This document describes the genetic algorithm process in 3 sentences: The genetic algorithm begins with an initial population of randomly generated solutions. It then iteratively applies genetic operators like selection, crossover and mutation to evolve the population toward better solutions, until a termination condition is reached. The fitness of each solution is evaluated at each generation to guide the selection of solutions to reproduce and create the next generation population.

1. 31
4:
4.1:
! "#
$ " %
! " #
! $
%
! & '
(
) $ *
+ , * &
( " - ' '
* . *
! '
!" " # $% &
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. " &! " ' ! ( #
!" " # $% &

2. A. "#
1. ! "#
2. " &! ) * ' ! ( #
" &! ) * ' ! ( # # 3 2 / ( *#
- " + ! "#
0 (" &! # TSP, SAT .!(.
0 " + (" &! # * # "
( "#(! ( 0! /+" , ( " , * # "
2 + .
# ( ! ! # ! & .
( 0
# ! ." 0"/
(" ( " . (".&! !
'!" " # $% &
A. "#
2. $ ! "#
(!" " # $% &
( ! # (. 2 & :
1. (! (Initialization)
2. ( 0! & :
1. / # (!
2. . 0 (! ( ! ( ! )
3. ! " / # (! ( ! * " )
4. # / # (! ( ! !! 2 )
. ( # !
A. "#
2. $ ! "#
1. "/ ( # (Initialization)
)!" " # $% &
" * $ " # 0! ' " /
( !0 0 ! 6 / # & " / .
$ :
" 0 " ( ("0( " :
• . # / # (! ( 0 (! # ".
& !#, pop_size)
• ( " # 0 / # ( ! ( ! #
( " ! * ( # ! )
* " + ,
-," " # #
#
, # #
$ %
A. "#
2. $ ! "#
1. "/ ( # ( " ! # * ( # )
.!" " # $% &
) " ! # + ! "# :
# "/ ! (/ "# * ( # ) !0 - . (
* ( # ! !0 . ( ( /" . )
bit . ( # 0 #* .
&
00010100010101
( " " )
(10,21)

3. A. "#
2. $ ! "#
1. "/ ( # ( * ( # )
/!" " # $% &
* ( # ! 2 " (. (".&! ( 0/
! .
) (" &! " & ! ( # ( !0
" ( ! ( "# (. # * *
& ! "
# (" &! * & ! ( # ("
" " .
(# * ( # ! ( " # 0/ &! .
( "# (" &! ! & "# )
A. "#
2. $ ! "#
1. "/ ( # (Initialization)
0!" " # $% &
" * $ " # 0! ' " /
1 . * ( # & " / # :
• =010111
• =110011
• =000101
• =111011
• =011100
• =001100
) / -+ *# * ( # !
$ %
A. "#
2. $ ! "#
2.1. 2 !. (Evaluation)
!" " # $% &
" * $ " # 0! ' " /
- "# " ( 2 ! # 0 & " / 0 " . (. 1-10,
2 ! & " / 2 / " . 1 . 2 !. & " / # ! :
$ :
" 0 " ( ("0( " :
• " # ( " " ( ( !!+ &! + ) (
2 ! # 0 " . / # . " !0
( )
8
4
9
2
6
1
* " + , 1 2 " -
% #& + & 3 &
1 "2 - + , "
, %& % #& + &
-," # 1 1 % # %
4 , # #
$
%
A. "#
2. $ ! "#
2.1. 2 !.
!" " # $% &
• " 2 !. ("0( # ( * ( "
( # ( #" " 0 0 (./ # *0 )
• "- :
, #
• 0/ (".&! " ( " ! /# )
( " "-+ 0 (".&! ( # ! :
• ’ ".( : # ( ! #, :
• 4( ! #,
• '’ ".( : # ( ! #,
• 4( ! #,
• . ( 0 . f ( #" .
• . * ( #" 0 0 , ( " (" 0
" , + ( #" . 0 0 .
• " ,. * ! * " :

4. A. "#
2. $ ! "#
2.2. ( !
!" " # $% &
" * $ " # 0! ' " /
1 . - " ., 2 0 " !0 (! . & " /
$ :
=>
" 0 " ( ("0( " :
• . / # ( !0 ( " &+ . . (! . )
• 0 * ( ! ((./. / # ( ! , 2 0 " !0 . .) ( ("0(
- ( " +" ( &# / # / ! & ! #
• ) *0/ ( ! / ( !!0 - "0 #*
( . ! (.* ( " ( ! 0/ # )
8
4
9
2
6
1
$
%
9 6 2 8 9 8
A. "#
2. $ ! "#
2.2. ( ! ( 0 * 2 0 !0 )
!" " # $% &
( !
• " 2 ! !+ :
• ( . ( ! !+ :
• !
"#$%&#'(
)
*
+,
- .
• !
"#$%&#/(
)
0
+,
-
• !+
"#$%&#1(
)
2
+,
-
• !0
"#$%&#3(
) +,
- .
• !4
"#$%&#1(
)
5
+,
-
• !5
"#$%&#3(
) +,
-
• " ( . !+ :
• 6 ! - .
• 6 ! ! -
• 6+ ! ! !+ -.
• 60 ! ! !+ !0 -..
• 64 ! ! !+ !0 !4 - .
• 65 ! ! !+ !0 !4 !5 -
# '
)
• " #, 2 !
!+ (! :
7 89:;&9<(
=>=?@ABC
DE
• ( . ( !
0! vi *# (. /0 :
!<
89:;&9<(
• 0! ( ! #,
" ( . :
6< 7 !F
A
FE
A. "#
2. $ ! "#
2.2. ( ! ( 0 * 2 0 !0 )
'!" " # $% &
( ! : $ * / (. " / #
" + 0/ :
• G -HH IJKLMNOPQMRPS
• G - IJKLMNOPQMRPI
• G -. IJKLMNOPQMRPT
• G - IJKLMNOPQMRPU
• G - IJKLMNOPQMRP S
• G - IJKLMNOPQMRPU
VWMXYWKZ[PJL]^RX_[P`aZbKPMP&SI T U SU(
( ! # 0 *
:
• pop_size - "0 ( !0 0
(" . " . r (. 0 + 1
• G c 6 ( !0 ("+
/" . .
• !! + ( !0 /" .
6< ( # / :
6<d e G c 6<
" " :
• 1 / # ( " # ( ! / # ( !!0
- "0 . . - # / # i
# !< f !g!?hij8
• (! . ( ( " ! #
"
/ 0
$
5
!
6
7
- .
- .
-
-.
-..
A. "#
2. $ ! "#
2.3. $ " (Crossover)
(!" " # $% &
" * $ " # 0! ' " /
# 2 * "+ (" 02 . 0 0! *0/ ( ! # ( !!0 - "0
$ ! " :
!
( )
" 0 " ( ("0( " :
• (! * "+ ( # ( + &
( ! 5 )
• 0! (! ( ! & 0! * "
• ".( ( # * " ( 0 * 1 # , 2 # .!(.)
4 1 -1"
2 " " , 2 &1
8 " 4 9
4 , # #
9 6 2 8 9 8 ’ $’
’ ’

5. A. "#
2. $ ! "#
2.3. $ " ( ) # )
)!" " # $% &
6" ( (" 2 * - " 0 * * " . (
/ # * " # . ) 0 * / "#,
* & ! "0 ( # ) 0 . # ( # * / " )
( " ( . 2 :
( ! # * / " # .!
( # * " . * ! 0 *
* " # .
'
’
'
$ "
) #
A. "#
2. $ ! "#
2.3. $ " ( 0 * ) # )
.!" " # $% &
$ " - " " #
& ! " ( ( " ! 0/
0 6.
( # * " # n-1=5.
0 0 # (#
( . 1/5=0.2.
) (+ # * / " ( !0
/ # & / # "
( !0 :
• 0 1-2 * [0.00, 0.20]
• 0 2-3 * (0.20, 0.40]
• 0 3-4 * (0.40, 0.60]
• 0 4-5 * (0.60, 0.80]
• 0 5-6 * (0.80, 1.00]
! " # ! (
" " # : 0 (# .!
* # * " .
• & ! " 0/ 0 n (n bits).
. ( # * " #
n-1.
• 2 1 2 0 .
• 2 2 3 0 .
• …
• 2 (n-1) n 0 .
• # (. ( " ( ( ! 0 #
(# ( . 1/(n-1)
• ( ! # * "
, # &
/ # " .
A. "#
2. $ ! "#
2.3. $ " ( 0 * ) # )
/!" " # $% &
$ " ( pc=0.60)
* " 2 ! # / #
" + (*#* (. -+ )
0.42 0.65 0.89 0.21 0.29
1 , ( , ).
• / # " . : 0.427pc. $ "+ !
• / # " . : 0.65, " 2 0 4-5.
• =0001|01 ’=0001|00
• =0111|00 ’=0111|01
2 , ($, ).
• / # " . : 0.89>pc. $ * "+ !
• # ( " (. (! .
/ "# * " :
• =111011 ’=111011
• =010111 ’=010111
3 , ( , ).
• / # " . : 0.217pc. $ "+ !
• / # " . : 0.29, " 2 0 2-3.
• =00|0101 ’=00|0111
• =01|0111 ’=01|0101
! " # ! (
- " * "
• 6 "#, (! . ,
( & " ( ! )
( . kl ( ! #
"
# # * (" &! )
• " & 0 / # " . r (.
0 + 1 r7pc .
, * "+
" " :
• pop_size:( " . ( !0
0 . (.
(" " . (! .
( ""#( 0 / #
( #" ( ! )
• pc=1 . ( !0 .!
/ # / "# " & 2
/ # "
4( "/ !! 0 * * " (.( (./ 0 *
* " * (! # )
0! ( "/ !! 0 * ( # 2 " + (. (".&!
((./ (".&! TSP ( "/ ! * " OX).
! ! (. .
A. "#
2. $ ! "#
2.3. $ " (8!! 0 * $ " )
0!" " # $% &
$ "
$ (!
) #
' '

6. A. "#
2. $ ! "#
2.4. !! 2 (Mutation)
!" " # $% &
" * $ " # 0! ' " /
) ( (. & " / !! + ( (. / " "
$ # :
"
" 0 " ( ("0( " :
• ".( ( ! / # (!
• ( . !! 2 ( / " " .
" %% :
%% 8 " + 2
# 1
, # #
2 "
:
4 ; 1 2
1% &
’ $’ ’ ’ ’ %’
’’ $’’ ’’ ’’ ’’ %’’
A. "#
2. $ ! "#
2.4. !! 2
!" " # $% &
#
0! (/" . ) - * 2 :
• bit ( #* ) (. " " (" * 2# :
• " & 0 / # " . r (. 0 + 1 r7pm . bit "0- .
• ) -+ *#* ! # / # " + (
/" ( .
" " :
• To pm ! # # # * (" &! .
• . (! / # (! ( ( ! !! 2 #
pop_size x m x pm
A. "#
2. $ ! "#
2.4. !! 2
!" " # $% &
" * ( . !! 2 pm=0.20
6" ( + 2 ! # / # " + : 0.77 0.23 0.12 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 6 bit
0.77
0
0.23
0
0.12
0
0.93
1
0.28
0
0.22
0
0.15
0
0.82
1
0.34
1
0.32
1
0.44
0
0.77
1
0.23
1
0.12
1
0.93
1
0.28
0
0.22
1
0.15
1
0.82
0
0.34
1
0.32
0
0.44
1
0.77
1
0.23
1
0.12
0
0.93
0
0.28
0
0.22
1
0.15
1
0.82
1
0.34
0
0.32
1
0.44
0
0.77
1
0.23
0
0.12
1
’=000100 ’’=001100
’=011101 B’’=111101
’=111011 ’’=101010
’=010111
’=000111
’=010101
’’=010111
’’=100101
’’=010100
A. "#
2. $ ! "#
2.4. !! 2
!" " # $% &
( 0! - " " + ! + # (. (! . )
(. ( ! 5 ( ! - # #* & * * # "0/ (! .:
’=000100 ’’=001100
’=011101 B’’=111101
’=111011 ’’=101010
’=010111
’=000111
’=010101
’’=010111
’’=100101
’’=010100
# ) ** +,- () .'/(,
=000101
=011100
=111011
=010111
=000101
=010111
-* ,0- 0 0- 1
=010111
=110011
=000101
=111011
=011100
=001100
=001100
B=111101
=101010
=010111
=100101
=010100

7. A. "#
2. $ ! "#
3. " " "
'!" " # $% &
" * $ " # 0! ' " /
(. 0 ! + 0/ &" # 0 " !. & " /
1 ) !:
# ! :
• $ .
• % .
.
• & ! (
– )
A. "#
2. $ ! "# .
(!" " # $% &
' # )' - ) . 0 )-1 . * '-2# .
" ' &
$ #" " # <
=>=?@ABC - " 1% D, & E
!m &
!n & " %% :
* $ & !" "8 D"1 % F"
% 2 E
A. "#
3. ) 5 . ! ."
1. 6 " "
)!" " # $% &
$ ! " 3 ( ( "
! & &! 0 ./ #* &! 0 (" &!
4 ./" ./ . 0
6" ( . #
( (". (! " - "#
6" ( " ! . & ./
"
A. "#
3. ) 5 . ! ."
2. ! + ! "#
.!" " # $% &
1. ( " ( ! * ! (" &! " " 2 .( .
2. ( " ! " ( "/ 0!
3. # ! ( 2 !#2 .
4. ( " 0/ &" * 0 "-0 !! .* .
5. - " ., ( ! ( " . " ( *# (. !! 0 * .
6. $ ( ( " " " ( ( 2 " , .
7. $ * -0" # (. 20 (! " - "# .
8. # # 0 * ( ./" 2 " /+"
, !! * ( 2 " 0 (! " - "# .
9. ( *0/ ( " !! ! ! ( # .

8. '.
- " 1
/!" " # $% &
$# .! (! . & ! "+ # / !! !. , 0:
6" . !! !.
A 011101 5
B 101001 1
C 111001 4
D 010000 2
E 011001 4
F 111101 4
" . :
1. . ! ." /" ( # ! ( ! ( & #, "
( ( !0 ! (.* ) ! # (! " .
( 0 0 * " - ( # (. ),
2. ( ! . ( 0/ * " # & ! ( ! / #
" ( (" 0 5 (. " / # " + . ! * " # #
( . * " 1.0, # * " ( !0 / # ,
3. ( . !! 2 # # 0,
4. * ( * ( (" ( (. # * " (" # (! . (. .
(# *# ( " !# / # " + ( 0/ ( " / # /" " / # " + : 0.12,
0.63, 0.20, 0.35, 0.48, 0.93, 0.51, 0.46, 0.28, 0.15, 0.52, 0.81, 0.65, 0.25, 0.73.
( ) " !0 ( ! . (. 0. - # ( . ( / #
"/ (! (" " . (! . .
( ) - " . * " , + (! ( (" 0 5 1.
0!" " # $% &
'.
- " 2
!" " # $% &
$# 2 (! . & ! "+ 0: A=11011, B=01011, C=11001, D=10111,
( " !! !. : f(A) = 2, f(B) = 1, f(C) = 3, f(D) = 4. (# *# ( " !# / #
" + ( 0/ ( " / # /" " / # " + :
0.25, 0.73, 0.15, 0.52, 0.81, 0.65, 0.15, 0.52, 0.81, 0.65, 0.25, 0.73, 0.15.
" . :
. . /" ( # ! ( ! ( & #, (.* "
. ( ( !0 ! (.* ) (! " .
( 0 0 * " - (. ).
( . !! 2 # # 0.
( ! . ( 0/ * " # & ! ( !
/ # " ( (" 0 5 (. " / # " + . ! * "
# # ( . * " 1.0, # * " ( !0 .
* ( * ( (" ( (. # * " (" # (! . (.
.
( ! # .! :
( ) " !0 ( /" ( # ( ! . (. 0. - #
" ( . ( / # "/ (! (" " .
(! ..
( ) (! . . 1.
!" " # $% &

9. '.
- " 3
!" " # $% &
( !02 / / 0 ( / ( .
( 1) /" + ! "# 0/ * * # 20! 2 ( - " .,
( 0 (! . /" ( # / # # , 0
0 /+" (. ( 0 ! . ( " # (" 9(. ( / 0 0 &
0 * * # , ( ! # 2 "".( * " . * * + .
# 0 ;
1. 2 !. .! ! .
2. !! * " ! " ! .
3. . * . ! " 2 " .! * .
4. 1 3.
5. 2 3.
( 2) # & * - " + ! "# ( ) /0 !! .*
, ;
1. # . 0 * ( 2 - !#, &0! ! .
2. 2 !# 0 (! . ! # !! .* ( ( 2 " ,
. 0 # /+" , .
3. # 0 * ( ! , .
4. 1 2.
5. 0 (. ( " ( .
!" " # $% &
( 3) $ 2 ( " # . ! * " .
! !! 2 * * # 20! 2 . (! ;
1. # * & # # ! 0 .
2. ' !! (! " - "# ( ( " .
3. ("+ 2 ( " # !! (! " - " + 2 ( + ! * "
2 ( " # 0 ( + ! .
4. 1 3.
5. 0 (. ( " ( .
( 4) & * . ! "# ( ! # (. ( " & :
1. "/ ( #
2. ( * ( #
3. 4( ! . . 2 !. .
4. ( "
1. ( !
2. $ "
3. !! 2
( ! 5 (. & (2) 0/" ( # " " " A
) 0 (!. . ! ." , ( ( (. & ( " # ( " ! - #;
1. & 1.
2. & 1 4. .
3. & 1 4. .
4. & 4. 4. .
5. 0 .