Constraint solving in uncertain and dynamic environments - a survey
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(14) T. Real world. Control system. User. Physical environment. Other entities. Physical system. Supervisor. Executive. Reasoning control. Solution execution. Time. reactive deliberative. Offline problem modelling and solving. Online problem modelling. Problem pre−processing. Problem definition. Online problem solving Search control. Online solution maintenance. Time. Problem solution. Search algorithms off line online. hÃCxudiN®*¯¡W¹W´z¶Ü¸¹¸¢z¡$¼C»"¸´z´¶¾f´éºw¿fwº ¹¼fÀ?¸j¡¼fº4·H¤·H¸wÏ ¼C» £Í´?¤·j¶Û¹£Cº ·H¤z·H¸ÏÕ @9Ig=O>KM"B GI*OqM!>K`=*zQ@6Wn[XJL= ° If] ">A= M±L~kO =cI?JK@!GGI@I?@!J1@>eI IfO=I*OA">G=cM!F O = fI ] uWJL=3s!=uJpI*M 6O>KM9Jq`"qO=aW²M!F=uIfO =?>à@9E@9OqM GM=WdM QÔ@>KO=?FÌ@'I*O MÌ>KM6Y:M'O P @!ILe> Ib>C@ F O P G@O=uJKJKIfO= P =3OKI ^M!>0@JK@>K]!=*q`"qO=aW M7[Q>KM"B GI*OGIfM P BXIKKO>AI@Y OGIfM P O>A@F u iI P 3= OKI ^ D
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(97) b B M!9F MI3Iu">G>G=G Ib= B @9 ]!=u¶ Wa@ `ÚY3= I*M=Wc[XJL3= O=ufJ `X"*= zG[3= I*O=uB ° M!>Ý*= zQ6 @ Wn[XJL= P Ig O = HxD)'@ [1[XJK@I I?@ OGfI M P O IKÆIK O Ó = I?@!Z= M!FÙ@ =?>AfI M Qy YQ>G=u@ J"GB MaLÔÎ M '@ö"3= L I?@> P L @I I IKNXAQ@!JKfJ `' M'O OG @ J!= Ig= OqM)'@ I3I*M X= OIg O = [XJK@9 QIg ]r[QK> MIb=uG P Y3= I?@9Q=/fI OÝIKt OqM M>A@>G= OqM Ig ù3"=G Ibh= O =ÆBQ= I?IKAfI M P XQJL=uGy@ O>A@ s!=uJ'@ IbK> M9A¦c@ L~IKBX=ÆBQ=uG=?K> O¦IK [ JK@9X"=uB ! IK¦F>C6 @ W 3= LXM!K> JIKk O = YX@!GIKl M!XF O = q Mu·I?@!JKJL=uÔ B +q?K-6"a),/ ½?/'@ [1[QK> M9'@ I =ul O @ O. ò @>Gk= [X>G=u== O=uB<IgZ D
(98) = I*OGfI M ¾ Ù O x = M'O =?> @9QB P F>A6@ W3= LNM!e> J
(99) AG I @! HxB!DF P F»BEDF P D1BEDGF P M!> BEDF @>A = WnM!>G=N>G=uq O>A@I I*OGfI s!= P Y6 OÝ>A@I I =?> P IgÏ O @ O9O 3= `ö@!GC1 W y= O @ OdO = WnM
(100) BQ=uJKJL=?Ï > [QK> M±s
(101) IKBQ=u_ O = q `
(102) K Oa= W L~fI O Ig"0F M!%> W@ OGfI M '@ Y:M O×O Ú = [RM9AG@I YXJL= I @9 ]!=u @9QB#q M=W3= OGI W =uÝ'@ Y:M O9O =uIL>'@ YXq M9Jg O= M!> >A=uJK@ OGfI s!=<JKfI J!=uJKI M M
(103) Ù B M!F MI3Iu">G>G=1 Ib= ° M!>**= z"6@ Wc[XJL= P Ig O = HrD.'@ [[XJK@I I?@ OGfI M P O IKIK» O m= I?@!G#= L~fI O Fj OA">Gm= L1=u@ O =?>@9QB O>A@ ÜcIÙ F M!j> L @I I F M!>G= I?@!K O!M!>ÔK OG@ OGIKq OG@I I?@!pJ WnM
(104) BX=uJKE W@ ` Y3= @ s@!IKJK' @ YXJLZ= s"IK× @ I*M XQ= I*OGfI M Ù OqMBXIKK OG@96 OIg"0F M!%> W.@ OGfI M #GfI O=u@9QÎ B W.@ ` Ig u w ! ù6Q=G Iby= O =/BX= I?IKGfI M =u=/FÌ>A6@ W 3= LXM!K> J"Ý@>G= O = YX@!GIK9 M!!F O = q Mu·I?@!JKJL=uB 8:+;$-6"a),/ ½?Ý' @ [1[Qe> M9'@ I =u! O @ O~@>Gk= [Q>A=u=6 O=uBIgZ D
(105) = I*OGfI M Ó ø . e*a*%3%33**%3*ea**%% *¡G¢ 3£1¤y¥K¡*¦§3¡¦*¡§*§3¨¤n¥;©Gª7¡«¤!¬¢0«.
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(108). Q BQ=?>XO =O=?>%W +;?e-6"),/0½Ã? P L=m]9@O =?>*@!JKJ:O =#W =3O M"BXNO @OQ=¦MlJQM±L~JÅu =uBG]!=tM!FNO =d[RM9AGI@YXJL=tI @9]!=u ! IKàBGM4=uÙGM'O#W=u@9¶O @O#O =u=nW =3O M"BX BGMÝM'OXO>K`dOqMÆ@9=OGI@I?I@[X@O=#O =m[:M9GGI@YXJL=I @9G]!=u P F M!>1=*z"@6Wc[XJL=jY`>G=I*M!>CBXIg] L =Ùq M9fJ s"Ig ]¦q M=W X= [:M'O=6 OGIK@!JKJf`ÝQ=?FjQJ Ig"F0M!>%W.@OGIfM ±! IKM QJf`9W =u@9QO @O O 3= ` Q= M#Ig"0F M!%> W@ OGfI M @'Y:M OO =[:M9GGI@YXJL=BXIL>G=I*OGIfM Q¶M!FhO =FjOA">G= I @9 ]!=u Á! =ØBX>A@ L!Y '@ IKJ¶M!wF O IKà'@ YX=1 Ibl= M!wF JQ MaLÔJL=uGB ]!t= W.@ `Y3=@ JK@'IKJZM!F >KM6Y6Qq OA"=uGk M!EF O y= [XK> M
(109) B6G Ib=uB)q M9Jg OGfI M X pj = @!GB s@9= OG@ ]!= W.@ `Y3= P M O = I*M = O>A@K> ` P @9<'@ YXIKJKfI O·`OqM >G=u'@ I*OEOqM.@9= `J
(110) IgQB M!wF I @9 ]!= j c = YX@!G@I I[Q>AIg1 I?@I [XJLc= M!oF O =uG= W3= O M
(111) B P L =)FÌ'@ I?Ig ]@"3= LÇ[XK> M6YXJLa= W @0F O=?>Ù@ I @9G ]!=.Igx O d= [QK> M6YXJLa= W BX3= i6QfI OGfI M P IK# OqMOK> `>G=QGIgG ]/@!k WÝG I @! [:M9GG@I Y JLo = L @ O @!N Y6=?=t [XK> M
(112) B6G Ib=udB Y=`d[Q>A3= s
(113) fI M Q¿ [QK> M6YXJLa= W K M9fJ s
(114) Ig ]9 M±L P ILF L1=Ù>G3= s"IL3= LgL @ O!I?@9Ó Y6l= [QK> M"B G Ib=uB L = q M9fJ s"Ig ] y@ [QK> M6YXJLa= W P Ll= ]!3= OÔ0F M "> J"IgQBX» M!FIg"0F M!%> W@ OGfI M Á ¸ fJ M I?@!: J I*M QGIKq O=1 I*`dM!>1IgG I*M XGIKq O=G I*`dM! F [X@e> OGIK@!J6@!GAfI ] 1 W == OG P '@ I3I*M!>AB Ig ] OqMnO =QG=uB JL3= s!=u J M!FfJ M I?@!J I*M QGIKq O=1 I*` U T ]9fJ M6YX@!w J I*M QGIKq O=1 I*`ÓM!>¦IgG I*M QAIKq O=G I*`xM!NF [X@K> OGIK@!J@!GAfI ] 1 W == OG P I = O = @ YXIKJKfI O·`M!>ÔG M'OEOqMcY3=¦*= z O=XBQ=uBEIg= OqM.q M9Jg OGfI M Q U ' É I*M QGIKq O=G I*`ÓM!>ÙIgG I*M QGIKK O=G I*`ZM!XF I*M=Wn[XJL3= O= @!GGfI ] W == OG P I = O =ÝFH'@ I*O M!2 F Y3=uIg ]@ K M9Jg OGfI M M!> M'O U ß [QK> M6YXJLa= W I*M QAIKq O=G I*`M!>*IgG I*M QGIKq O=1 I*` P I = O m= ]9fJ M6YX@! J I*M XGIKq O=G I*`M!> IgG I*M QGIKq O=1 I*`M!2F O =¦a= Wc[GO·`/@!GGfI ] W == O M'O9= O =q `GWcW3= O>A@I IkY3= a@ s
(115) fI M "> M!ºF I*M QGIKK O=G I*`<@9QBIgG I*M QGIKq O=1 I*`<Ig u F0M!%> W@ OGfI M x LÔfI O >G3= ]9@>A B OqMZ[XK> M6YXJLa= W >G=uJKÃ@ zQ@ OGfI M )@9QB)>G=uq O>A@I I*OGfI M P I = I*M u q O>C@!Ig6 O >Ga= WnMas@!J@9QB#@!BXBXIg ] BXM XGIKq O=G I*`öIg" F M!> W@ OGfI M IKd [Q>G=uG=?K> s!=uÙ B Y=` [Qe> M6YXJLa= Wï>G=uJKÃ@ zQ @ OGfI M 0M L @ OlL1@!9 I*M QGIKK O=6 OÝ>Ga= W.@!IgQh I*M QAIKq O=6 Ob^ P Y G OØIg u I*M QAIKq O=G I*`Ig"0F M!%> W.@ OGfI M IK M'O 0M L @ O9L@! IgG I*M QGIKq O== OnWa@ `=ufI O =?> >G*= u W.@!Ig IgG I*M QGIKK O=6 OjM!j> Y3= I*M=W k= I*M QAIKq O=6 Ob^ BXM = s!=?>A=ufJ ` P IgG I*M QGIKK O=G I*`EIg u F0M!%> W@ OGfI M ÝIKw [X>G=u=?K> s!=unB Y`l[XK> M6YXJLa= W >G=uK O>A@I I*OGfI M P Y OwI*M QAIKq O=G I*` Ig"0F M!%> WÃ@ u OGfI M IK$G M'O Ð h I?@!X= M!FXGI WÝQfJ OG@9"3= M X M!>= Ø
(116) Q=6 OGIK@!J [QK> M6Y JLa= W >G=uJKÃ@ zQ@ OGfI M Ý@9QB >G=uK O>A@I I*OGfI M P F M!>¦*= zQ6@ Wn[ JL=ÆIgr I?@!t= M!F1@ I @9 ]!=IgÓ O = BQ3= i6XfI OGfI M x M!FÉ@ I*M u q O>C@!Ig6 O1Ig6 s@!JKIKBX@ OGIg ]lO j= Iu">A>G=6 Oq M9Jg OGfI M P 3= s!=?K> `O Ig ]IK1fJ M9q Oà7M I*M XGIKq O=G I*` @9QB Ig1 I*M QGIKq O=G I*` Ig"0F M!%> W.@ OGfI M 3^ {!M ] fJ ` K [3=u@ J
(117) Ig ] P (3$>f ),/7$'&+q?3(3?nO= I X@I Ø
(118) "=u MH= I*OGfI M Q ò }T @9QB ò }É ^ OK> `à>G=QAIg ]oI*M QGIKq O=G I*`ÙIgQ F M!%> W.@ OGfI M P L =?>G=u@!N +;?e-Ã(*$6&1/ & #+q?3(3?¿O= I Q@I Ø
(119) Q=u MH= I*OGfI M X ò ß @9XB ò }ò ^ OK> `Ý>G=QAIg ]¦IgG I*M QGIKq O=1 I*`Ig" F M!> W@ OGfI M ¾ Ys
(120) fI M XGfJ ` P á. %a**%3*33*3e3*e±*%% a¡¢03£G¤¥q¡*¦§3¡*¦¡§*§3¨ ¤d¥q©ª7¡«¤j¬1¢¥q§.
(121) '. X>AIKB = QI ""=u I > >G=QGIg. QAIK = @9XB Ig XGIK = ,Ig"F !> @ GI @>G= 9GGI JL= MH= GI 4^ > X>G=
(122) I X =?> s@ GI QÝ>G=uJK@ =uB Q> JL= >A=uJK@ "@ GI #@9XB >A=u >AI GI 1= ?@9 BX=uB b= O @ = @!JKJL= != !F$ 9Jg GI />G=QG= = QI ""=u*IK .BQ=u@!J ~I X> XJL= >G=u >AI GI Mj Ig @! 3=ØB "=ØIg ?@!G= !F>G=uJK@ Q@ GI 3^ =?>G=u@! = M "= !F>G=u@! QIg >G=X= = XI
(123) "=uÔIK .BQ=u@!J ~I Q> JL= >G=uJK@ Q@ GI O. P L @I O K` ` Y ÎO I @Ø ]ÏY:M'O I*M qO GI*` GI*M ;u ò ø k° KM=W [ 3s fM ÓM6Y qu GI*` 0M %W O fM P Î[:M @Y I*O fM O fM O OqM[ KM6Y aW Ãz O fM qO @I*O fM P L I GI OoO kI ] lM KM O fM #O I @Ø EOqM ÁL fO [ KM6Y aW P L KO @I*O fM GM'O ] EOqMyY 1M ¶I hM Ãz O fM !O #M KM ] #O I @Ø oOqM L fO [ KM6Y aW Ãz O fM . ò }T A@Á=æR7 Ï Q1æ
(124) ar:RçR Q,Bæ
(125). 9Jg GI )>G=X= = QI ""=uÝBQ=u@!J ~I GI AQ@ GI X =?>G= MHIÌ^ = Q>G= "I Q Q> XJL= @! 3=?=N 9J !=uB<@9QB X> !=uB 3= QGIK = MHIKIÌ^@Ý 9Jg GI !F @! 6=?= Q> "B b=uB @9QB >G= !>ABQ=uB MHIKIKIÌ^@ @9 != u">G>G=uB Ig =EBX= 6QI GI !F >A=uAQJ GIg Ig'@"= Q> XJL= MHI ^B6"= = X> XJL= >G=u >AI GI IKÝ J !=?>.@ 9Jg GI = @ ILF IK @ >G=uJK@ Q@ GI !F IK "I QGJ 9Jg GI !F @9QB = X@!GI @!GC GI !F0 9Jg GI >G=Q= = XI
(126) "=uàIK @ 3= ?@9QG= IK ?J 9= @< 9Jg GI !F ?@9 3= >G=u@! Q@ XJ )G=u@> =uBöF !>Ig = "I "IgQI !F F IKØ@!GA GI IK !>A>G= IK@ Q> 9@ FH@ ">A =u@> = ?IL= '@9QB' 9Jg GI G@ XIKJKI I = =<G= QB@9QB = IL>CB !F = @ !=.>G=
(127) XIL>G= = GMH=?= "= GI ^ ØIK = !=?>Æ=u@! XIKJKB X =?>G= Q@ JL=u =?>G=*@Ø @!JKJ @9 !=ÔIg = Q> JL= BQ= 6XI GI Ý>G=uAQJ GÉIg@ .IgQI Ý BXIK G@9 b=.M NBXIK G@9 b=¦F !>= Q@ XJL= I = =Ø
(128) 3=?> !F BXI µ=?>G= @>AIK@ XJL=@!AGI = Gb^ 3= =?=@. 9Jg GI !F @9XB<@ 9Jg GI !F @ IKÆ@! I @!Æ>G=
(129) XIL>G=uB à X> =uB = 6=?>CI = G A @9 @ Q> 9@ !>
(130) /Ig 9 ?@!=u @ 6= = = GI =u !=?> Ig"= ?IL= ÔJ = !=?> ?JK@!GGI ?@ GI IK@> Q@ XJL= = ?@9BXIK GIg QIK Ig =ÙJKI =?>A@ A">G=F "> "IgQBX !F = QI ""=u !F IK 3= ),+;?%?(3?K-6+."3Ä;<e-Ã(3?e W 3= O M"BX E! = WdM9q O<I WyW =uBXIK@ O = L@ `bM!FÝ>G=XGIg ] @ [Q>G3= s"fI M Qq M9Jg OGfI M 2Igb ^ O Ï = I*M 6 O*= zOrM!FÝBX= [GO uCiX>AK O¶O>G=?= G=u@e> I @!ÅJ u ]'M!>AfI O W P IKt OqMX= fI OÝ@!.@ =">AIKq OG@I I? Ð _ O =<"3= L O>G=?=E=u@%> I ÁP 0F M!> P =u'@ I s@>AIK'@ YXJL= O = s@!Jg"= @!GAfI ] "=uÏ B OqMfI OÝIg_ O = [Q>G3= s"fI M QK M9Jg OGfI M IK iX>Aq OmI M9G= Q! IKàIK F M!>*= zQ6 @ Wn[XJL9= L @ OIK¦GB M "=ÝIg M v == O="K> `IKJ@9QB F0K> M±s'M9q O PkS'S ^ Ð O/IK MaL13= s!=? > L1=uJKjJ JQ M±LÔË O @ ON@ BQ= [1O uCiX>Aq OcO>G=?= =u@e> I GB M
(131) =u0 M'O*= z[ fJ M!>GE= O =*K [ '@ Ibo= M!:F [:M9GG@I Y JL=*@!GGfI ] 1 W=6 OG'@ I3I*M!>AB Ig ] OqMØ@9ÝIgG Ib>G=u@!GIgG ]ÙBXIKq OG@9G IbE= OqM#O o= iX>Aq O =">CIKq OG@I I@!GGfI ] 1 W=6 O DM P QGIg ] @ >Å/0At/ )·?ek'/4(*"a+;?.8-'&"a¼(3?K-6+."3Ø@!fJ ]'M!>AfI O W M v @K> s!3= `Ù@9XB : IgQe Y6=?e> ] P6S'S'ò ^ # L~fI O @9 IgG Ib>G=u@!AIg ]öJKI W.fI O IK Ib=?K> OG@!IgQfJ `ÚWdM!>G=<'@ [[QK> M6[Q>AIK@ O=Ig AG I @ I*M 6 O*= zO T >f$"%->X(3?e-'+."3Äq<K-Ã(?KÎW3= O M
(132) B ë MI?@!J=u@e> I @!fJ ]'M!>CfI O WÝ@>G = Ib=?K> OG@!IgQfJ ` O M9X = O @ OiOO »= Y3=uq O@àGB `QQ6@ W@I I¿I*M 6 O*= zO 6! X= [Q>G3= s"fI M Qq M9Jg OGfI M 9 I?@9 GI Wn[XfJ `xY3= X=uB@!Ø@ q OG@e> OGIg ]<@!GGfI ] W == O¦ F M!k> O =."3= L fJ MI?@!J0=u@e> I Á = I?@9X=~fJ MI?@!J =u@e> I IKº Y @!G@I I?@!JKfJ ` @>G= [X@!IL¿> [Qe> M Ib=uGº O @ OºO>AIL=uw OqM@!BX'@ [GO D M GO fM cO I @Ø ºL fO fO O fM lL mO [ 3s fM P [ eM6Y aW oY qM fs [ KMas OqMnY #I*M qO =O qM GO fM C M P Y Ë[ KM GI I*M _I ] rMI3I O 3i fO fM ÙM P fO ] 3L [ eM6Y aW &D P Y GO P fs OqM D qM=W [ KM6Y aW qO @I*O fM P C GM fM G] qM O fM M'O O O P &D 2j Y @I Ãz O fM ÙM P C tM6Y=s fM f` qM O fM ÏM D I fM 9OqM P 1Wn[GO fM M qM O fM lO I @Ø jO O Y I P D & D C qM GO fM M I Y qM 'Y f` eI 0M O cs fs fO·` M C Ð NO Wn[GO fM kI*M I*O P O '[1[ KM 'I s'M 9Y:M'O eI 3ÜcI 1I*` qM O fM qO 'Y fO` P O I*M ^O ¶O ÎM mO É ÐO 'Y:Mas Ø aW =O D I*O fM M±L 3s q`rOqMZY I*M u O *z 6Wn[ wL eW GI ] nO E[ KM6Y aW 3i fO fM fO W W 1W KO GI FEh-6A9At/0& qO 1I M *z 6Wn[ P O 1W9Y NM 54 =OEs 'Y f] 1W =O NY 3OL qM GO fM ¶M qM GO fM & D M O O f] Ø ³ lI*M Gi %W Y=` *zG[ W =O P GI P '[1[ eM 'I LXM KJ bWnM qOyI Y OW `ËY I*M=W KM=W 3O W s K` 3ÜyI 6O ³ fO M G] 3s K`dI fiRI O fM K] 'Y P L I qO G] O fO O M oJ EM O I @Ø EM 2O oO` [ '¸. %a**%3*33*3e3*e±*%% a¡¢03£G¤¥q¡*¦§3¡*¦¡§*§3¨ ¤d¥q©ª7¡«¤j¬1¢¥*¥.
(133) T. É . ß . @9Ø@!GAIf] 1W ==OOqMà@~=3OpM!F1I*M QqO>A@!Ig=OG P O =?>G=1IK$MàBXI54µ=?>G=GIb= P FÌ>KM=WÍO = @!fJ ]'M!>AfI O W [:M9Ig=O#M!FNs"IL=3L P Y3=3OL=?= P M O =dM "= @9XB P @EQAQ@!JºWnMas!= O @ OÙ>G=uAXJfOGÙFÌ>KM=Wï@¶I @9]!= IgO =cIu">G>A=6OÙ@!GAIf] 1W ==OØ@9QB P M ×O = M'O =?> @9QB P @ I @9 ]!= Ig¶O =9Iu">G>G==O=3OjM!FºI*M XqO>A@!Ig=OGmOqMI*M QAIKBQ=?> ! =~fJ MI?@!J =u@%> I s!=?>AGIfM dM!FwAt/0&1Ä."%$'&G»/0"a)0(ÝM,HIg6OqM .=3O@!J @P:S'S'T ^IK@9 =*z"6@ Wc[XJL#= M!FAG I n@ W 3= O M"B (*$>f),/0$'&Ô8G?3+),+*<e-'),/0$6&1Ä;<e-Ã(3?eÖW3= O M
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