison of branch and bound and outer approximation algorithms for 0–1 mixed integer nonlinear programs
URI https://dx.doi.org/10.1016/S0305-0548(97)00002-6
https://www.proquest.com/docview/195837328
Volume 24
WOSCitedRecordID wos10_1016_S0305_0548_97_00002_6&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: 1873-765X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000721
  issn: 0305-0548
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLZKhxAIcRkgyhjyA5NAVUaam53HDloBGmUSndQ3y3HsUam0Jc2mil_HT-P4kqTVBoMHXiIraWKr5_PJsXPO9yH0knLR41L62vtJL-pFwuNBDhMvTmTmKx4pwY3YBBmN6GSSnrRaP6tamIsZmc_pep0u_6up4RwYW5fO_oO564fCCWiD0eEIZofjXxm-b9LEz8tql09sKg12My2kYavZMq2oZFoLretg6cXXU1vL2OWzs0UxLb9awoau7_W636ZrmVuCCfj53JJsaKpsm-O12gx0K7WIlcHWYikLl3Pn2IXqXeijhWYTsUJtR8UGWD9NS5OlWiUMu5qJ3JXskTo_zmLqRBZnWjnJJpVs53dqd-NB1GhdsLzinHPSttDagZFueNzE6itdehPYTYkv9cMgXtecw1ojFd4BV7Bvjz6z4enxMRsPJuPtq3axFCY0SUl8EA6X3z2tWqa_7h-E7yyCbqCdgMQpbaOd_ofB5GMTDRBT-1ePo6kie9MM7lVKXruB_S4-urvkK5i1ysqtXIocTDg0foDuuXUM7lv8PUQtOd9Ft6oyil10vwIAdm-PXXRng_vyEfrRx1s4xQ1O8UJhi1MM6MQGp6ZlcIq3cIobnGLAKQacYoNT7HCKa5ziCqeP0elwMH773nNCIJ4Ik7D0YsKDgPuJonmkejxOch6mnCpYngiVxxIaIuHgbLRmSZRFBJZBkeBZlgZKhHkYPkFt6Ew-RVikPs96uSSpolGe0ywBJxaRDAyioAvSQVH19zPhWPK1WMuMNemQYDWmrcZs7oYfsKSDDuvblpYm5robaGVb5mJdG8MyAPB1t-5vYaHuEAAYw_q_g_YqbDDnl1ZMc0qFmpjr2R-v7qHbzQx-jtplcS730U1xUU5XxQuH7V-DeNwO
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=A+computational+comparison+of+branch+and+bound+and+outer+approximation+algorithms+for+0-1+mixed+integer+nonlinear+programs&rft.jtitle=Computers+%26+operations+research&rft.au=Borchers%2C+Brian&rft.au=Mitchell%2C+John+E&rft.date=1997-08-01&rft.pub=Pergamon+Press+Inc&rft.issn=0305-0548&rft.eissn=0305-0548&rft.volume=24&rft.issue=8&rft.spage=699&rft_id=info:doi/10.1016%2FS0305-0548%2897%2900002-6&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=13686975
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0305-0548&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0305-0548&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0305-0548&client=summon