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Uploaded byDimitris Psounis
ΠΛΗ31 ΜΑΘΗΜΑ 4.3 (ΕΚΤΥΠΩΣΗ)
This document discusses genetic algorithms and provides examples of calculating fitness values and estimating the number of generations needed for a population to reach a target fitness level.
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ΠΛΗ31 ΜΑΘΗΜΑ 4.3 (ΕΚΤΥΠΩΣΗ)
- 1. 31 4: 4.3: ! " #$ % # ! "# $% & '! ( ) #! ) ! ( $% & * ( % % )% % & ! % ! + % & ! & ) , % & ! !! - ( . % / 0 ' & 1 $ ! "# $ % & A. 1. & & 1. & '# ( &)" # ! "# $ % & * + &)" S=11*10 , ( *% &( - & # {11010,11110} + &)" S=*1*1 , ( && # &( - & # {0101,0111,1101,1111} : .& + / - &( -' 0 ( ) & 0 '# ' # * 0 & ) & ( 0 (& %. . &)" S (" 0 ' (0 S) ) '& 0 ( ) & 0 * (* - , * / &% - ) 0 0 & & 0' 0 *"0 &% - ( / -" (. . & &)" 0 & '0 ' ) &' 0 ( 0 % 1 ( &)" & # * &% - 0 ( 0 % 0' / - . A. 1. & & 1. & '# ( &)" # ! "# $ % & * + &)" S=11*100**1 , ( 23=8 &( - & # + &)" S=********* , ( 29=512 &( - & # &)% ( ' ( & ' ( &)" #: .& ' ) ( 0 '- , 0 ( ) '& 0 & *( * " &( - & " (# n: • . &)" * 0 & &( - & • . &)" k * 0 & 2k &( - & # • . &)" 0 ( 0 ' 0' * 0 & 2n &( - & #
- 2. A. 1. & & 1.& '# ( &)" # '! "# $ % & * &( - & 101 , & 8 &)" : 101,10*, 1*1, *01, 1**, *0*, **1, *** +( - , ( c 0 ( / -" ( (c=|+| * *" 0 " # &( -' ( / -" (). .& ' ) ( 0 '- , 0 ( ) '& 0 & *( * " &( - & " (# n: • *( &)" 0 ( 0 % & ( & % (c+1)n • / % & 0 0 0 *"0 &% - ( / -" ( ) " * • &( - & , & 2n * / &)" . • / % &( - & , ' & &)" 0 ( & & ) & '# &( -' ( 0 0 ) " * &% - " * A. 1. & & 2. 1 & ' " # &)" # (! "# $ % & * &)" S=11***1 ) 1 3 & ' " # 6-1=5 &)" S=*0*111* ) 1 4 & ' " # 6-2=4 1 '# &)" # o(S): • '# & 0 1 • (* *" 0 " # & 0 ( * ) ( *) • &* , 0'& * ' &)" ( 1 => 1 * (& , " 1 => " 1 * (& &( - & ) & ' " # &)" # *(S): • 0'& & # 0 # # ( # & "# & # • ((0 , # * / # ( # & # 0 ( ) ( &% - 0 & 0 ( ) ( &% - ) • &* , 0( ' # 0 / # 0 ( 0 ) & &)" A. 1. & & 3. +( " & 0'* & (& % )! "# $ % & .& # ( 0 (& % (pop_size) f(v) " &( & '# % (: t ) " & " # & # ( (: • +( " 0'* & ( 0 (& % & ) " & " , # & ' 1 "& ( 0 (& %: • • & 0'* & ( 0 (& % & ) " & " , # &( " 0'* & 0 # # ( 0 (& % • A. 2. +)" & ( % ( 1. 0'* & &)" # *! "# $ % & + ) " & " ( 0 0 ' % ( ' () t ) ( pop_size (= ) ) & . • .& &)" S & ' p 0 " # ) & 0 ( , ( &)" S ) " & " t. , ( #: • eval(S,t) & 0'* & '# &)" # ) " & " t # • 0 ' & 0'* & ( &)" # & # ' # 0 *'& ) & 0 ( , ( &)" ) (& ) " & ". , ( 0 & # #: • 0 ' 0 "# # &( - & # 0 ( , & &)" S, #:
- 3. A. 2. +)" &( % ( 2. ! & & 0 & 0' (# %0 (# +! "# $ % & • , ( # 1(S,t) 0 " # ) & 0 ( , ( &)" S ) " & " t. • 0 * 1 ( ' 0 " # ) & 0 ( , ( &)" S ) " & " t+1 * 0' %0 : ! " # $ ! ! % & ' • 0 0 &) & & ( & & * # 0 * & 3 & . • ( & " 0 "# • ( & " * & % & # • ( & " 1 #. A. 2. +)" & ( % ( 3. ! * & # 0 "# ,! "# $ % & -" # 0 "# '# &( - & 0 ( , ( & &)" S 1(S,t+1). &)% ' : 1 ( )*+, - 0 ( 0 # ' : • & 0'* & &( - & ( &)" # • 1(S,t) 0 " # &( - & ( &)" # S • 2 ' (# 0'* & &( - & • F(t) &( " 0'* & ( 0 (& % • 2 * # F(t) 0 ( 0 ' 0 "# 0 ( (# ( &)" # • ( ( & / #, %0 # # * 0'& ) & 0 ) % 0' ( 0 ( , ( & &)" S. A. 2. +)" & ( % ( 3. ! * & # 0 "# ! "# $ % & A0 * % 0 & # ' : • 1 )*+, - ./ +( 0 # )*+, - ./ 0 121 0 * *" & 0'* & ( &)" # % 0' & 0'* & ( 0 (& %), ' (1 0 " # &( - & ( &)" # & 0' . 3 ' 0 " # &( - & ( &)" # & 0' . A. 2. +)" & ( % ( 3. ! * & # ! & % & # ! "# $ % & ' ( / % & " * * & # * & % & # % & ( & &( - & # 0 ( ) ( m bits & * 0 &" (#. , ( # 0 ' # 0 - & # & /"# '# &)" # # 1"#: ' & /"# +)" #: 45 6 47 8 6 9 ! : 30 (: pc 0 ' * & % & # *(S) & ' " # ( &)" #. ' 0 - & # +)" #: 46 6 : ! 45 6 : ! 47 8 6 9 ! : 30 (: pc 0 ' * & % & # *(S) & ' " # ( &)" #.
- 4. A. 2. +)" &( % ( 3. ! * & # ! & % & # ! "# $ % & 0' 0 0 0 * % ' ' # '# &( - & ( &)" # S * * & # * & % & # :: ; 6 < : 46 6 ! *" 0 0 & , ( ' 0 " # &( - & * * & # 0 "# 0 ' 0 - & # &( - & ( &)" #. & *% 0 0 &) & / : ; 6 < : : ! 47 8 6 9 ! : +( 0 # &)" ' & ' " # ( & ( ' ( (1 ( 0 " # &( - & (# ' ( '. A. 2. +)" & ( % ( 4. ! * & # 1 # ! "# $ % & 0 ' 0 - & # '# &)" # S * * & # 1 # : 46 6 : ! 49 = 6 > : ! = 6 49 30 (: pm 0 ' 1 # (S) 1 ( &)" #. +( 0 # &)% ' ' &( - & ( &)" # S 0' * * & # 1 # ' :: ; 6 < : ! " # $ ! ! ? @ 49 0' 0 0 %0 * % ' ( (& ') : +)" ( & ( ' ( 0'* & #, ' & ' " # " 1 - ( (1 ' # &( - & # & * * ) # # '# % (. A. 3. 0 & – 1 / & +) 1. & '# '! "# $ % & 0 %0 # * 0 " # &( - & &( - & 0 ( , ( & &)" S 0' #, / ', ' 0 " (') * & % & 1 ) ; 6 < A B C 30 ( 0 # ' 0' & # & # 0'* & # ( 0 (& % & &) & & 0'* & ( &)" # * 0' %0 : B ! 30 ( eval(S) & 0'* & ( &)" # & 0'* & ( 0 (& %. A. 3. 0 & – 1 / & +) 2. * (! "# $ % & 1: .& " &( & f, 0 ( ' * ) & * *( * " &( - & x, " # = 4, * 0 & 0 ( & % 0 ( 0 & 0' *( * ' ' x (0.). f(0011)=3, f(1111)=15 .). 1. & 0'* & ( &)" # S1=1**** , & &) & " &( & f; & 0'* & ( &)" # S2=0**** & &) & &( & f; (0 & ' 0 (& '# 0 16 ) & , * / ' *( * ' ' 0' 0000 # 1111 2. 0' *% &)" 0 "& & ' 0 (& ' 0' 0 # # 0 1 / & 0' 0 (& '; (0 & 0' 0'& # # &( - ( ', 0 0 & , "& ( 0 * & # * & % & # # 1 # .
- 5. )! "# $% & 1: + &)" S1=1*** , ( 0 &( - & #: 1000 eval(1000) = 8 1001 eval(1001) = 9 1010 eval(1010) = 10 1011 eval(1011) = 11 1100 eval(1100) = 12 1101 eval(1101) = 13 1110 eval(1110) = 14 1111 eval(1111) = 15 0 # & 0'* & ( &)" # S1 & % : 5.118/)15141312111098(SF 1 + &)" S2=0*** , ( 0 &( - & #: 0000 eval(0000) = 0 0001 eval(0001) = 1 0010 eval(0010) = 2 0011 eval(0011) = 3 0100 eval(0100) = 4 0101 eval(0101) = 5 0110 eval(0110) = 6 0111 eval(0111) = 7 0 # & 0'* & ( &)" # S2 & % : 5.38/)76543210(SF 2 A. 3. 0 & – 1 / & +) 2. * *! "# $ % & 2: &( " 0'* & ( 0 (& % : F=0+1+2+…+15=120 & 0'* & 7,5 2 , & 0'* & ( S1 53.33% % # & # 0'* & # ( 0 (& %, =0.53 ( S2, 53.33% ' , =0,53. 4 & 0 % 1 & & : 1(S, t+k) = 1(S, t)*(1+ )k t=0 ) ( 1(S1,0)=8, 0 0 (0 & ( : 1(S1, t+k) = 8*(1+ )k. ) =0.53 1(S, t+k)=16 ( S1, 0 "& & ' 0 (& ') ) ( : 16 = 8 *(1+0.53)k = 8 * 1.53k 2 = 1.53k & ( *% ) ( : log 2 = k * log (1.53) k = (0.301/0.185) k= 1.63. +( 0 #, 0' 2 # ( ' &)" S1 0 "& & 0 (& '. 5) = -0.53 1(S1, t+k) <1 ) ( : 1 > 8 *(1-0.53)k = 8 * (0.47)k & ( *% ) ( : 0 > log 8 + k * log (0.47) 0.903 +k (-0.327) < 0 (-0.327) k < -0.903 k > 2.73. 2 , 0' 3 # ( ' &)" S2 1 / & 0' 0 (& '. A. 3. 0 & – 1 / & +) 2. * +! "# $ % & 2: .& &)" S 0 ( 0 & 0 % , 0, & 60% '# 0 (& % (# n=100 ' # 0 ' # & /"# 0' * & % & 1 . (0 & 0' 0'& # # &)" S … (1) … 0 "& & ' 0 (& ' ( S ) ( ' 25% % 0' & ' ( ) 0 (& % : 4 & 0 % 1 & & : 1(S, t+k) = 1(S, t)*(1+ )k t=0 ) ( 1(S,0)=60, 0 0 (0 & ( : 1(S, t+k) = 60*(1+ )k. =0.25 1(S, t+k)=100 ) ( : 100 = 60 *(1+0.25)k = 60 * 1.25k 0 ( Log *% ) ( : Log 100 = Log 60 + k * Log (1.25) k=2.28, 0 ( & k=3. 2 , 0' 3 # &)" S 0 "& & 0 (& '. A. 3. 0 & – 1 / & +) 2. * ,! "# $ % & 3: .& &)" S 0 ( 0 & 0 % , 0, & 60% '# 0 (& % (# n=100 ' # 0 ' # & /"# 0' * & % & 1 . (0 & 0' 0'& # # &)" S … (2)… 1 / & 0' 0 (& ' ( S ) ( ' 10% ' 0' & ' ( ) 0 (& % : 4 & 0 % 1 & & : = -0.10 1(S, t+k) <1 ) ( : 1 > 60 *(1-0.10)k = 60 * 0.9k 0 ( Log *% ) ( : 1 > Log 60 + k * Log (0.9) k=38.8, 0 ( & k=39. 2 , 0' 39 # &)" S 1 / & 0' 0 (& '. A. 3. 0 & – 1 / & +) 2. *
- 6. 5. & "&# / " 1 "& # *( * # &( - & # 1=11101111, 2=00010100, 3=01000011 1 &)" : H1=1******* H2=0******* H3=******11 H4=***0*00* H5=1*****1* H6=1110**1* 1. # &( - & # , ( & &)" ; 2. 5 1 & ' " # &)" # 3. 60 & 0 ' 0 - & # &)" #, * & % & 0 ' * & % & # pc=0.85 4. 60 & 0 ' 0 - & # &)" #, 1 0 ' 1 # pm=0.001 ! "# $ % & 5. & "& # / " 2 ! "# $ % & .& ' 0 (& '# 0 ( * & 0 0 ) '# 0 (& '# '# % ( 0 ( ) & 0 & 0 & # &( & #: 2 1 2 221 ),( xxxxf '0 ( x1 x2 & * & [0, 7]. 0 & & 1 # - "# ) & 0 % 3 bits (2 3 = 8), 0' 0 & & ) & # ( 0 (& % ) & 0 % 6 bits 3 & 0 & % - " x1 3 * 1 - " x2. 0 "& & , " 0 ( ( % &( 0 & 0 ( # 0 1 # - 4 * * 7 / ). - - (FITNESS) 101011 5 111000 111011 ! 101000 111001 ! "# $ % & ( ) (5/15) ( 1) (3/5) (0 & 0'* & (Fitness) (# ( 0 (& % ( 7 0 &" & # & 0 0 0 ). 0 *" ' ( ' ) 0 ) # #, * 0 % (0 & % 0 ' # 0 "#. # 0 0 & ( ' 0 '- ; "& 0 &" & # &( 0 & " & " ( 0 0 , ' . 0 '- (0 ) (0 & ' # 0 ' # 0 "# ( 2 ( ' (; # 0 0 & ; ( 2) (2/5) (0 & 0 ' 0 "# ' (, ) & 0 # 0 " 1 & # ( # ( 7 0 &" & # & 0 0 0 ). ( ) (3/15) (0 & ' ' / ' ( & 0' ( 7 0 &" & # & 0 0 0 ). ! "# $ % & ( ) (7/15) .& ' 1 0 ( 0 %0 / " & # 0 "#, * & % & # 1 # ( " 0 ( 0 , & 0 . – 111 100 5 110 110 111 000 ! 110 011 111 011 ( 1) (2/7) .) - & 0'* & ( 0 (& % & 1 & &) & 0; '& ) - 0'* & ( % ( (# ( 0 (& % & 1 & &) & 0;
- 7. '! "# $% & ( 2) (5/7) # ' # '# ' , &% / &) (Schema Theorem), 0 ( & ) % & &)" S1=111*** & 2 "& ( ' / ', * & % & 0 ' Pc=0.5 1 0 ' Pm=0.1;