edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j...

21

Transcript of edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j...

Page 1: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

����������� ����� ����������

� ������� ����� � ��!#"%$'&(��� )*�,+.-0/21 3 !�!#/4+*����!#"5$6 3 7'8 &93%: $;3 !.- � <=�><?!.@ A B.-C��� �ED.+2-F��<?!

G ��!#H./I!.- 3 J�� �,HK�MLN/O�P�,<

QR<?�*< -C�,HTS UV!WSX-C�Y-Z).-X/� +#L[!\/2"]�^/ _ /`�P�E<a! b ! �Yc#/`LdSe�Y-f@

g�h�h�h i <�L[�*/TS 3 c#/I!�)#/jR�k-l-mST��)*Ln"aop$Rj*3 q g�r q.s

H#�,H#��LN/O�P�,<]t Lu�vJwH � )pJw/.1a)

x

Page 2: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � �� ���P� � � �����P�� �

�� � � ��� � � � �� � � � � �

� � � � ��� � ��� � ��� � ��� �

�� � ��� � �

o�)�!#1=Ln/21 S <�� cO+KLu� + �*�E/ SW$?-Zo#<a)4S +�!#1 S <�� H`�,+�)4SF/TS

� � �

A

BC

D

E

FG

H

o�)�!#1 LN/.1 S <�L /�c#/ ! -Zo\<a)4S + !\1 S <�� HK�k-C�,/TS

Page 3: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

����� � � � �� � � �����P�� � ���� p�#� �=� �w� �����`�

j Ln<a�*�>/ � S ��! � o �,H o��

: o#/OLN/ �>S SF<a� / H.<a� � ��!K+2-0<�L � +*� SX-�L[)\H�-Z)ILN/ -X<<aB -C��� �>D /

: o#/OLN/ �>S SF<a� / H.< SX- � )�!#H -C�,<a!�� & -�L[)#H -Z)*Ln/ QR/W+ � $9-0< �*/ <aB.-F��� �>DT/.1 <�L +.- �E/4+4SX- + Ln/4+4SF<a!O+ �I�>/SF<=��).-C�,<a! �>S -0< �*/ �f<a)�!#1

&9/4+#LNH o ��!\" + �P� B*< S Se���*�E/ SX-�L )#H -Z)*LN/TS �>S ��!.-�L +KH��- +��*�>/

i & + B�B\LN<�+#HIo#/TS +KLn/ -0<=< /���B*/I!WSe�YcK/�J

: o#/OLN/ �>S !\< �O!#<�� ! + �E"�<�Lu�Y-Zo�� �f<�L�� !#1]��!#" <aB��-C��� + �]SF<=�w).-F�,<a!4S /�� HK�,/ !.-�� @

&(��� ��� +KL SF<=�w).-C�^<a!4S oK+2c#/ Se��� ���,+#L H.< SX-mSWJ

Page 4: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� ���=� ������ � � � ��� ��� �� � � �

U !.-Z) �k-C�,<a!�� � <a!4Se�^1�/`L�-Zo#/ B*< S Se���*�E/ H.<a! �9"a)*L +2-C�^<a!4S-0< �*/ �,+ �,1 <?).- <a! -Zo#/ ST)IL � +#H2/ <�� + �,+�!#1 SFHW+ B*/�J: o#/ o#/K�^"ao.- <�� /W+KH o H.<a! �9"a)IL +2-F�,<a! <?! -ZoO+2- �^+ !#1 �SFHW+ B*/ �>S 1�/�-X/`L � ��!#/.1 �e@ + � /4+4ST)*LN/ <�� �k-mS �a)O+*���Y- @TJ6 / � + ! - -0< � !#1 -Zo#/ o �^"ao#/TSX- B*<]��!.- J

6 / 1�<a!���- BO+#L -C�^HI)*�^+KL � @ H4+#LN/ o#<�� � / "�/ - -Zo\/`Ln/�J

�fU -0/OL +.-C�Yc#/ UV� B\LN< c#/ � /I!.-�� � / -Zo#<=1 S �

& - +KL - +2- L + !#1�<?� H.<a! �9"a)*L +2-C�^<a! U -0/OL +.-C�Yc#/`� @ H2<?!4Se�,1�/OL c`+#L �,<?)4S � < c#/TS 3 H2H./IB - SF<a� / +�!#1 LN/ /2H - SF<a� / 6 o\/I! SX-Z)#H �*$�LN/TSX- +#L -TJ

6 / � )4SX- ��!.c#/I!.- + _ < cK/.&9/ - -eoO+2- 1�/TSFH`Lu���*/ S � oO+2-� < c#/TS +#LN/ +*�P�>< � /.1 �lLn<a� + "p�YcK/ ! H2<a! �9"a)*L +.-C�,<a!J

Page 5: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���F� ��� � � � ���

� �M�P� �lHO�P� � � � !#" � : L @ -X< � + � ��� �>D / �9cO+ ���� � @� < c ��!#" -0< -eo#/ o �,"ao#/TSX- H.<a! �9"?)*L +.-C�,<a! "]�Yc#/I! <a)*L� < c#/TSF/�-TJ U � + ��� ST)\H2H./ S SF<�L S +#LN/ �>< � /OL -ZoO+�! � /+#LN/ +.- + �0�><=HW+ �]<aB -C��� )�� J��

q�J 7p/�- � � � ��! �Y-C� +*�9H2<?! �9"r J 7p/�- � � � �9cO+ ���� s%J 7p/�- � � � � < cK/TSF/�- ��Se�>D /��� � J i <�L � ��� q �������

7]/ - ��� � � �9cO+ ��� � < cK/��� $����g J U � +*�P� � ��� � $ -X/`L � ��!O+2-X/�$�LN/ -Z)*L[! � J ��� SF/ �E/�- �"! � +#LN"a� + �#� ��� $ J 7p/�- � � � � < cK/��� $�� ! % J 7p/�- � � � � �'&( J ) < -0< s

*

Page 6: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� ��� ��� ���O� � � � � ���F� ��� � � � � �

q�J 7p/�- � � � ��! �Y-C� +*�9H2<?! �9"r J 7p/�- � � � �9cO+ ���� s%J 7p/�- � ��� L + !\1�<a� � < cK/ �lLn<a� � < cK/TSF/�-� J 7p/�- � � ��� � c`+*��� � < c#/��� $����g J U � � � � � -Zo#/ !

7p/�- � � � � < c#/��� $ ��7p/�- � ��� � �

J ) < -0< s )�! -C���'�*<�Ln/21

6 oO+.- SX-X<aB�B ��!\" HOL �Y-X/`Lu�,<a! STo#<a)*�E1 � / )4SF/��

6 oO+.- +KLn/ SF<a� / B#Ln< S + !\1 H.<a!4S H.<a� BO+#LN/.1 � �Y-eoB\LN/ cI�,<?)4S o �M�P�aHO����� �*/OL��

Page 7: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���F� ��� � � � � � � ��������

: Lu�Yc � + �=-0< B#LN<�"=L +�� Q�/ �a) ��LN/TS !#< � /I� <�L @ � !#< �K+KH �e-�L +KH �4��!#" _ < c#/2&9/ - 1�/TSe�,"a! �>S HOL �Y-F�,H4+*� �9cO+ ��)O+2-C�^<a! �m)�!#H -C�,<a! 1�/TSe�,"a! �ES H`Lu�Y-C�,HW+ � � +.cK<]�^11�/ !4SF/ �><=HW+ � <aB.-C��� + +�!#1 BI�,+2-0/W+ )WD � o#/ ! B*< S Se� ��*�E/ � !\<�L[� <?)4S _ < c#/2& /�- � +e@ LN/TST)*� - ��! ��!#/�� H#�,/ !#H @

: ��!.@ _ < cK/.&9/ - � +Z@ LN/TST)*� - ��! "�/�-l-F��!#" SX-Z)#H �/W+\Se��� @ 6 oK+2- � � �k-mS H o#/4+�B*/`L=-X< / c`+*�w)O+2-X/ + ! ��!#HOLN/ � / !��- +*� H oO+ !#"�/ <�� + B#Ln/�c �,<a)WS � @ /�cO+ ��)O+2-0/.1 <a� /2H - �� + ! � / 1�< -ZoO+2- � �Y-Zo o ���P� � H`�P� � � � !#"��

Page 8: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���C� ��� � �=� � � � � �� � �P��� � � �

� ��� � �

�� � � � �

� � � � ���

��� � ��� � ���

�� � ��� � �

� <a! �9"a)IL +2-F�,<a!�� � q�$ h $ q�$ h $ q

_ + � ��� �>DT/ � � c`+*���X� <?! �9" � � <�� S +.-C�>S �9/.1HO�,+ )WSF/ S

_ < cK/.&9/ -�� �'��B + !.@ q cO+KLu� + �*�E/

Page 9: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � � � � � � � � � ���`� � � � �

jR�^H � + L + !#1�<a� )�!WS +2-C�>S �9/.1 HO�,+ )4SF/

� <?!4Se�,1�/OL s � < c#/TS � �'��B�B ��!#" /4+#HIo c`+#L � +��*�>/�J

U � +�!.@ ��� B\LN< c#/ � c`+*� $'+#H2H./IB - -Zo\/ �*/ SX-TJ

U � !#<a!\/ ��� B#Ln< c#/ �9cO+ � $]-eo#/I! g�h�� <�� -Zo#/ -C��� /B �^H � -Zo\/ �>/W+\SX- �K+K1 � < c#/ +�!#1 g�h�� <�� -Zo#/ -C��� /B �^H � + L +�!#1�<a� <a!#/�J

Page 10: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���F� ��� � � � ��� � � �� ���P��� � � �

� <a! �9"a)IL +2-F�,<a!��

A

BC

D

E

FG

H

_ ��! ��� �>D /�� � c`+*���X� <?! �9" � �E/I!#" -Zo <�� -0<?)*L

_ < cK/.&9/ -�� r � HIoO+�!#"�/�$ ����� $����lH oO+ !\"�/

� �`+�� B*�>/ � r �lH oO+ !\"�/

A

BC

D

E

FG

H

A

BC

D

E

FG

H

x��

Page 11: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� �C���� ��� � � � �� ���P�

A

BC

D

E

FG

H

A

BC

D

E

FG

H

A

BC

D

E

FG

H

A

BC

D

E

FG

H

A

BC

D

E

FG

H

A

BC

D

E

FG

H

x�x

Page 12: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���F� ��� � � � ��� � � �� ���P��� � � �

: o �>S H`�,+4S S <�� + �>"�<�L �k-Zo�� S �f<�L�-Zo#/ : &Rj �>S )4ST)O+*�P� @Ln/ �f/OLfLn/21 -X< +\S ���l<?B.- �F_ < c#/.&9/�- � r �lH oO+�!#"�/�$ ����� $���lH oO+�!#"�/ � <�L SF<a� / H.<a!4SX- +�!.- �pJ

7?��! STo\<�� /21 / � B ��Lu�,H4+*�P�Y@ �

s �l<?B.- SF<=�w).-C�^<a!4S +KLn/ � )#H o �*/ -l-0/OL�-ZoO+�! r �l<aB -

� � <aB.- SF<=��).-C�,<a!WS +#LN/ !\< - ST) � HK�^/I!.- � @ �*/�- -0/`L-ZoK+ ! s � <aB.- -0< F)4SX-C� � @ -eo#/ /��.-�L + H.<a� B�).-0/ -F��� /

3 s �l<aB.- -0<a)IL �f<�L9-Zo#/ � % �lH#�Y-f@ B\LN<a�I�>/I� <�� �R/`�E1+�!#1 8 +#L[B oK+\S + �*<a).- + B\LN<a�O+�� �����k-f@ <�� h J h g <���*/#��!#" <aB.-F��� + � � q h�h L + !#1�<a� Ln/ SX- +KL -mS � �M�P� @ �,/O�>1-Zo\/ <aB.-C��� +*�]SF<=�w).-C�^<a! � �k-Zo B#Ln<a�O+�� �����Y- @ h J ( (

i )*L -Zo#/OL �f<�L o �ES BO+#L -C�,H )*�,+#L H`�^+\S S <�� : &Rj $ +s � <aB.- -X<a)*L �ES <aB -C��� + � � �Y-eo B\LN<a�K+ � ��� �Y-f@ r���������� o#/`Ln/ �>S !�)�� �*/`L <�� HK�k-C�,/TSWJ

: o#/`Ln/ �>S !#< -Zo#/.<�Ln/�-C�^H4+*� C)4SX-F� �9H4+.-C�,<a! �f<�L + !.@ <��-Zo\/ SF/ LN/TST)*� -mSWJ

x �

Page 13: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���P�� � � � � ������ � �

q�J 7p/�- � � � ��! �Y-C� +*�9H2<?! �9"r J 7p/�- � � � �9cO+ ���� s%J 7p/�- � ��� L + !\1�<a� � < cK/ �lLn<a� � < cK/TSF/�-� J 7p/�- � � ��� � c`+*��� � < c#/��� $����g J U � � � � � -Zo#/ !

7p/�- � � � � < c#/��� $ ��7p/�- � ��� ���

��� SF/ � �Y-Zo SF<?� / B#LN<?�O+ � �M���Y-f@ $ +#H2H./IB - -Zo\/ � < cK/+�!.@ � +e@7p/�- � � � � < c#/��� $ ��7p/�- � ��� ���

J ) < -0< s )�! -C���'�*<�Ln/21

: o �>S � +e@ � + � / -Zo#/ SF/4+#LNH o � + ���I<?).- <�� � /.1]�,<=HOLN/�><=HW+ �%� ��! ��� + + !#1 ��!.-0< �*/ -l-0/OL �><=HW+ �%� + � ��� +]J

x �

Page 14: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���P�� � � � � ������ � �

�R< � STo#<a)I�>1 � / HIo\<=< SF/ B#Ln<a�O+�� �����Y- @ <�� +#H2H./IB -C��!#"+ � <�L SF/ ! ��!\" � < c#/�� �R/OLN/ +KLn/ SF<?� / �,1�/W+\S �

q�J j Ln<a�O+ � �����Y- @ � h J qr J j Ln<a�O+ � �����Y- @ 1�/.H`Ln/4+4SF/ S < c#/`L -C��� /s%J j Ln<a�O+ � �����Y- @ 1�/.H`Ln/4+4SF/ S < cK/OL -C��� / +�!#1 + �YSF<+4S � � � � ��!#HOLN/W+\SF/TS

x �

Page 15: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���P�� � � � � ������ � �

U � ����� � -Zo#/ ! 1�/�� ! �Y-X/`� @ +KH.H./IB.- -Zo#/ H oO+�!#"�/

U � ��� � � -Zo#/ ! +#H2H./IB - -Zo\/ HIoO+�!#"�/ � �Y-ZoB\LN<a�O+�� �����k-f@��

/���B � ����� ������ �

� H4+*�P�>/.1 -eo#/ � <=� -mDO� + ! 1]�ESX-�L ����).-C�,<a!�

� o#/`Ln/ � �ES + �f-X/I� B*/OL +.-Z)*LN/ � BO+#L +�� /�-0/OL -ZoO+.-"=L +K1a)K+ �P� @ 1�/.H`Ln/4+4SF/ SWJ : @�B �,HW+ �=H2<=< ����!#" SFH o#/21?)*�>/ � � � � ���

� �^"ao -X/I� B�� +#H2H./ B.- +*�P�'� < c#/ S �XL + !\1�<a� � + � � 7p<�� -0/ � B�� &=-X<=HIoO+4SX-C�,H o ���P� �lHO�M��� � ��!#"

6 o#/ ! !#< ��� B\LN< c#/ � /I!.- + � -X/`L9/ !#<a)#"?o �Y-X/`L +2-C�,<?!4SW$-0/OL[� ��!O+2-0/�J

x *

Page 16: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���P�� � � � � �� ��� � � � ��������

: Lu�Yc � + �=-0< B#LN<�"=L +�� Q�/ �a) ��LN/TS !#< � /I� <�L @ � !#< �K+KH �e-�L +KH �4��!#" _ < c#/2&9/ - 1�/TSe�,"a! �>S HOL �Y-F�,H4+*� � c`+*�w)O+.-C�,<a! �m)�!\H�-C�^<a! 1�/TSe�,"a! �>S <�� -0/ ! H`Lu�Y-C�,HW+ � 3 !�!#/W+ ����!\" SFHIo\/21a)I�>/ <�� -0/I! HOL �Y-C�^H4+*� 6 oK+2- � � �k-mS H o#/4+�B*/`L=-X< / c`+*�w)O+2-X/ + ! ��!#HOLN/ � / !��- +*� H oO+ !#"�/ <�� + B#Ln/�c �,<a)WS � @ /�cO+ ��)O+2-0/.1 <a� /2H - �� + ! � / 1�< -ZoO+2- � �Y-Zo Se��� )*�,+.-0/21 +�!�!#/W+ ����!\"��

x

Page 17: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � � �P���� � � � ������ ��� � �w� � �� �.�w� �

&'��� )*�,+2-X/21 3 !�!#/4+*����!#" � +\S ��! -�LN<=1a)\H2/.1 ��! q ( g s� @ _ /�-�Ln<aB*<=���ES +�!#1 �>S �O+\SF/.1 <?! +�! + !K+ �><�" @ � �Y-eo-Zo\/ � +e@ -eoO+2- +*�P�><4@4S � +�!O+K"�/ -0< � !#1 + !#/W+#Lf� @"=�E<a�O+ � � ��! ��� )�� / !#/OLN" @ �>/ cK/O� � o#/ ! -Zo#/ @ +#LN/H.<=<=�>/.1 S �E<�� � @TJ

&'��� )*�,+2-X/21 3 !�!#/W+ ����!#" �>S SF<?� /�-C��� / S / � B ��Lu�,HW+ �P�Y@� )#H o �*/ -l-0/OL'+.- +2c#<]�,1]��!\" �E<=H4+*�I� ��! ��� + -ZoO+�! o ���P� �HO����� � ��!#"%J

�R< - � )#HIo <aB�B*<�L -Z)�! �Y-f@ -0< S +Z@ +�!.@2-eo ��!#" �f<�L[� +*�+��*<a).- �Y- � -Zo#/OLN/ �>S + B\LN<=<��%-ZoO+.- � �Y-Zo + ! ��! � ! �k-0/`� @S �>< � H2<=<=� ��!#" L +2-X/�$ @T<a)�� �P� � !#1 -Zo#/ "=�E<a�O+ � <aB.-F� �� )�� eJ

x �

Page 18: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ���P� ��� � ����� � ���`����w� � � � � �

U 1�/W+ � &9/ - �><=< SF/ <?! @ <?)*L B#Ln<a�*�>/ � + H.<=�><a! @ <��+�!.-mSWJ � +KH o +�!.- SX-0<=HIoK+\SX-C�,HW+ ��� @ ��) �M�>1 S + SF<=�w)��-C�^<a!pJ 3 SToO+#LN/.1 /I!.c ��Ln<a!�� / !.- �ES )�B*1�+2-X/21 -0< Ln/ ��9/.H�- �a)K+ ���Y- @ <��'SF<=�w).-C�^<a!4S + !#1 B#Ln<a� �>Se��!\" BO+#L -mS <��SF/W+KLnHIo STBK+KH./�J QR/ B*/4+.- )�!.-C���=+*�P�?+ !.- S ��) ���>1 S +�� /SF<=��).-C�,<a! <�L )�!.-C�M� �*<�LN/.1%J

� +\SF/.1 <a! +�! +�!O+ �E<�" @ <�� +�!.- B�o\/`Ln<a� <a!#/ -�L +I����f< �P�><�� ��!#"%J

3 �,+KLn"�/ BO+#L - <�� � & � +#L[� UV! -0/`�����,"�/ !#H./�� i LN<a� � +2- �)*L + �.-0< 3 L -C� �9HK� +*� &=@\SX-X/I� S � � � <a!O+��*/4+�)p$ <�Lu�,"�<%$: o#/`L + )*�^+\D*$ q ( ( ( �ES 1�/21p�,H4+.-0/.1 -0< �Y-TJ

x �

Page 19: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� �[ � ���� � � � �P��� � � ���

q�J 7p/�- � � ��� � � �*/ -Zo#/ ��! �Y-C� +*�%+ � <a)�!.- <��B�o\/`Ln<a� <a!#/ �*/�- � /./I! H#�Y-C�,/TS � + !#1 �

r J 7p/�- � � ��� � �� ��� � o#/`Ln/ � � ��� �>S -Zo#/1]�ESX- + !#H./ �*/ -�� /2/ ! H#�Y-C�^/ S � +�!#1 �

s%J i <�L /4+#HIo + ! - �

� J 7]/ - �� ��! �Y-F� + ���Y@ H2<a!WSe�>SX- <�� +*�P�=HK�Y-F�,/ Sg J 7]/ - � � � L + !#1�<?� SX- +#L - H#�Y- @ J QR/ � < cK/ � � LN<a� � $ J 6 o ���>/ �� !#< - / � B.-f@% J : L + !WSe�Y-C�,<a! �lLn<a� � -X< � � �Y-Zo

B#LN<?�O+ � �M���Y-f@

� � ��� ��� � ��� ������� �� ��� ��� ��� ��� ��� �"! ��� ��� � ��� � ��� �#� � ��� �( J 7]/ - � � � + !#1 Ln/I� < c#/ � �lLN<a� � q h J 7]/ - � � ��� � � q � $ %� � ���'& � )(+*

��� �, !� o#/OLN/ � �>S �>/ !#" -Zo <�� -0<a)*L �f<a)�!\1 �e@ +�!.- �

+ !#1 � ��� +KLn/ -Zo\/ + !.-mS -ZoO+.- )4SF/.1 /.1�"�/ ���-.� x �

Page 20: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� �[ � ���� � � � �P��� � � ���

A

B

C

D

E

F

JkTour

A

B

C

D

E

F

JkTourA

B

C

E

F

JkTour

A

B

C

E

F

JkTour

A

B

C

E

F

JkTour

A

B

CE

F

JkTour

D D

D D

JkTour

A

B

C

E

F

D

ABCDEF

A B C D E FABCDEF

A B C D E FDistance matrix

Pheromone matrix

� �

Page 21: edge.cs.drexel.eduedge.cs.drexel.edu/regli/Classes/AI/slides/stochastic_search... · P p# = w ` j Ln/ S ! o ,H o: o#/OLN/ >S SF

� � � ��������

: L +�!4S �f<�L[� ��!#" @ <?)*L B#LN<?�*�>/ � ��!.-0< <a!#/ <�� � !#1 ���!\" + BK+2-Zo -ZoILN<a)#"?o SF<a� / SF<�L - <�� "=L +�B�o SX-�L )#H �-Z)ILN/ �>S <�� -0/I! HOL �Y-C�^H4+*� J j%+KL + � / -0/OL=-Z)�! ��!\" �>S <�� -X/I! HOL �k-C�,HW+ �T-0< +.cK<p�,1 /#� �-Zo\/`L�/W+KL � @ H.<a!.c#/`Ln"�/I!\H2/ � �Y-Zo �O+K1 LN/TST)*� -mS <�L%cK/OL @�><?!#" S �E<�� H.<a!.c#/OLN"�/ !#H./�J : o#/OLN/ /�� �>SX- 1p���R/`Ln/I! - cO+KLu� +2-F�,<a!4S <�� H#�Y- @ -�L + !��Se�Y-F�,<a! L )*�>/�J 6 o �^HIo -0< )4SF/�� : o#/OLN/ /�� �>SX- c`+#L � +.-C�,<a!WS -ZoO+.- + �P�E<�� <a!*� @ -eo#/�*/TSX- + !.- -0< )�B*1�+2-X/ -Zo\/ -X<a)*Ll$ -Zo#/ � �*/TSX- + !.-mS-0< )�B*1�+.-0/ -eo#/ -X<a)*Ll$ + !.-mS � �Y-eo �O+K1 SF< �w).-C�,<?!4S-0< !#/."�+2-C�kcK/O� @ Ln/K��! �f<�LnH2/ -Zo#/ -0<a)*L $R+ !#1 SF< �f<�L -ZopJ6 o �^HIo -0< )4SF/�� 6 oO+.- � � <a)*L B#Ln<a�*�>/ � oO+\S !\< <a�.c �,<a)WS -�L + !4S ��f<�L[� +.-C�,<a! -X< + : &Rj � ��� ��/ B#Ln<a�*�>/ � � � + ! � / SX-C���P�)4SF/ 3 � A � 6 oO+2- + �*<a) - �f<�L &93%: �

� x