Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm

The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2022; pp. 1 - 18
Main Authors: Yuan, Yu, Wang, Pengcheng, Wang, Minghui
Format: Journal Article
Language:English
Published: New York Hindawi 28.08.2022
John Wiley & Sons, Inc
Subjects:
Algorithms
Buses (vehicles)
Collaboration
Commuting
Constraint modelling
Engineering
Integer programming
Linear programming
Multiple objective analysis
Normal distribution
Operating costs
Optimization
Optimization models
Pareto optimization
Passengers
Planning
Public transportation
Quality of service
Random variables
Randomness
Scheduling
Sensitivity analysis
Stochastic programming
Synchronism
Timetables
Transportation services
Transportation systems
Travel time
ISSN:1024-123X, 1563-5147
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.
AbstractList The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.
Author Wang, Minghui
Yuan, Yu
Wang, Pengcheng
Author_xml – sequence: 1
  givenname: Yu
  surname: Yuan
  fullname: Yuan, Yu
  organization: Information Engineering SchoolNanchang UniversityNanchangChinancu.edu.cn
– sequence: 2
  givenname: Pengcheng
  surname: Wang
  fullname: Wang, Pengcheng
  organization: Information Engineering SchoolNanchang UniversityNanchangChinancu.edu.cn
– sequence: 3
  givenname: Minghui
  orcidid: 0000-0002-4436-7299
  surname: Wang
  fullname: Wang, Minghui
  organization: School of Economics and ManagementBeijing University of Posts and TelecommunicationsBeijingChinabupt.edu.cn
BookMark eNp9kctq3DAUhkVJoEnaXR9A0GXrRpYtabycmvQCGSaQBLozknw01mBLU0lOSN-ob1lNJmQRaFbnou8_B53_FB057wChDyX5UpaMnVNC6XlDKeUVf4NOSsargpW1OMo5oXVR0urXW3Qa45YQWrJycYL-ruYx2WKttqCTvQN8nbweZExW4-sHp4fgnZ8jvrETJKlGwOtdspP9I5P1Dq98DyP-KiP0OJcSt4N0GorWu5iCtC73r4LfBDlN1m3wCtLge9z6ST2-3ds04OW8mcClXF7soh3znGd5wstx40Ompnfo2MgxwvuneIZuv13ctD-Ky_X3n-3ystCUi1RAYwxrwJgFcL3oJTU1FwSYqgWIxlSGaq20MorXqtIaetEsqKAgOFFG5gudoY-Hubvgf88QU7f1c3B5ZUcFaVjDKROZ-nygdPAxBjDdLthJhoeuJN3ejG5vRvdkRsbpC1zb9HjC_TfH_4k-HUSDdb28t6-v-AdB7aBB
CitedBy_id crossref_primary_10_1109_TITS_2024_3371439
crossref_primary_10_3390_info16050376
crossref_primary_10_1016_j_ejor_2024_07_035
Cites_doi 10.1016/j.trb.2016.07.009
10.1016/j.trc.2020.102661
10.1016/j.tra.2008.03.011
10.1016/j.ejor.2007.02.005
10.1201/b12853
10.1007/s00500-018-3266-y
10.1016/j.tra.2010.03.007
10.1016/j.trc.2019.05.032
10.1016/j.trc.2013.12.005
10.1016/j.trc.2019.04.005
10.1016/j.trb.2021.01.010
10.1016/j.ejor.2003.02.002
10.1016/j.trc.2014.12.012
10.1016/j.trc.2014.09.005
10.1016/j.trc.2019.12.001
10.1177/0361198106197100109
10.1016/j.trb.2015.03.002
10.1016/s0965-8564(00)00032-x
10.1061/(asce)0733-9488(2005)131:2(112)
10.1109/TSMCC.2008.923872
10.1016/j.trc.2019.05.029
10.3141/2276-07
10.1061/(asce)te.1943-5436.0000311
10.1016/j.trb.2019.01.010
10.1016/j.trb.2018.01.012
10.1016/j.trb.2019.12.002
10.13196/j.cims.2019.01.024
10.1016/j.trc.2021.103086
10.1016/j.trb.2015.05.012
10.1016/j.trb.2012.01.006
10.1016/j.trc.2022.103657
10.1016/j.trc.2016.02.007
10.1109/tits.2020.3025031
10.1016/j.amc.2013.03.002
10.1016/j.tra.2005.11.006
10.1061/(asce)te.1943-5436.0000536
10.1016/j.trb.2020.12.003
10.1080/23249935.2017.1353555
ContentType Journal Article
Copyright Copyright © 2022 Yu Yuan et al.
Copyright © 2022 Yu Yuan et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
Copyright_xml – notice: Copyright © 2022 Yu Yuan et al.
– notice: Copyright © 2022 Yu Yuan et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
DBID RHU
RHW
RHX
AAYXX
CITATION
7TB
8FD
8FE
8FG
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
CWDGH
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
M7S
P5Z
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOI 10.1155/2022/9222636
DatabaseName Hindawi Publishing Complete
Hindawi Publishing Subscription Journals
Hindawi Publishing Open Access
CrossRef
Mechanical & Transportation Engineering Abstracts
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials - QC
ProQuest Central
Technology Collection
ProQuest One
Middle East & Africa Database
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Engineering Database
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
Proquest Central Premium
ProQuest One Academic (New)
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle CrossRef
Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
Middle East & Africa Database
ProQuest Central Korea
ProQuest Central (New)
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
Engineering Database
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
DatabaseTitleList
CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: RHX
  name: Hindawi Publishing Open Access
  url: http://www.hindawi.com/journals/
  sourceTypes: Publisher
– sequence: 2
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Engineering
EISSN 1563-5147
Editor Kaur, Amandeep
Editor_xml – sequence: 1
  givenname: Amandeep
  surname: Kaur
  fullname: Kaur, Amandeep
EndPage 18
ExternalDocumentID 10_1155_2022_9222636
GroupedDBID 29M
2WC
3V.
4.4
5GY
5VS
8FE
8FG
8R4
8R5
AAFWJ
AAJEY
ABDBF
ABJCF
ABUWG
ACIPV
ACIWK
ADBBV
AENEX
AFKRA
AINHJ
ALMA_UNASSIGNED_HOLDINGS
ARAPS
BCNDV
BENPR
BGLVJ
BPHCQ
CCPQU
CS3
CWDGH
E3Z
EBS
ESX
GROUPED_DOAJ
HCIFZ
I-F
IAO
IEA
IOF
ISR
ITC
K6V
K7-
KQ8
L6V
M7S
MK~
M~E
OK1
P2P
P62
PIMPY
PQQKQ
PROAC
PTHSS
Q2X
REM
RHU
RHW
RHX
RNS
TR2
TUS
XSB
YQT
~8M
0R~
24P
AAMMB
AAYXX
ACCMX
AEFGJ
AFFHD
AGXDD
AIDQK
AIDYY
ALUQN
CITATION
H13
OVT
PHGZM
PHGZT
PQGLB
7TB
8FD
AZQEC
DWQXO
FR3
GNUQQ
JQ2
KR7
PKEHL
PQEST
PQUKI
PRINS
ID FETCH-LOGICAL-c267t-e9ff59eff8e6c8da2f4670e5b47e79f3f2ccbcbfb64b3cced798272e760bfa123
IEDL.DBID RHX
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000863265200006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1024-123X
IngestDate Fri Jul 25 10:08:07 EDT 2025
Sat Nov 29 06:37:37 EST 2025
Tue Nov 18 22:04:19 EST 2025
Sun Jun 02 18:51:58 EDT 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Language English
License This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c267t-e9ff59eff8e6c8da2f4670e5b47e79f3f2ccbcbfb64b3cced798272e760bfa123
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-4436-7299
OpenAccessLink https://dx.doi.org/10.1155/2022/9222636
PQID 2709596257
PQPubID 237775
PageCount 18
ParticipantIDs proquest_journals_2709596257
crossref_primary_10_1155_2022_9222636
crossref_citationtrail_10_1155_2022_9222636
hindawi_primary_10_1155_2022_9222636
PublicationCentury 2000
PublicationDate 2022-08-28
PublicationDateYYYYMMDD 2022-08-28
PublicationDate_xml – month: 08
  year: 2022
  text: 2022-08-28
  day: 28
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle Mathematical problems in engineering
PublicationYear 2022
Publisher Hindawi
John Wiley & Sons, Inc
Publisher_xml – name: Hindawi
– name: John Wiley & Sons, Inc
References 22
23
24
25
26
27
28
29
T. Takahama (38)
30
31
10
32
11
33
12
34
13
35
14
36
15
37
16
17
39
18
19
2
3
4
5
6
7
8
9
40
A. Ceder (1) 2007
20
21
References_xml – ident: 7
  doi: 10.1016/j.trb.2016.07.009
– ident: 21
  doi: 10.1016/j.trc.2020.102661
– ident: 3
  doi: 10.1016/j.tra.2008.03.011
– ident: 33
  doi: 10.1016/j.ejor.2007.02.005
– volume-title: Public Transit Planning and Operation: Theory Modeling and Practice
  year: 2007
  ident: 1
  doi: 10.1201/b12853
– ident: 36
  doi: 10.1007/s00500-018-3266-y
– ident: 11
  doi: 10.1016/j.tra.2010.03.007
– start-page: 1
  volume-title: IEEE
  ident: 38
  article-title: Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation
– ident: 8
  doi: 10.1016/j.trc.2019.05.032
– ident: 5
  doi: 10.1016/j.trc.2013.12.005
– ident: 18
  doi: 10.1016/j.trc.2019.04.005
– ident: 15
  doi: 10.1016/j.trb.2021.01.010
– ident: 16
  doi: 10.1016/j.ejor.2003.02.002
– ident: 6
  doi: 10.1016/j.trc.2014.12.012
– ident: 12
  doi: 10.1016/j.trc.2014.09.005
– ident: 14
  doi: 10.1016/j.trc.2019.12.001
– ident: 10
  doi: 10.1177/0361198106197100109
– ident: 9
  doi: 10.1016/j.trb.2015.03.002
– ident: 19
  doi: 10.1016/s0965-8564(00)00032-x
– ident: 31
  doi: 10.1061/(asce)0733-9488(2005)131:2(112)
– ident: 23
  doi: 10.1109/TSMCC.2008.923872
– ident: 37
  doi: 10.1016/j.trc.2019.05.029
– ident: 24
  doi: 10.3141/2276-07
– ident: 4
  doi: 10.1061/(asce)te.1943-5436.0000311
– ident: 17
  doi: 10.1016/j.trb.2019.01.010
– ident: 27
  doi: 10.1016/j.trb.2018.01.012
– ident: 13
  doi: 10.1016/j.trb.2019.12.002
– ident: 40
  doi: 10.13196/j.cims.2019.01.024
– ident: 22
  doi: 10.1016/j.trc.2021.103086
– ident: 35
  doi: 10.1016/j.trb.2015.05.012
– ident: 20
  doi: 10.1016/j.trb.2012.01.006
– ident: 29
  doi: 10.1016/j.trc.2022.103657
– ident: 25
  doi: 10.1016/j.trc.2016.02.007
– ident: 2
  doi: 10.1016/j.trb.2019.01.010
– ident: 28
  doi: 10.1109/tits.2020.3025031
– ident: 39
  doi: 10.1016/j.amc.2013.03.002
– ident: 32
  doi: 10.1016/j.tra.2005.11.006
– ident: 34
  doi: 10.1061/(asce)te.1943-5436.0000536
– ident: 30
  doi: 10.1016/j.trb.2020.12.003
– ident: 26
  doi: 10.1080/23249935.2017.1353555
SSID ssj0021518
Score 2.2957764
Snippet The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation...
SourceID proquest
crossref
hindawi
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1
SubjectTerms Algorithms
Buses (vehicles)
Collaboration
Commuting
Constraint modelling
Engineering
Integer programming
Linear programming
Multiple objective analysis
Normal distribution
Operating costs
Optimization
Optimization models
Pareto optimization
Passengers
Planning
Public transportation
Quality of service
Random variables
Randomness
Scheduling
Sensitivity analysis
Stochastic programming
Synchronism
Timetables
Transportation services
Transportation systems
Travel time
SummonAdditionalLinks – databaseName: Engineering Database
  dbid: M7S
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwELYotBI9lJYWQYHKB3qqIhYnjp1TtVQgDi0gLVR7i-yJzW61L0i2VX9S_2VnHO9SCZUeeozjJI48mVdmvo-xA9cRPjVHaQJU4ZrlwhLkrU5MLsGgx2B14Fj6-lmdn-t-v7iMCbc6llUudGJQ1NUUKEd-KBRlrNBbVx9ntwmxRtHf1Uih8YStEUrCUSjd6y0DLhxpW-EEYfOl_UXhu5QU84vDAo1jHsCZ703SswHFwj-GD3RzMDinG_-71JfsRXQ1ebeVjVdsxU022UZ0O3n8qOtN9vwPTMLX7FdoyU0u7LdWFfJeM4WBIThn3vs5AQLTnc5rTr0jDfVd8QvUOuPYzsmJW23Ej9E2VhwPDaf2BXAJEYMGOgocv2xrwsb4PP4lMFhzVEs2nKO8MO_ObwJWaMVPZvVwhPdZXt7w7ugGX7YZjN-w69OTq09nSeRzSEDkqklc4b0snPfa5aArIzxq6Y6TNlNOFT71AsCC9TbPbArgKlVooYRTecd6gxu4xVYn04nbZjxTSqMniwbeVZmX2lQSOsbmgEGxsKB32IfFlpYQwc5plaMyBD1SliQAZRSAHfZ-OXvWgnz8Zd5BlI5_TNtbyEUZNUJd3gvF28dP77J1uhnlrYXeY6vN3dzts6fwvRnWd--CgP8GIusFsw
  priority: 102
  providerName: ProQuest
Title Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm
URI https://dx.doi.org/10.1155/2022/9222636
https://www.proquest.com/docview/2709596257
Volume 2022
WOSCitedRecordID wos000863265200006&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: PRVPQU
  databaseName: Advanced Technologies & Aerospace Database
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: P5Z
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: K7-
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: M7S
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Middle East & Africa Database
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: CWDGH
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/middleeastafrica
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: BENPR
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 20250131
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: PIMPY
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
– providerCode: PRVWIB
  databaseName: Wiley Online Library Open Access
  customDbUrl:
  eissn: 1563-5147
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0021518
  issn: 1024-123X
  databaseCode: 24P
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://authorservices.wiley.com/open-science/open-access/browse-journals.html
  providerName: Wiley-Blackwell
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1Lb9QwELa6LUhcoDwqSsvKh3JCEYsTP3Lcoq2K2m6jLqCFS2Q7drtoH9UmBfGT-i-ZcbwrQYXoJZLjsRVl4vk8zsw3hBy4HvOpfp8mFiNcM8EMUt6qRAtuNewYjAo1lr6cyuFQjcd5EUmS6ru_8AHt0D1n73LAMZGKDukojpFbF8fjtV8FoNVmvDGk4EvHq_j2v8b-gTwPr9Dl_Tm5Y4IDrhxtk8dxQ0j7rQafkg03f0aexM0hjUuvfk5uQ6pscm6-tyaKjpqFvdJIs0xHv-YWSW7Bi6eY09FgPhQ9B2swi2mWFGueTekhYFZFoakpphVYl2DBzlAmAu4XbazWDNCMnoXK0hTMhQl9eF5L-zeXgcOzooPrejKFedbDG9qfXi6WIDV7QT4fDT59OE5inYXEMiGbxOXe89x5r5ywqtLMg_XsOW4y6WTuU8-sNdZ4IzKTWusqmSsmmZOiZ7yGN75DNueLuXtJaCalgh0mAK-rMs-VrrjtaSMsOKvMWLVL3q50UNpIQo5POS2DM8J5iRoro8Z2yZu19HVLvvEPuYOozv-I7a90XcaVWpdM4kkoeIHy1f1m2SOPsInnykztk81meeNekwf2RzOpl12ydTgYFhdd0jmRSRcjSUdwLfg36Ck-nhVfu-Hb_Q1xO-Y1
linkProvider Hindawi Publishing
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LbtQwFLWqAoIuKBRQCwW8aFco6tSJY2eB0ACtWs10WqkFzS61HbszaF40Gap-Ehu-kXsdZ4qEgFUXLJM4Dzkn5z7iey4hW7bFXKx248jgCtckZRolb2WkUm4UeAxa-h5Ln7ui15P9fnayRH40tTC4rLLhRE_UxdRgjnyHCcxYgbcu3s2-Rtg1Cv-uNi00alh07PUVhGzl28OP8H63GdvfO_twEIWuApFhqagimznHM-uctKmRhWIOuKJluU6EFZmLHTNGG-10mujYGFuITDLBrEhb2qldFDoAyr-TxFLgd9UR0SLAA-tZl94x1AKM-81Ce84xx8B2MjDGqReDvjGB9wYYe18Nf7MF3sDtr_5vU_OIPAyuNG3X2H9MluxkjawGt5oG0irXyMovmotPyHdfchwd6y811dPTamoGCuWq6en1xKBY8HReUqyNqbCujB4Dq45DuSrF3nEj-h5sf0FhU1EszzA2wsanvt0G7D-p17yN4X70yHfopkC72h_DvDdtzy-8FmpB92blcATXWZxe0fboAia3Goyfkk-3Mn3PyPJkOrHrhCZCSPDUwYGxReK4VAU3LaVTA0E_00ZukDcNhHITxNzxKUe5D-o4zxFweQDcBtlejJ7VIiZ_GLcV0PiPYZsNDvPAeGV-A8Lnfz_8mtw_ODvq5t3DXucFeYAXxhw9k5tkubqc25fkrvlWDcvLV_7jouT8tiH7E06XZvc
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwELaqUhAcKBQQhRZ8aE8o2q0Tx84BoYV2RdWyXamAVlyC7djdRftHk6XqI_EKPB0zjrNFQsCpB45JHCdyPs9fZr4hZMe2mYvVXhwZzHBNUqaR8lZGKuVGgcWgpe-x9PFY9HpyMMj6K-RHUwuDaZWNTPSCupgZjJG3mMCIFVjrouVCWkR_v_tq_jXCDlL4p7Vpp1FD5MheXoD7Vr483IdvvctY9-D9m7dR6DAQGZaKKrKZczyzzkmbGlko5kButC3XibAic7FjxmijnU4THRtjC5FJJpgVaVs7tYekByD-bwjwMTGdsM8_LZ090KR1GR5DXsB40CTdc47xBtbKQDGnnhj6Sh3eHKIffjH6TS94Zddd_5-X6R65G0xs2qn3xH2yYqcbZD2Y2zQIs3KD3PmFi_EB-e5LkaMT_aVWAfS0mpmhQhpreno5NUgiPFuUFGtmKqw3oycgbSehjJViT7kxfQ02QUHhUFEs2zA2woaovg0HnO_XuXATeB595zt3UxDH2l_DeDjtLM48R2pBD-blaAzzLG-vaGd8BotbDScPyYdrWb5HZHU6m9rHhCZCSLDgwbCxReK4VAU3baVTk4Glp43cJC8aOOUmkLzjW45z7-xxniP48gC-TbK7HD2vyU3-MG4nIPMfw7YaTOZBEpb5FSCf_P3yc3ILkJofH_aOnpLbOC-G7pncIqvV-cJukzXzrRqV58_8PqPk83Uj9iefS3Ab
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+Stochastic+Synchronous+Timetable+Optimization+Model+Based+on+a+Chance-Constrained+Programming+Method+Combined+with+Augmented+Epsilon+Constraint+Algorithm&rft.jtitle=Mathematical+problems+in+engineering&rft.au=Yuan%2C+Yu&rft.au=Wang%2C+Pengcheng&rft.au=Wang%2C+Minghui&rft.date=2022-08-28&rft.pub=Hindawi&rft.issn=1024-123X&rft.eissn=1563-5147&rft.volume=2022&rft_id=info:doi/10.1155%2F2022%2F9222636&rft.externalDocID=10_1155_2022_9222636
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1024-123X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1024-123X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1024-123X&client=summon