ΠΛΗ31 ΜΑΘΗΜΑ 4.2 (ΕΚΤΥΠΩΣΗ)

31
4:
4.2:
!" # $
% # & ' ( &
! " " # $
%
! & "
'
( )
* + , &
'
! ,- . )/0 1
' ,- !. )/0 1!
( ,- '. )/0 1'
2 #
! " #$ %& '
A. $
1. )$)#
1. * # #& &
! " #$ %& '
• ! * # #& * &, & + #
" f * , * ( &.
• # -# :
( ,
• " f (objective function)
• . , .* & & " &
( ( " / ") ( - " 0 .*
) & ( &:
• ) :
•
• . " 0 " . f . 0& 0&.
• . + 0& 0&, ( ) " #
, . 0& 0&.
• ) ,. + +# " :
• ( .& ) " # " 0 ( .
" ) . .* . 1/ " 0& )) & ) + #
" " * # &.
• + ) 0/ " :
• / .- " " " (2 " ) - #
& " &
• " & $& 0 /
,# & , & 0 . . *0 .
21
A. $
1. )$)#
1. * # #& &
! " #$ %& '
( (

A. $
2. .& ). & ) 0& !" # &.
(! " #$ %& '
. 2#& *# :
1. " " ( (Initialization)
2. 0 * :
1. / " " " (
2. .& 0 " " ( ( #& )#&)
3. ! " / $ " " ( ( #& + ( $ &)
4. # / $ " " ( ( #& 2 &)
$& . " ! "
# " $& ( / # " ) .
). ) ) # " # "
A. $
2. .& ). & ) 0& !" # &
)! " #$ %& '
• .& ). & ) 0& !" # & " , 2#&
+ . :
• 0 - 0 & . & ) $ $
* # .
• / +" + # $+
• . & ) ")/ " # *
+ + 3 - $ * .
• . & ) ) $+
$+ $ *
• . & " .& ") 0 & " & . &
+ - &.
• " . *# + " " + . . ). :
• )# ) 2 ) 0 " 0 .
• + ( $ ( ".
• 2 ) )# bit * "& "/ "& (&.
A. $
2. .& ). & ) 0& !" # &.
*! " #$ %& '
$ # %$ & % ' ( %&) ' * $&+# ' & #& $&+#,%&),
-'( $%,-,:
$ " &
( + & " # # %& # ,!
- # !
./.01234 56 & & 78 ' + 9
+ '
+ :
; " + < $ 7 = &
6 ! &9
A. $
2. .& ). & ) 0& !" # &
-1. % ( $ " ( * # & ) &
>! " #$ %& '
+ )
% + # " :
(
(
(
(
4 " !! ( !
, ( 0 . 0)
"#$%&'( )#' '*(+),&(-. /012*&,/,
(
3
,
. 0&
/ . +
" :
• -
• - )
• - &
• -

A. $
2. .& ). & ) 0& !" # &
0. $+ $ ( $ +" + . (
?! " #$ %& '
, " ! ! . . -
& + " # * + + 3 - , 0 $ q :
% + / ) * # x1,x2,…xn
• 5$ , " + 4 5 6 !78
+ #
• , " / 9 ) /( : :; <; 6 =>? @ AB; =
• # " / 9 bits.
!" & ( :
• 9 bits ( 1 * #
• . 9( bits ( 2 * #
• …
• . . .
A. $
2. .& ). & ) 0& !" # &
0. $+ $ ( $ +" + . (
@! " #$ %& '
+ )
! # " :
(
(
(
(
4 " !! ( !
6 0 + + 3 - .
!" & ) * # / :
!! 6 !7C
@ D E ! F G @ D E ! F HIJK @ HIJD E F HIJK @ 9 .
7 3 bits.
) * # ( / :
! 6 !7C @ D L ! F M @ D L ! F HIJ @ HIJD L F HIJ @ 9( .
7 2 bits.
!" . ( 5 bits. ( # & x1
+ ( * # x2
A. $
2. .& ). & ) 0& !" # &
0. $+ $ ( $ +" + . (
! " #$ %& '
+ )
! # " :
(
(
(
(
4 " !! ( !
$+ & ( & (6,2)
NO P Q NO P D 7!7
NO P D ! NO P ! 7!
7 ( $+ $& 01001.
$+ " + " & 01111
RSTN9 H 7!!
!!
DU !
M G
( ( RSTN9 H !!
!
D( !
! M
( (7,4)
). &) &,-,
$+ & #& &
* #& xi ) $& 2#&:
/ , +" + # " *
bin_stri, 0 :
NO P 4 6 4D V !55
). &) &,-,
$+ & +" + #&
" * & / + + #
# ) ( :
RSTN9 H4 NOWXYP 5
D V !
A. $
2. .& ). & ) 0& !" # &
1. /
! " #$ %& '
/
1 $ . " .& 0/ pop_size=4
) " 4 +" + 0& " * 0&
# "& 5 "/ . :
: 00110
: 11000
: 01101
: 11111
! *# & / &
+ " ) ( 0 "/ " .
. +" 0& ( &
# & $ "/ $ ( $ "
) pop_size ( &
" * # &
0) & " " ( 0
. + " ) ".

A. $
2. .& ). & ) 0& !" # &
2.1. 2 .)
! " #$ %& '
2 .)
: 00110
$+ … Z (5,3)
2 .) : (
(
(
( !Q
7 : SZ H Z !Q
: 11000
$+ …(10,1)
2 .) : (
(
(
(
[[
7 : SZ H Z( [[
: 01101
$+ …(7,2)
2 .) : (
(
(
(
7 : SZ H ZU
: 11111
$+ …(11,4)
2 .) : (
(
(
( !7
7 : SZ H Z] !7
2 .) ) +( *# .
1) $+ & ( &
/ + " : Z .
2) ( " ) , # &
#& " &: SZ H4Z 5.
A. $
2. .& ). & ) 0& !" # &
2.2. )#
! " #$ %& '
- )# & )#& + )
• $ 2 )# $ $ :
^ !Q [[ !7 DQ
• . )#& $ :
•
_àb4È5
c
d
( de
7f7Q7
• (
_àb4`L5
c
gg
( de
7fMG
• U
_àb4`h5
c
]e
( de
7f!G7
• ]
_àb4ì5
c
Ce
( de
7fM[Q
• # . $ :
• j 7f7Q7
• j( ( 7f M
• jU ( U 7fQ7
• j] ( U ] !f777
)# ) 0 + & :
A. $
2. .& ). & ) 0& !" # &
2.2. )#
(! " #$ %& '
)#: % + / . ) # "/ $ 0/ " :
• P 7f kl(mno. &n0 p
• P 7fK[ kl(mno. &n0 "
• P 7fG kl(mno. &n0 "
• P 7f7[ kl(mno. &n0 q
r*n/s*(1tu lm,+0/)tu %#1'( n 4p" " q5
3 #
"
<
7f7Q
7f M
7fQ7
!f7
7
A. $
2. .& ). & ) 0& !" # &
2.3. % ( $
)! " #$ %& '
% ! 8 9! 8 ! 8 – !
" * " ( 0/ 0) & 5.
+ " $ & n-1=4. 0 " 0
. 1/4=0.25.
!" & + /$ ( 0) "/ * "& "/ "& (&
0) &:
• 0 & 1-2 + [0.00, 0.25]
• 0 & 2-3 + (0.25, 0.50]
• 0 & 3-4 + (0.50, 0.75]
• 0 & 4-5 + (0.75, 1.00]
! "
+ ( $ " ) ( "

A. $
2. .& ). & ) 0& !" # &
2.3. % ( $
*! " #$ %& '
% ( $ ( pc=0.80)
• 0) " "/ "& (& . 0 & 1 ) 0 & " $ (
" ( ( ,%,%, ) 0 $ . & + . " "/ $
• 0.45 0.68 0.77 0.93 0.35 0.22
1 , () & ( ,%).
• "/ & .&: 0.45:pc. % " !
• "/ & .&: 0.68, 2( 0 $ 3-4.
• =011|01 ’=011|11
• =111|11 ’=111|01
2 , () & (%, ).
• "/ & .&: 0.77:pc. % " !
• "/ & .&: 0.93, 2( 0 $ 4-5.
• =1111|1 ’=1111|0
• =1100|0 ’=1100|1
A. $
2. .& ). & ) 0& !" # &
2.3. % ( $
>! " #$ %& '
% ( $ ( pc=0.80)
!" & " .& *# & + " $ & :
• ’=01111
• ’=11101
• ’=11110
• ’=11001
A. $
2. .& ). & ) 0& !" # &
2.4. 2
?! " #$ %& '
#
bit / $ & , "/ & .& " 0) "
. & . . 2 & pm.
% ( $ ( pc=0.30)
5 & 2#& " "/ $ : 0.77 0.23 0.09 0.93 0.28
0.22 0.15 0.82 0.34 0.32 0.44.
1 bit 2o bit 3 bit 4 bit 5 bit
0.77
0
0.23
1
0.09
1
0.93
1
0.28
1
0.22
1
0.15
1
0.82
1
0.34
0
0.32
1
0.44
1
0.77
1
0.23
1
0.09
1
0.93
0
0.28
1
0.22
1
0.15
0
0.82
0
0.34
1
’=01111 ’’=01011
’=11101 ’’=11101
’=11110 ’’=11100
’=11001 ’’=11001
A. $
2. .& ). & ) 0& !" # &
@! " #$ %& '
0 # 3 ) . ). ) * &
#& " &. 2 )# " " . " 0 "3 :
2 .)
: 01011
$+ … Z (6,4)
2 .) : (
(
(
(
D7
7 : SZ H Z D7
: 11101
$+ …(11,2)
2 .) : (
(
(
(
!!G
7 : SZ H Z( !!G
: 11100
$+ …(11,4)
2 .) : (
(
(
(
!7
7 : SZ H ZU !7
: 11001
$+ …(10,2)
2 .) : (
(
(
(
[Q
7 : SZ H Z] [Q

A. $
3. )# " ( ) "
! " #$ %& '
• %8,
• 0 $ 2 $ .
• / +. 0 $ ) .
! * * " ( " &) / " ) (
) ".
• *# & )#& + !
• *# & + ( $ & + - !
• *# & 2 & + !
+ ( 0 $ " + ) & " * * ".
A. $
3. )# " ( ) "
1. $+
! " #$ %& '
, " .
A. $
3. )# " ( ) "
1. $+
! " #$ %& '
, " .
A. $
3. )# " ( ) "
2. /
! " #$ %& '
, . . . bit

A. $
3. )# " ( ) "
3. 2 .)
(! " #$ %& '
, . " -'
A. $
3. )# " ( ) "
4. )#
)! " #$ %& '
, . - - $
A. $
3. )# " ( ) "
4. )#
*! " #$ %& '
, . - - $
A. $
3. )# " ( ) "
4. )#
>! " #$ %& '
, . - - $
& .& r = 0.513870 ) ( & " q10 . & " q11, ) ) .& " .
v11 0) ) v w 0 " .. + ( & .& r = 0.175741 ) ( &
" q3 . & " q4, . v4 0) ) 0 " .. !" / , & + .
" , " 0 " .:
! " # , 0 0 , - " / ( " ( " 0/ "
( ) - ) . ) .

A. $
3. )# " ( ) "
5. % ( $
?! " #$ %& '
$ - /,! .
! " %'/ & - $&+# - 0 pc
A. $
3. )# " ( ) "
5. % ( $
@! " #$ %& '
1 2 ! # (
! " ! .
A. $
3. )# " ( ) "
5. % ( $
! " #$ %& '
" . / $& 0/ " . ) .
A. $
3. )# " ( ) "
6. 2
! " #$ %& '
2 ) + . . bit 0) "/ & .&.
! + ) (" ) ) 2 . pm=0.01

. # &
%8/ -1
! " #$ %& '
% 2#& " .& ) 0:
=11011, =01011, =11001, %=10111
2#& # " ) 2 .) $ " " (:
NYOSXX x
! 4 !5yV3
D
]
zC
. " bi i- . +" + . 3 - ( +" + . 3 - 0/ + i=0).
&, + $ "/ $ " 0/ / / # & ) # &
"/ $ :
0.25, 0.73, 0.15, 0.52, 0.81, 0.65
$ # . :
1. . . / # )#& roulette wheel selection.
2. . 2 & 0.
3. H . + ( $ & 1.0.
4. )# $ . $ " " 0/ " + ( $ ) * # )#&
"& "/ "& (& " 0 "3 . ) # "/ $ . #& + ( $ &
( " + ( $ & 0) "/ 0
+ ( $ & / $ &. * "/ . + ( $ &
0) . & + 2 + . ) 0 (0.25 )
# 0 ). % +# "/ & .& 0.45 + ( $ &
+" + . 3 - 1 +" + . 3 - 2 ( . 3 - " * & 0/ . 0).
5. +( + " ( " . + ( $ ( "& ) & "&
" . & . & ) &.
* & $ " 0 & " ) . " :
. # &
%8/ -1
! " #$ %& '
) % ! 0.
.+ . " " " ( ) 0 :
f(11011) = 2
f(01011) = 1
f(11001) = 3
f(10111) = 4
b) % ! 0.
0 .+ " " ( ) 0 :
" # .+ ) ) 0 : 2+1+3+4 = 10, . 0 .+ & ) & 0
" . 4 10/4=2.5.
c) %
" " 0. ( 3
!
!.
" 0 " + " ) * .+ $
. $ + . . " /# , . "
( ) * 20%, + (
( ) 10%, ( ) 30% 0
(%) 40%.
. # &
%8/ -1
(! " #$ %& '
d) % " " 1.
" .& $ . $ ) 1 " ) , $& 2#&:
: . & )#& ) 0 & " " ( :
pA = 0.2, pB = 0.1, p = 0.3, p% = 0.4
8 ) , " & 0& . &. " 0& :
q = 0.2, q = 0.3, q = 0.6, q% = 1.0,
0) " " " . ( $ .) " .. " .
) / # $ $ $ "/ $ " & 0/ " + .
1 0/ " 0.2<0.25<0.30 . 0) , 0.6<0.73<1.0 .
0) %, 0.15<0.2 . 0) 0.3<0.52<0.6
. 0) . 7 $ .& " .& :
01011 ( ), 10111 (%), 11011 ( ), 11001 ( )
: +" , ") " 0 "3 ) + ( $ :
01011 ( ) 10111 (%)
11011 ( ) 11001 ( )
+# . + ( $ & 1.0 (100%) +" , ") + " $ ( /$ &
) 0 )/ & "/ .. 0 . + ( + ( $ &
(0 ) , ") ). 1 ) , ") + ( $ & ( / # "
0 " "/ " (
" 0.81 + $& + ( $ & " .
0 +" + . 3 - , . ( ) 3 " ) , ") . :
. # &
%8/ -1
)! " #$ %& '
1 ) , ") + ( $ & ( / # " 0 " "/ "
( " 0.81 + $& + ( $ & " .
0 +" + . 3 - , . ( ) 3 " ) , ") . . :
0101|1
1011|1
. " ) # ( | ) + + ( $ &. .) "
( " :
01011
10111
+ ( , ") , + ( $ & * / # " " "
"/ " ( (0.65) ( . 2( + ( " "
+" + ( 3 - ". 7 + ( , ") ) - :
110|11
110|01
.) " ( " :
11001
11011
: +# . 2 & 0 + ) 2 .
. , ( & " .& & ) & 1 . $& 0 "3 . & +"
+ " &:
=01011, =10111, =11001, %=11011

0 .+ " " ( ) 1
" # .+ ) ) 1 1+4+3+2 = 10, . 0 .+ &
) & 1 10/4=2.5.
. # &
%8/ -1
*! " #$ %& '
e) % ! 1.
.+ . " " " ( ) 1 :
f(01011) = 1
f(10111) = 4
f(11001) = 3
f(11011) = 2
f) % ! 1.
/ # .& ( ) " ( " ( " .* & ( &
" byte " 0/ & . & + &. 1 $ . " . . ()
0) . 2#& 4 :
=01101100
=10100010
=00110001
%=00111101
. " . / ( " 2 .) & " $
+" + 3 - $ . ":
x
{
z
. " bi i- +" + . 3 - " . " i 0& . 1 0$& 8.
1 $ . . . % 0 (roulette wheel selection),
# + ( $ & .& " ! " 0.8 # 2 &
0.2.
1 $, &, . + $ 4 - " 1 :
0.9501 0.2311 0.6068 0.7860 0.8913 0.7621 0.4565 0.0185 0.8214
0.4447 0.6154 0.7919 0.9218 0.7382 0.1763 0.4057 0.9355 0.9169
0.4103 0.8936 0.0579 0.3529 0.8132 0.0099 0.1389 0.2028 0.1987
0.6030 0.8381 0.0196 0.6813 0.3795 0.83180 0.5028 0.7095 0.4966
0.8998 0.8216 0.6449 0.2897
. # &
%8/ -3
>! " #$ %& '
$.%,# %
( 1 a) * " 2 .) & " 02 " (a) *
# 2 .) & . " & ) & 0, " # .+ & ) & 0
0 .+ & ) & 0.
( : .+ $ " " ( :
f(A) = 4
f(B) = 3
f( ) = 3
f(%) = 5
& ) & 0 4+3+3+5 = 15
15/4=3.75.
1 b) / # $ + 0 $ 3 "+.- "/ $ ( / ( . , #
/ ( . , . "& / 2 + . /#)
- )# $ )
• )#&,
• + ( $ &
• 2 &
* " " ( & . & ) & () 1). $ . - ( $
+ + & )#& ) . " ., + " +"
" 0 "3 . + + & )#&. & $ . #& 2 &
- ., # $ & + + & + ( $ & ) . " ..
. # &
%8/ -3
?! " #$ %& '
: - . " # #& ) #& )#& 0 " ) "
& " $ " 0 & . & $ . $ " " ( " " " 0 .
. & )#& ) 4 " " ( :
pA = 4/15 = 0.26667, p = 3/15 = 0.2, p = 3/15 = 0.2, p% = 5/15 = 0.33333
/ & " $ " 0 & . & :
q(A) = 0.26667, q( ) = 0.46667, q( ) = 0.66667, q(%) = 1.0
1/ & " ) & " $ " 0 & . & ( " / # " # &
#& ) #& )#& * + 0 " 3 "+. "/ $ (
* ( " / ( " ( " « " » $ . " ..
• / # " " 3 "+ "/ " ( 0.9591 & * + (0.6667,
1], 0) %.
• / # " + ( " 3 "+ "/ " ( 0.2311 & * + (0,
0.26667), 0) .
• / # " " 3 "+ "/ " ( 0.6068 & * + (0.4667,
0.66667), 0) .
• / # " 0 " 3 "+ "/ " ( 0.7860 & * +
(0.66667, 1.0), 0) %.
$ .& " .& " ( :
00111101 (%), 01101100 ( ), 00110001 ( ), 00111101 (%)
. # &
%8/ -3
@! " #$ %& '

:
1/ & + + )#&, (
/$ # " + + & + ( $ &. !( -$ - "
* # & + " +" " 0 "3 .
+ + & )#&.
• 1 , ") ) + ( $ . % & ) & 0.
2 , " " . , ") . $& + " $ ") & . ( 0 )
3 "+ "/ . 0.8913 . + ( $ & " 0.8. +#
3 "+ "/ & .& ) ( & & . & + ( $ & + 0/ "
+ ( $ , . +( " $ ( " ( 0 " $& 0/ " .
• + ( , ") , , . %. 2 , " +" "
+ " ") & . (0 ) 3 "+ "/ . 0.7621
. + ( $ & " 0.8. +# 3 "+ "/ & .& . &
) + ( $ , . 0 ) + ( $ &. " .
0) * . (0*+ ) 3 "+ "/ . " & 0.4565 ) ) .&
" + ) )# " " + ( $ & 2( 4 " 5 " +" + ( 3 - " $
. $ . !/ " . :
0011|0001
0011|1101
$ /# + ). "& 00111101 00110001.
. # &
%8/ -3
! " #$ %& '
# $ & + + & + ( $ & " .& " 0/ (3
0/ $& 2#&:
00111101 01101100 00111101 00110001
:
0 - #& 2 &. ) " .
/ ,. 4x8 = 32 3 "+ "/ "& (& / , & . 8 & + 0 &
" &. !" & 3 "+ "/ " / # " :
0.0185 0.8214 0.4447 0.6154 0.7919 0.9218 0.7382 0.1763
0.4057 0.9355 0.9169 0.4103 0.8936 0.0579 0.3529 0.8132
0.0099 0.1389 0.2028 0.1987 0.6030 0.8381 0.0196 0.6813
0.3795 0.8318 0.5028 0.7095 0.4966 0.8998 0.8216 0.6449
8 ) 0 " . " 0.2 " / ( bits:
00111101 01101100 00111101 00110001
0- :
10111100 01101000 11101101 00110001
. # &
%8/ -3
! " #$ %& '
1 c) * " 2 .) & * .+ $ . $ & ) & 1,
" # .+ & ) & 1 0 .+ & ) & 1. ()
/ 0 & ) & 0
.+ $ " " ( & ) & 1 :
f(A;) = 5
f(B;) = 3
f( ;) = 7
f(%;) = 3
. " # .+ & ) & 1 5+3+7+3 = 18 0 .+ "
" ( 18/4 = 4.5.
( , . , -# * $ . " #, . 0
.+ " " ( & ) & 1 /0 " . & ) & 0.
. # &
%8/ -3
! " #$ %& '
. # &
- )# 1
! " #$ %& '
:
2
1
2
221 ),( xxxxf x1 x2 [0, 7].
3 bits (23
= 8),
6 bits 3 x1 3 x2.
! ( 4 " # ).
-
-
(FITNESS)
101011
$ 111000
111011
% 101000
& 111001

(! " #$ %& '
( ) " ) .+ (Fitness) 0 "& " " ( ( ) 3 #
& $ ). +# . ( . ) 0/ 0& 0&, +
( " ) ( . & )#&.
& $ " . .* ; )# # &
" # # " $ , 0 . . .*
" / " ) . & . & )#& " 2 " . "; $&
$ ;
( ) " ) . )#& . ", / & )#
2 ) 0 & " 0 & ( ) 3 # & $ ).
)! " #$ %& '
( ) " ) . . ) -$ . " . ) (
) 3 # & $ ).
( ) 1 $ . 1 ) " ( - )# $ ) & )#&,
+ ( $ & 2 & " # " , .
1/ * $ 0 .+ " " ( ) 1 /0 ) 0; . 0/
* .+ " ( " 0 "& " " ( ) 1 /0 ) 0;
–
111 100
$ 110 110
111 000
% 110 011
& 111 011

ΠΛΗ31 ΜΑΘΗΜΑ 4.2 (ΕΚΤΥΠΩΣΗ)

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