Evolutionary computation B> 0%CDE&'F&&5...
10
Evolutionary computation !"#$%"& ()*+,-.)/0 1 (23%45"& 6!*78+ !93$:;3%47&<2 Outline => 6$5?;5$" @> )?&3?%&A B> 0%CDE& F&"&5< !E9$3%#2C G0F!H I> )D5C%4;5$" A%#2 F! J> 72&$3&5<;E K$L"M;5$"4 N> :3$OE&C 4$E?%"9 A%#2 F! P F&"&5< :3$93;CC%"9 Q> ($1&?$EL5$" =NR=@R=S @ T?$EL5$";3U ($CDL#;5$" 1 V !> ($3"LWX$E4 Motivation ! !"#"$%"&' &)*+,)- ./0-+10& #$ &?$E?& O&Y&3 Z 4$EL5$"4 [ ! F&"&3;5$" $K 4L<<&44%?& 202+-)10&3 • A%#2 3+,/"/)- ;"M ,.2,04+$10& $K #2& 56.3*3 • ,4%"9 #+*)10& ;"M $,03370/., ;4 3&D3$ML<5$" $D&3;#$34 ! !"#$%&'" ?4> )*"#$%&'" ! ! \%"M $K '.&.,)-"8.4 021#"8)10& #.*904 • ! 202+-)10& $K ]4$EL5$"4^ P +,-" • *&D3$ML<5$" $'"./%$.+ • 0"1"23$# $K #2& _Y&4#4 =NR=@R=S B T?$EL5$";3U ($CDL#;5$" 1 V !> ($3"LWX$E4 Motivation : history ! ]T?$EL5$";3U <$CDL5"9^ • 8> *&<2&"O&39 %" #2& NS4> • !"#$%&'#() () +,'- .'-/,0 0($'%)1 ! F&"&5< ;E9$3%#2C4 • .$2" `$EE;"Ma ]20'"3'#() %) 4'3/+'- ')0 2+#56%'- 7813,$1^a =bQJ> • 9%3 +,"+,1,)3'#() : 76;,$' 3;,(+,$ : <+(=-,$>7(-.%)? $,3;(0 ! F&"&5< :3$93;CC%"9 • .$2" c$d;a e%34# O$$\ $" F&"&5< :3$93;CC%"9a =bb@> • <+(?+'$1 +,"+,1,)3,0 '1 3+,,1 =NR=@R=S I T?$EL5$";3U ($CDL#;5$" 1 V !> ($3"LWX$E4
Transcript of Evolutionary computation B> 0%CDE&'F&&5...
Evolutionary computation
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Outline
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Motivation
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! !"#$%&'"((?4>'')*"#$%&'"(
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Motivation : history
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Overview : principle
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Overview : illustration
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Simple GA
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Representation / chromosome encoding
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Representation / chromosome encoding
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Representation / chromosome encoding
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Functioning of the Genetic Algorithm
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Initial Population
Selection
Reproduction
Mutation
Next Iteration
(Generation)
Prototype EC Method
Initialization of the population
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Fitness function
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Selection
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Selection: Roulette-wheel
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h1 h2 h3 h4 h5 h6 h7 h8 h9 h10
0
100
200
300
400
h1 h2 h3 h4 h5 h6 h7 h8 h9 h10
h1
h2h3h4h5
h6
h7 h8
h9
h10
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Selection: rank
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h1 h2 h3 h4 h5 h6 h7 h8 h9 h10
0
100
200
300
400
h1 h2 h3 h4 h5 h6 h7 h8 h9 h10
h1
h2h3h4h5
h6
h7 h8
h9
h10
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h6
h7 h8
h9
h10
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Selection: Tournament
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Genetic operators
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Genetic operators: mutation
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0 0 0
pmut = 1
pmut = 0,5
pmut = 0,3
pmut = 0,1
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Genetic operators: crossover
1 0 0 0 1 1 0 1 0 0 1 1 0 1 1
0 0 1 0 1 0 0 1 0 1 1 1 1 0 1
1 0 0 0 1 1 0 1 0 0 1 1 0 1 1
0 0 1 0 1 0 0 1 0 1 1 1 1 0 1
1 0 0 0 1 1 0 1 0 0 1 1 0 1 1
0 0 1 0 1 0 0 1 0 1 1 1 1 0 1
1 0 0 0 1 0 0 1 0 1 1 1 1 0 1
0 0 1 0 1 1 0 1 0 0 1 1 0 1 1
(a)
1 0 0 0 1 0 0 1 0 1 1 1 0 1 1
0 0 1 0 1 1 0 1 0 0 1 1 1 0 1
(b)
1 0 1 0 1 0 0 1 0 1 1 1 1 1 1
0 0 0 0 1 1 0 1 0 0 1 1 0 0 1
(c)
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Genetic operators: role
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Genetic operators
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Replacement of the population
N N
PG(t) PG(t+1)
!!
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$K'$#2&34'
Replacement of the population: 3 strategies
N N
PG(t) PG(t+1)
!!
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=> ($CDE&#&EU'3&DE;<&'#2&'D3&?%$L4'D$DLE;5$"''
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B> '0%"/?&(+%/%"(
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Simple GA: example (from Goldberg, 1989)
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Simple GA: example (from Goldberg, 1989)
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Simple GA: example (from Goldberg, 1989)
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Simple GA: example (from Goldberg, 1989)
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Illustration: Traveling Salesman Problem
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Lessons
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Why GAs work: the schema hypothesis
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Why GAs work: the schema hypothesis
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Why GAs work: the schema hypothesis
! 0<2&C;4''
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Why GAs work: the schema hypothesis
! /&#'M'O&';'4<2&C;'A%#2';#'E&;4#'$"&'%"4#;"<&'D3&4&"#'%"'#2&'D$DLE;5$"';#'5C&'3*
! /&#'$GMJ*3H'O&'#2&'"LCO&3'$K'%"4#;"<&4'$K'M';#'5C&'3*
! /&#'G'O&';"'%"4#;"<&'$K'M';"M'AGGH'O&'%#4'_#"&44'
! 72&'&gD&<#&M'"LCO&3'$K'$t4D3%"9'$K'G'%4'''AGGHRAG"("H''GOU'_#"&44'D3$D$35$";#&'4&E&<5$"H'
F$;EP'$0#2+*.(ET9NCD%EFPU''G#2&'&gD&<#&M'"LCO&3'$K'%"4#;"<&4'''''''$K'4<2&C;'M';#'5C&'#NOH'
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Why GAs work: the schema hypothesis
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E[m(s, t + 1)] =!(H, t)
!(t)m(H, t)
!
1 ! Pcrossover
d(H)
L ! 1
"
(1 ! Pmut)o(H)
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9/3*%3*,#%.$?52"+(%*"(;."/%(,?"/($<(,9'1,2,%("='1$./3$#*(A*3;,*1,'+6;*1"'6,*
Conclusions
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The Traveling Salesman Problem
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!
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References
! T%O&"a'!>';"M'0C%#2a'.>''P)3+(0/6#()*3(*Q.(-/#()'+8*R($"/#)?>'0D3%"9&3a'@SSQ>'
! F$EMO&39a'n;?%M>'H,),#6*2-?(+%3;$1*%)*7,'+6;J*!"#$%&'#()*')0*S'6;%),*@,'+)%)?>'!MM%4$"1r&4E&Ua'
=blb>'
! `$EE;"Ma'.$2">*20'"3'#()*%)*4'3/+,*')0*2+#56%'-*7813,$1>',"%?&34%#U'$K'6%<2%9;"':3&44a'=bQJ>'
! c$d;a'.$2">'H,),#6*<+(?+'$$%)?T*!)*3;,*"+(?+'$$%)?*(A*6($"/3,+1*=8*$,')1*(A*)'3/+'-*1,-,6#()>'
687':3&44a'=bb@>'
! 6%#<2&EEa'6&E;"%&>'2)*P)3+(0/6#()*3(*H,),#6*2-?(+%3;$1a'687':3&44a'=bbQ>'
! C0&M.,.&$.3(
• FT(()'G72&'F&"&5<';"M'T?$EL5$";3U'($CDL#;5$"'($"K&3&"<&H'
=NR=@R=S' T?$EL5$";3U'($CDL#;5$"''1''V''!>'($3"LWX$E4''' Bl'
