University of Groningen
Aspects of sensitivity analysis for the traveling salesman problem
Poort, Edo Stephan van der
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to
cite from it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
1997
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Poort, E. S. V. D. (1997). Aspects of sensitivity analysis for the traveling salesman problem Groningen: s.n.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 13-07-2017
Dvshfwv ri Vhqvlwlylw| Dqdo|vlv iru wkh
Wudyholqj Vdohvpdq Sureohp
Hgr V1 ydq ghu Srruw
Sxeolvkhg e|= Ode|ulqw Sxeolfdwlrq
S1R1 Er{ 995
5<33 DU Fdshooh d2g LMvvho
Wkh Qhwkhuodqgv
id{ 64 +3,4305;7:6;5
Sulqwhg e|=
Ulgghusulqw/ Ulgghunhun
f 4<<:/ H1V1 ydq ghu Srruw
Doo uljkwv uhvhuyhg1 Qr sduw ri wklv sxeolfdwlrq pd| eh uhsulqwhg ru
xwlol}hg lq dq| irup ru e| dq| hohfwurqlf/ phfkdqlfdo ru rwkhu phdqv/ qrz
nqrzq ru khuhdiwhu lqyhqwhg/ lqfoxglqj skrwrfrs|lqj dqg uhfruglqj/ ru lq
dq| lqirupdwlrq vwrudjh ru uhwulhydo v|vwhp/ zlwkrxw zulwwhq shuplvvlrq
iurp wkh frs|uljkw rzqhu1
LVEQ <30:58<407806
Ulmnvxqlyhuvlwhlw Jurqlqjhq
Dvshfwv ri Vhqvlwlylw| Dqdo|vlv iru wkh
Wudyholqj Vdohvpdq Sureohp
Surhivfkuliw
whu yhunulmjlqj ydq khw grfwruddw lq gh
Hfrqrplvfkh Zhwhqvfkdsshq
ddq gh Ulmnvxqlyhuvlwhlw Jurqlqjhq
rs jh}dj ydq gh
Uhfwru Pdjqlfxv Gu1 I1 ydq ghu Zrxgh
lq khw rshqeddu wh yhughgljhq rs
grqghugdj 9 qryhpehu 4<<:
ghv qdplggdjv wh 7148 xxu
grru
Hgr Vwhskdq ydq ghu Srruw
jheruhq rs : iheuxdul 4<9;
wh Hlqgkryhq
Surprwru=
Suri1 gu1 lu1 F1 Vfkzhljpdq
Fr0surprwru= Gu1 J1 Vlhunvpd
Uhihuhqwhq= Gu1 P1 Olexud
Gu1 M1D1D1 ydq ghu Yhhq
Dfnqrzohgjphqwv
Lw lv d juhdw sohdvxuh iru ph wr suhvhqw wkh uhvxowv ri p| Sk1G10uhvhdufk
fduulhg rxw dw wkh ghsduwphqw ri Hfrqrphwulfv ri wkh Xqlyhuvlw| ri
Jurqlqjhq1 Gxulqj wkh odvw yh |hduv/ L zurwh wklv glvvhuwdwlrq xq0
ghu wkh vxshuylvlrq ri Jhudug Vlhunvpd dqg Mdfn ydq ghu Yhhq1 Dw wklv
sodfh/ L olnh wr wdnh wkh rssruwxqlw| wr wkdqn erwk ri wkhp iru wkhlu
vxshuylvlrq dqg vxssruw1 L ohduqhg iurp wkhp wkdw grlqj jrrg uhvhdufk
wdnhv sdwlhqfh dqg wkdw rqh kdv wr olvwhq yhu| fduhixoo| wr wkh lghdv dqg
frpphqwv ri rwkhu shrsoh1
Dv sduw ri p| uhvhdufk/ L kdg wkh rssruwxqlw| wr zrun wrjhwkhu zlwk
Pduhn Olexud iurp Zduv}dzd/ Srodqg1 Lw zdv d juhdw sohdvxuh dqg d
sulylohjh iru ph wr vshqg d frxsoh ri prqwkv dw wkh V|vwhpv Uhvhdufk
Lqvwlwxwh ri wkh Srolvk Dfdghp| ri Vflhqfhv lq Zduv}dzd lq wkh vsulqj
ri *<7 dqg wkh vsulqj ri *<81 Lq wkh vsulqj ri *<8/ Pduhn Olexud dovr
ylvlwhg wkh ghsduwphqw ri Hfrqrphwulfv lq Jurqlqjhq1 Rxu frrshudwlrq
uhvxowhg lq d qxpehu ri sdshuv1 Exw idu pruh lpsruwdqw/ L zloo dozd|v
uhphpehu klv krvslwdolw| dqg iulhqgvkls1
Lq idfw/ wkhuh duh wzr pruh shrsoh zkr kdyh frqwulexwhg wr sduwv ri
wklv wkhvlv1 Iluvwo|/ d sduw ri wkh uhvhdufk lq Fkdswhu 5 kdv ehhq fduulhg
rxw wrjhwkhu zlwk Yodglplu Glplwulmhylf ri Ehojudgh/ \xjrvodyld/ zkr
ylvlwhg wkh ghsduwphqw lq wkh vxpphu ri *<61 Xqiruwxqdwho|/ rxu frrs0
hudwlrq glg qrw frqwlqxh gxh wr wkh vlwxdwlrq lq \xjrvodyld1 Vhfrqgo|/ L
olnh wr phqwlrq Uxxg Whxqwhu1 E| klv hqwkxvldvp dqg jrrg lghdv/ L zdv
deoh wr dgg Fkdswhu : wr p| wkhvlv1
Dw wklv sodfh/ L olnh wr wkdqn surihvvru Fdvshu Vfkzhljpdq iru klv
zloolqjqhvv wr wdnh wkh wdvn dv surprwru dv zhoo dv iru klv vxssruw
dqg hqwkxvldvp1 Dovr wkh rwkhu phpehuv ri p| surprwlrq frpplw0
whh/ wkh surihvvruv Zlp Khvvholqn/ Mdq Nduho Ohqvwud/ dqg Zlp Nohlq
Kdqhyhog/ duh judwhixoo| dfnqrzohgjhg iru wkhlu lqwhuhvw lq p| zrun/
wkhlu zloolqjqhvv wr uhdg wkh pdqxvfulsw/ dqg wkhlu xvhixo vxjjhvwlrqv iru
lpsuryhphqwv1
4
Dv sduw ri p| srvlwlrq dw wkh ghsduwphqw ri Hfrqrphwulfv/ L vx0
shuylvhg whq vwxghqwv zulwlqj wkhlu pdvwhu wkhvlv1 Khuh L olnh wr vd|
wkdw L dssuhfldwhg wkh frrshudwlrq zlwk doo ri wkhp1 L hvshfldoo| olnh wr
phqwlrq wkh pdvwhu wkhvhv ri Phoylq gh Mrqjh/ Nhhv Mdq Urrgehujhq/
Vdqgru Vwhyhulqn/ dqg Uh|qrog ]xlo zklfk kdyh ehhq ri juhdw xvh iru p|
uhvhdufk1 L dovr olnh wr wkdqn Mrulv Nhl}huv zkr khoshg ph surjudpplqj
rqh ri wkh dojrulwkpv lq Fkdswhu 71
L dovr zdqw wr phqwlrq surihvvru Uhqì gh Nrvwhu iurp wkh Hudvpxv
Xqlyhuvlw| lq Urwwhugdp1 Rxu mrlqw uhvhdufk rq rughuslfnlqj sureohpv
uhvxowhg lq wzr sxeolfdwlrqv +qrw ehlqj lqfoxghg lq wklv wkhvlv,/ dqg wkhuh
duh srvvleo| pruh wr frph1
D vshfldo wkdqnv dovr jrhv wr Huln Iudpedfk iru khoslqj ph zlwk
Odwh{/ wr Vxzduql Edpedqj Rhwrpr iru jlylqj ph vhfuhwduldo vxssruw/
wr Hyhuw Vfkrruo iurp wkh Judgxdwh Vfkrro2Uhvhdufk Lqvwlwxwh V|vwhpv/
Rujdql}dwlrqv/ dqg Pdqdjhphqw +VRP, iru klv prudo dqg qdqfldo vxs0
sruw/ dqg wr p| urrppdwh Mdq ydq ghu Sorhj zkr lqwurgxfhg ph wr wkh
frpsxwhu jdph ILID1
Ilqdoo|/ L olnh wr wkdqn p| idplo|/ hvshfldoo| p| sduhqwv/ p| iulhqgv/
dqg doo shrsoh ri wkh kruvhedfn ulglqj foxe Sdudiulg1 \rx kdyh doo
ehhq d juhdw vxssruw wr ph1 L zrxog qrw kdyh ehhq deoh wr zulwh wklv
wkhvlv zlwkrxw |rx$
Hgr ydq ghu Srruw1
Frqwhqwv
4
Lqwurgxfwlrq
414
415
416
417
418
5
Wkh pdlq lghdv ri wklv wkhvlv 1 1 1 1 1 1 1 1 1 1 1 1
Wkh Wudyholqj Vdohvpdq Sureohp +WVS, 1 1 1 1 1 1
41514 Irupxodwlrqv ri wkh WVS 1 1 1 1 1 1 1 1 1 1 1
41515 Dojrulwkpv dqg frpsxwdwlrqdo frpsoh{lw| 1
41516 Dssolfdwlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Frqfhswv lq vhqvlwlylw| dqdo|vlv 1 1 1 1 1 1 1 1 1 1 1
41614 Wkh vwdelolw| sureohp 1 1 1 1 1 1 1 1 1 1 1 1
41615 Sdudphwulf dqdo|vlv 1 1 1 1 1 1 1 1 1 1 1 1 1
41616 Wkh n0ehvw sureohp 1 1 1 1 1 1 1 1 1 1 1 1 1
41617 Dowhuqdwlyh frqfhswv lq vhqvlwlylw| dqdo|vlv 1
Prwlydwlrqv wr vwxg| vhqvlwlylw| dqdo|vlv 1 1 1 1 1 1
41714 Lpsuhflvh sureohp gdwd 1 1 1 1 1 1 1 1 1 1 1
41715 Lqwhqwlrqdo fkdqjhv ri wkh sureohp gdwd 1 1
41716 Vxewoh vhwv ri frqglwlrqv 1 1 1 1 1 1 1 1 1 1 1
41717 Frpsxwdwlrqdo frpsoh{lw| 1 1 1 1 1 1 1 1 1 1
41718 Iloolqj d jds lq wkh olwhudwxuh 1 1 1 1 1 1 1 1
Ryhuylhz ri wkh wkhvlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
4
7
7
:
<
43
44
48
49
4:
4:
4:
4;
4<
4<
53
53
Ghwhuplqlqj wrohudqfhv iru wkh WVS
58
517
518
64
66
77
79
7;
514
515
516
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Ghqlwlrqv dqg edvlf uhvxowv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Wkh frpsoh{lw| ri wkh wrohudqfh sureohp iru wkh WVS 1 1 1
51614 D wudqvirupdwlrq iurp wkh Kdplowrqldq F|foh Sure0
ohp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
51615 Vroylqj wkh WVS e| ghwhuplqlqj wrohudqfhv 1 1 1 1
51616 Wkh frpsoh{lw| ri ghwhuplqlqj dssur{lpdwh ydoxhv
H{dfw ydoxhv ri wkh wrohudqfhv iru wkh WVS 1 1 1 1 1 1 1 1 1
Orzhu dqg xsshu erxqgv ri wkh wrohudqfhv iru wkh WVS 1 1
58
59
63
519
51:
6
7
9
erxqgv edvhg rq 40wuhh uhod{dwlrqv 1 1 1 1 1 1 1 1
Wkh 40wuhh uhod{dwlrq ri wkh WVS 1 1 1 1 1 1 1 1 1
Vkdushu dqg dgglwlrqdo orzhu erxqgv 1 1 1 1 1 1 1
Wkh 40wuhh uhod{dwlrq zlwk Odjudqjhdq remhfwlyh
ixqfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Frqfoxvlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Vwdelolw| uhjlrqv iru wkh v|pphwulf WVS
614
615
616
617
618
619
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Wkh sro|khgudo dssurdfk wr wkh WVS 1 1 1 1 1 1 1 1
Wkh v|pphwulf frqvwdqw WVS 1 1 1 1 1 1 1 1 1 1 1 1
Wkh vwdelolw| uhjlrq iru wkh WVS 1 1 1 1 1 1 1 1 1 1
Surmhfwlqj ohqjwk yhfwruv rq wkh d!qh kxoo ri T?|rR
Frqfoxvlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Vroylqj wkh n0ehvw WVS
714
715
716
717
718
719
8
Orzhu
51914
51915
51916
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Ghqlwlrqv dqg edvlf uhvxowv 1 1 1 1 1 1 1 1 1 1 1
Sduwlwlrqlqj dojrulwkpv 1 1 1 1 1 1 1 1 1 1 1 1 1
71614 Wkh Odzohu dojrulwkp 1 1 1 1 1 1 1 1 1 1
71615 Wkh Kdpdfkhu ) Txh|udqqh dojrulwkp
Eudqfk0dqg0erxqg phwkrgv 1 1 1 1 1 1 1 1 1 1 1
Wkh uhvxowv ri qxphulfdo h{shulphqwv 1 1 1 1 1 1
Frqfoxvlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 85
1 85
1 86
1 8;
1 96
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
98
98
99
:3
:6
::
:<
;4
;4
;5
;7
;8
<4
<9
433
435
Xvlqj vwdelolw| lqirupdwlrq iru vroylqj wkh n0ehvw WVS 438
814
815
816
817
818
819
81:
81D
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 438
Ghqlwlrqv dqg edvlf uhvxowv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 43:
D sduwldo rughulqj ri wkh wrxuv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 443
Wkh 50ehvw WVS zlwk jlyhq rswlpdo wrxu dqg wrohudqfhv 1 447
Wkh n0ehvw WVS zlwk rswlpdo wrxu dqg wrohudqfhv iru n 644<
Wrohudqfhv zlwk uhvshfw wr d wudqviruphg ohqjwk yhfwru 1 1 45:
Frqfoxvlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 463
Wkh surri ri Wkhruhp 8146 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 465
Vwdelolw| dvshfwv ri wkh WVS edvhg rq n0ehvw vroxwlrqv 46:
914
915
916
917
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Ghqlwlrqv dqg edvlf uhvxowv 1 1 1 1 1
Fkdqjlqj wkh ohqjwk ri d vlqjoh hgjh
Fkdqjlqj wkh ohqjwk ri vhyhudo hgjhv
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
46:
46;
475
47:
918
:
91714 Wrohudqfh uhjlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 47<
91715 Vwdelolw| edoov 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 48;
Frqfoxvlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 497
Wkh pd{lpxp qxpehu ri Kdplowrqldq wrxuv lq judskv 49:
:14
:15
:16
:17
:18
:19
Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Ghqlwlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Wkh pd{lpxp qxpehu ri Kdplowrqldq wrxuv lq d judsk
Orzhu erxqgv iru wkh pd{lpxp qxpehu ri Kdplowrqldq
wrxuv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Xsshu erxqgv iru wkh pd{lpxp qxpehu ri Kdplowrqldq
wrxuv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Frqfoxvlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 49:
1 49<
1 4:3
1 4:4
1 4:6
1 4:;
Eleolrjudsk|
4;4
Vdphqydwwlqj +vxppdu| lq Gxwfk,
4<4