0 X O W L G L V F L S O L Q D U \ 6 \ V W H P ' H V L J Q 2 S W L P L ] D W L R Q
* H Q H W L F $ O J R U L W K P V , ,
7 D E X 6 H D U F K
0 D U F K
/ H F W X U H
2 O L Y L H U G H : H F N
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
7 R G D \ ? V 7 R S L F V
? 0 R U H R Q ) L W Q H V V ) X Q F W L R Q $ V V L J Q P H Q W
? 0 X W D W L R Q
? & R Q V W U D L Q W L P S O H P H Q W D W L R Q L Q * $ V
? 0 X O W L R E M H F W L Y H R S W L P L ] D W L R Q Z L W K * $ V
? 7 D E X 6 H D U F K
? 6 H O H F W L R Q R I 2 S W L P L ] D W L R Q $ O J R U L W K P V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
) L W Q H V V ) X Q F W L R Q 0 D S S L Q J ,
? 2 E M H F W L Y H ) X Q F W L R Q P H D V X U H V K R Z L Q G L Y L G X D O V
S H U I R U P L Q W K H S U R E O H P G R P D L Q
? 5 D Z P H D V X U H R I I L W Q H V V X V X D O O \ R Q O \ X V H G D V
L Q W H U P H G L D W H V W D J H L Q G H W H U P L Q L Q J U H O D W L Y H
S H U I R U P D Q F H R I L Q G L Y L G X D O V L Q D * $
7 U D Q V I R U P R E M H F W L Y H I X Q F W L R Q Y D O X H L Q W R D P H D V X U H
R I U H O D W L Y H I L W Q H V V
I R E M H F W L Y H I X Q F W L R Q
()
= J I [ ) [
(
()
)
J W U D Q V I R U P D W L R Q
) U H O D W L Y H ) L W Q H V V !
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
) L W Q H V V ) X Q F W L R Q 0 D S S L Q J , ,
I ) 6
0 D S S L Q J D O Z D \ V Q H F H V V D U \ I R U P L Q L P L ] D W L R Q
V P D O O H U R E M H F W L Y H Y D O X H K L J K H U I L W Q H V V
2 I W H Q I L W Q H V V I X Q F W L R Q Y D O X H F R U U H V S R Q G V W R W K H Q X P E H U
R I R I I V S U L Q J Z K L F K D Q L Q G L Y L G X D O Z L O O O L N H O \ S U R G X F H
( J 3 U R S R U W L R Q D O I L W Q H V V D V V L J Q P H Q W
L
()
=
()
) [
L
1
L Q G
I [
()
) L W Q H V V R I L W K L Q G L Y L G X D O
|
I [
L
L Q G L Y L G X D O V U D Z S H U I R U P D Q F H U H O D W L Y H
L=
W R W K H Z K R O H S R S X O D W L R Q
1
L Q G 3 R S X O D W L R Q V L ] H
[
L
3 K H Q R W \ S L F Y D O X H R I 3 L ′
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
) L W Q H V V ) X Q F W L R Q 0 D S S L Q J , , ,
+ R Z W R D F F R X Q W I R U Q H J D W L Y H R E M H F W L Y H I X Q F W L R Q Y D O X H V "
/ L Q H D U W U D Q V I R U P D W L R Q Z L W K R I I V H W () ()
) [ D=+ I [ E
6 F D O H I D F W R U D ! I R U P D [ L P L ] L Q J D I R U P L Q L P L ] L Q J
2 I I V H W E H Q V X U H V Q R Q Q H J D W L Y H I L W Q H V V Y D O X H V
3 R Z H U O D Z V F D O L Q J
() ()
N
) [= I [
N H [ S R Q H Q W S R Z H U F D Q E H F K D Q J H G G X U L Q J H [ H F X W L R Q
7 X Q L Q J . Q R E 3 6 3 ′ V H O H F W L Y H S U H V V X U H
G H J U H H R I E L D V W R Z D U G V W R Z D U G V I L W W H V W
[ S R V L W L R Q R I L W K
L
L
) [
()
=? 6 3 +
(
6 3 ?
)
1
[
L Q G
?
?
L Q G L Y L G X D O L Q R U G H U H G
L
S R S X O D W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 X W D W L R Q ,
Q R W R R O L W W O H P X W D W L R Q O H D G V W R D Q L P S R Y H U L V K H G
J H Q H W L F S R R O Z L W K L Q F U H D V L Q J Q X P E H U R I J H Q H U D W L R Q V
G L O H P P D
7 R R P X F K P X W D W L R Q G H F U H D V H V F R Q Y H U J H Q F H U D W H
D Q G X Q G H U P L Q H V I L W Q H V V E D V H G V H O H F W L R Q E L D V
: K D W L V P X W D W L R Q " ? D J H Q H W L F R S H U D W R U
? 0 R G L I L H V F K U R P R V R P H V W R U H V W R U H G L Y H U V L W ? 3 H U P L W U D Q G R P F K D Q J H V L Q D P H P E H U R I D S R S X O D W L R Q
( [ D P S O H V
Z L W K S U R E D E L O L W \ U D Q G R P O \ I O L S D V L Q J O H E L W R I
D V R O X W L R Q I U R P W R R U W R
S U R E D E L O L W \ R I P X W D W L R Q R I W H Q F D O O H G 3 P X W D W L R Q U D W H ′
H [ S U H V V L Q J W K H S U R E D E L O L W \ 3
P
W K D W D E L W L V F K D Q J H G
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
( [ D P S O H Z L W K 0 X W D W L R Q
, P S U R Y H G S R S X O D W L R Q I L W Q H V V Z L W K P X W D W L R Q U D W H
2 U L J L Q D O J H Q
W K J H Q
W K J H Q
?
?
?
$ Y J ) L W Q H V V
$ Y J ) L W Q H V V
$ Y J ) L W Q H V V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
( [ D P S O H Z L W K R X W 0 X W D W L R Q
6 W D J Q D Q W S R S X O D W L R Q Z L W K P X W D W L R Q U D W H
2 U L J L Q D O J H Q
W K J H Q
W K J H Q
1 R 3 ′
?
? ? & D Q
1 H Y H U
$ F K L H Y H
$ Y J ) L W Q H V V
$ Y J ) L W Q H V V
$ Y J ) L W Q H V V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 X W D W L R Q , ,
( [ D P S O H
% H I R U H P X W D W L R Q
$ I W H U P X W D W L R Q
? 0 X W D W L R Q U D W H F D Q E H
Y D U L D E O H X V X D O O \ J U D G X D O O G H F U H D V L Q J Z L W K L Q F U H D V L Q J
Q X P E H U R I J H Q H U D W L R Q V
? 0 X W D W L R Q U D W H L V D Q L P S R U W D Q W 0 X W D W L R Q U D W H
3 W X Q L Q J N Q R E ′ I R U D * $
? W R R K L J K
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
* $ & R Q Y H U J H Q F H
J O R E D O
7 \ S L F D O 5 H V X O W V
R S W L P X P
J H Q H U D W L R Q
X Q N Q R Z Q
$ Y H U D J H
) L W Q H V V
& R Q Y H U J H G W R R
I D V W P X W D W L R Q U D W H
W R R V P D O O "
$ Y H U D J H S H U I R U P D Q F H R I L Q G L Y L G X D O V L Q D
S R S X O D W L R Q L V H [ S H F W H G W R L Q F U H D V H D V J R R G L Q G L Y L G X D O V
D U H S U H V H U Y H G D Q G E U H G D Q G O H V V I L W L Q G L Y L G X D O V G L H R X W
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
& R Q V W U D L Q W V L Q * $
( V V H Q W L D O O \ W K U H H R S W L R Q V
? , P S O H P H Q W L P S O L F L W H O \ L Q F R G L Q J G H F R G L Q J V F K H P H
? 3 H Q D O L ] H R E M H F W L Y H I X Q F W L R Q I R U F R Q V W U D L Q W Y L R O D W L R Q
? 6 H O H F W L R Q R S H U D W R U R Q O \ V H O H F W Y D O L G V R O X W L R Q V I R U P D W L Q J
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
( Q F R G L Q J ' H F R G L Q J 6 F K H P H
; L G H V L J Q Y D U L D E O H
5 D G L X V J H Q R W \ S H
[
5 D G L X V 5 > P @
( Q V X U H W K D W R Q O \ 3 P D [ L P X P ′ D Q G
3 P L Q L P X P ′ Y D U L D E O H Y D O X H V D U H
F D S W X U H G E \ F R G L Q J V F K H P H
( J
: R U N V Z H O O I R U L P S O H P H Q W L Q J
P P L Q
E R X Q G V [
L / %
[
L
[
L 8 %
P P D [
E X W Q R W J H Q H U D O F R Q V W U D L Q W V
V X F K D V J [ K [
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
3 H Q D O W \ $ S S U R D F K ,
8 V X D O O \ V R P H F D O F X O D W L R Q L V Q H F H V V D U \ W R Y H U L I \ L I
D F R Q V W U D L Q W L V P H W R U Q R W H J V W U H V V H V S R Z H U R X W S X W
6 R O X W L R Q 3 H Q D O L ] H W K H I L W Q H V V R I V R O X W L R Q V W K D W Y L R O D W H F R Q V W U D L Q W V
Y D O L G
] R Q H
] R Q H ] R Q H
3
S H Q D O W L Q Y D O L G L Q Y D O L G
()
= ) [? 3 [ 6 [
L
() ()
L L
) L [ H G 3 H Q D O W \ I R U & R Q V W U D L Q W 9 L R O D W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
3 H Q D O W \ $ S S U R D F K , ,
) L [ H G S H Q D O W \ S U R Y L G H V Q R U D Q N L Q J R I W K H G H J U H H
R I F R Q V W U D L Q W Y L R O D W L R Q L Q W U R G X F H Y D U L D E O H S H Q D O W \
S H Q D O W S H Q D O W 3
3
Y D O L G
Y D O L G
] R Q H
] R Q H
L Q Y D O L G L Q Y D O L G
L Q Y D O L G L Q Y D O L G
] R Q H ] R Q H
] R Q H ] R Q H
/ L Q H D U Y D U L D W L R Q 6 W H S S H G S H Q D O W 2 W K H U V F K H P H V S R O \ Q R P L D O H [ S R Q H Q W L D O F O R V H W R 6 $
, P S R U W D Q W Z K H Q F R Q V W U D L Q W V D U H K D U G W R P H H W
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
3 U R E O H P V Z L W K S H Q D O W \
? : K D W L V W K H U L J K W 3 E D O D Q F H ′ E H W Z H H Q R E M H F W L Y H I X Q F W L R Q
D Q G S H Q D O W \ F R Q V W U D L Q W V "
? 8 V X D O O \ U H T X L U H V V R P H D P R X Q W R I W U L D O D Q G H U U R U W X Q L Q J
? 8 V X D O O \ D P R X Q W R I S H Q D O W \ Y D U L H V G X U L Q J R S W L P L ] D W L R Q
? , Q W L D O O \ V P D O O S H Q D O W \ O D U J H V H D U F K V S D F H
? / D W H O D U J H S H Q D O W \ I R F X V R Q J R R G I H D V L E O H V R O X W L R Q V
? % X W D O V R R S S R U W X Q L W \ $ O O R Z V I R U U H O D W L Y H Z H L J W K L Q J R I
F R Q V W U D L Q W V F U D V K Z R U W K L Q H V V Y V I X H O H F R Q R P \
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
6 H O H F W L R Q 2 S H U D W R U
6 H W W L Q J W K H ) L W Q H V V R I D Q \ R I D Q \ L Q Y D O L G
V R O X W L R Q W R ] H U R H Q V X U H V W K D W R Q O \ Y D O L G
V R O X W L R Q V D U H F R Q V L G H U H G V H O H F W L R Q
* H Q H U D W L R Q Q
U D Q N H G
1
1
* H Q H U D W L R Q Q
( O L P L Q D W H G
G X H W R S R R U
P D W H
( O L P L Q D W H G G X H W R
I L U W Q H V V
F R Q V W U D L Q W Y L R O D W L R Q
& D X W L R Q & D Q H O L P L Q D W H Y D O X D E O H V R O X W L R Q V I U R P J H Q H S R R O
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
2 S H U D W R U V * H Q H U D O 5 H P D U N V
? S R L Q W F U R V V R Y H U L V R Q H R I P D Q \ D O W H U Q D W L Y H V
? * R D O R I F U R V V R Y H U 7 D N H W Z R S D U H Q W V R O X W L R Q V
D Q G F U H D W H W Z R F K L O G U H Q V R O X W L R Q V
? 0 X W D W L R Q V ) O L S S L Q J E L W V L V R Q H R I P D Q \ R S W L R Q V
? & D Q W D N H D Q \ Q H L J K E R U K R R G R S H U D W R U D V L Q
6 L P X O D W H G $ Q Q H D O L Q J R U 7 D E X 6 H D U F K
? , Q V W H D G R I G R L Q J U D Q G R P S R S X O D W L R Q
L Q L W L D O L ] D W L R Q V W D U W Z L W K D 3 I L W ′ L Q L W L D O S R S X O D W L R Q
? 6 H H G L Q L W L D O S R S X O D W L R Q Z L W K L Q G L Y L G X D O V N Q R Z Q
W R E H L Q W K H Y L F L Q L W \ R I W K H J O R E D O R S W L P X P
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
3 D U D O O H O * $ ? V
* $ ? V D U H Y H U \ D P H Q L D E O H W R S D U D O O H O L ] D W L R Q
0 R W L Y D W L R Q V I D V W H U F R P S X W D W L R Q S D U D O O H O & 3 8 ? V
D W W D F N O D U J H U S U R E O H P V
L Q W U R G X F H V W U X F W X U H D Q G J H R J U D S K L F O R F D W L R Q
7 K H U H D U H W K U H H F O D V V H V R I S D U D O O H O * $ ? V
? * O R E D O * $ ? V
? 0 L J U D W L R Q * $ ? V
? ' L I I X V L R Q * $ ? V
0 D L Q G L I I H U H Q F H V O L H L Q
S R S X O D W L R Q V W U X F W X U H
P H W K R G R I V H O H F W L Q J L Q G L Y L G X D O V I R U U H S U R G X F W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
* O R E D O * $
$ V V L J Q ) L W Q H V V
: R U N H U
& U R V V R Y H U
0 X W D W L R Q
: R U N H U
& U R V V R Y H U
0 X W D W L R Q
: R U N H U 1
& U R V V R Y H U
0 X W D W L R Q
3 S D Q P L [ L D ′
* $ ) D U P H U
6 H O H F W L R Q
) X Q F W L R Q H Y D O X D W L R Q ) X Q F W L R Q H Y D O X D W L R Q ) X Q F W L R Q H Y D O X D W L R Q
? * $ ) D U P H U Q R G H L Q L W L D O L ] H V D Q G K R O G V H Q W L U H S R S X O D W L R Q
? , Q W H U H V W L Q J Z K H Q R E M H F W L Y H I X Q F W L R Q H Y D O X D W L R Q H [ S H Q V L Y H
? 7 \ S L F D O O \ L P S O H P H Q W H G D V D P D V W H U V O D Y H D O J R U L W K P
? % D O D Q F H V H U L D O S D U D O O H O W D V N V W R P L Q L P L ] H E R W W O H Q H F N V
? , V V X H R I V \ Q F K U R Q R X V D V \ Q F K U R Q R X V R S H U D W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 L J U D W L R Q * $
3 S R O \ W \ S L F ′
* $
* $
* $
* $
* $
' R H V 1 2 7 R S H U D W H
J O R E D O O \ R Q D V L Q J O H
S R S X O D W L R Q
( D F K Q R G H U H S U H V H Q W V
D V X E J U R X S U H O D W L Y H O L V R O D W H G I U R P H D F K R W K H U
3 E U H H G L Q J J U R X S V ′ G H P H V
-- Each node (Gai)
WHILE not finished
0 R U H F O R V H O \ P L P L F V
SEQ
… Selection
E L R O R J L F D O P H W D S K R U
… Reproduction
… Evaluation
) L U V W L Q W U R G X F H G E \ * U R V V R
PAR
L Q
… send emigrants
… receive immigrants
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
' L I I X V L R Q * $ ? V
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
-- Each Node (Ii,j)
WHILE not finished
SEQ
… Evaluate
PAR
… send self to neighbors
… receive neighbors
… select mate
… reproduce
1 H L J K E R U K R R G F H O O X O D U
7 R U R L G D O 0 H V K S D U D O O H O S U R F H V V L Q J Q H W Z R U N
R U I L Q H J U D L Q H G * $
? 3 R S X O D W L R Q L V D V L Q J O H F R Q W L Q X R X V V W U X F W X U H E X W
? ( D F K L Q G L Y L G X D O L V D V V L J Q H G D J H R J U D S K L F O R F D W L R Q
? % U H H G L Q J R Q O \ D O O R Z H G Z L W K L Q D V P D O O O R F D O Q H L J K E R U K R R G
? ( [ D P S O H , R Q O \ E U H H G V Z L W K , , , ,
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 X O W L R E M H F W L Y H * $ ? V
? 0 D Q \ H Q J L Q H H U L Q J G H V L J Q S U R E O H P V K D Y H P X O W L S O H
R E M H F W L Y H V R I W H Q F R P S H W L Q J
? ( [ D P S O H 0 D [ L P L ] H U D Q J H P L Q L P L ] H I X H O X V D J H
P D [ L P L ] H F U X L V H V S H H G P D [ L P L ] H S D V V H Q J H U Y R O X P H
* $ ? V D U H D P H Q L D E O H W R P X O W L R E M H F W L Y H S U R E O H P V
7 \ S L F D O O \ * $ ? V D U H X V H G V L P L O D U W R W U D G L W L R Q D O 2 S W L P L ] H U V
D Q G P X O W L S O H R E M H F W L Y H V D U H V F D O D U L ] H G
- M W K R E M H F W L Y H Y D O X H
Q
]
-
M
M
Z
M
Z H L J K W R I M W K R E M H F W L Y H
-
L
=
|
Z
M
M=
Q
M
Q M W K R E M H F W L Y H Q R U P D O L ] D W L R Q
M
* $ ? V F D Q Q D W X U D O O \ G H D O Z L W K P X O W L S O H R E M H F W L Y H V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
/
L
I
H
F
F
O
H
&
R
V W
E
L
O
O
L
R
Q
V
3 D U H W R 2 S W L P D O L W \ 5 D Q N L Q J
6 L P S O H 3 D U H W R 5 D Q N L Q J 6 F K H P H V
& R P S O L F D W H G 0 D W L Q J 5 H V W U L F W L R Q V
0 X O W L 2 E M H F W L Y H , O O X V W U D W L R Q
3 D U H W R R S W L P D O % H V W L Q
L
L
L
L
' H V
' H V J Q
' H V J Q
' H V J Q
%
%
%
%
%
D W U D G H R I I V H Q V H
J Q
$ Q L P S U R Y H P H Q W L Q R Q H
R E M H F W L Y H F D Q R Q O \ E H
D F K L H Y H G D W W K H H [ S H Q V H R I
' H V L J Q
D W O H D V W R Q H R W K H U R E M H F W L Y H
3 H U I R U P D Q F H W R W D O L P D J H V
: K L F K G H V L J Q V D U H S D U H W R R S W L P D O " P L Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
3 D U H W R ) L W Q H V V 5 D Q N L Q J
2
0
0
f
2
f
1
0
0
0
4
1
Pareto Ranking For A Minimization Problem
? 3 D U H W R U D Q N L Q J V F K H P H
? $ O O R Z V U D Q N L Q J R I S R S X O D W L R Q
Z L W K R X W D V V L J Q L Q J S U H I H U H Q F H V
R U Z H L J K W V W R L Q G L Y L G X D O
R E M H F W L Y H V
? 6 X F F H V V L Y H U D Q N L Q J D Q G
U H P R Y D O V F K H P H
? ' H F L G L Q J R Q I L W Q H V V R I
G R P L Q D W H G V R O X W L R Q V L V P R U H
G L I I L F X O W
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 X O W L R E M H F W L Y H * $
Goldberg, David E. Genetic Algorithms in Search,
Optimization, and Machine Learning.
Addison-Wesley Professional, January 1, 1989. ISBN: 0201157675.
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
( [ D P S O H
0 L Q L P L ] D W L R Q
(
a
Q
§
o
I [ [
Q
)
=? H [ S
?
?
|
¨
[ ?
·
?
?
2 E M H F W L Y H
?
L= ?
L
Q
1
?
? ?
(
a
Q
§
o
I [ [
Q
)
=? H [ S
?
?
|
¨
[ +
·
?
?
2 E M H F W L Y H
?
L= ?
L
Q
1
?
? ?
1 H H G W R W K L Q N D E R X W P D W L Q J U H V W U L F W L R Q V L Q P X O W L R E M * $
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
Images removed due to copyright considerations.
* R R G 1 H Z V D E R X W * $ ? V
? * $ Z R U N Z H O O R Q P L [ H G
G L V F U H W H F R Q W L Q X R X V
S U R E O H P V
? * $ ? V U H T X L U H O L W W O H
L Q I R U P D W L R Q D E R X W
S U R E O H P
? * $ ? V D U H Y H U \ U R E X V W
? * $ ? V D U H V W R F K D V W L F
W K D W L V W K H \ H [ S O R L W
U D Q G R P Q H V V
? * $ ? V F D Q E H H D V L O S D U D O O H O L ] H G
? 1 R J U D G L H Q W V U H T X L U H G
? 6 L P S O H W R X Q G H U V W D Q G
D Q G V H W X S D Q G
L P S O H P H Q W
? & D Q R S H U D W H R Q Y D U L R X V
U H S U H V H Q W D W L R Q V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
% D G 1 H Z V D E R X W * $ ? V
? * $ L P S O H P H Q W D W L R Q L V
V W L O O D Q D U W D Q G U H T X L U H V
V R P H H [ S H U L H Q F H
? & R Q Y H U J H Q F H E H K D Y L R U
Y H U \ G H S H Q G H Q W R Q
V R P H W X Q L Q J
S D U D P H W H U V P X W D W L R Q
U D W H F U R V V R Y H U
S R S X O D W L R Q V L ] H
? ' H V L J Q L Q J I L W Q H V V
I X Q F W L R Q F D Q E H W U L F N ? & X P E H U V R P H W R W D N H
L Q W R D F F R X Q W F R Q V W U D L Q W V
? * $ ? V F D Q E H
F R P S X W D W L R Q D O O H [ S H Q V L Y H
? 1 R F O H D U W H U P L Q D W L R Q
F U L W H U L D
? 1 R N Q R Z O H G J H R I W U X H
J O R E D O R S W L P X P
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
) U H T X H Q W $ S S O L F D W L R Q V R I * $ ? V
? 6 F K H G X O L Q J D Q G 3 O D Q Q L Q J $ V V \ 6 H T X H Q F L Q J
? 3 D F N L Q J ' D Q G '
? 7 U D Y H O 3 D W K 3 O D Q Q L Q J 7 U D M H F W R U \ 2 S W L P L ] D W L R Q
? 3 D U D P H W H U 6 H O H F W L R Q I R U & X U Y H ) L W W L Q J
? & D W D O R J 6 H D U F K
? 6 W U X F W X U D O 7 R S R O R J \ 2 S W L P L ] D W L R Q
? 0 X O W L G L V F L S O L Q D U \ ' H V L J Q 2 S W L P L ] D W L R Q 0 ' 2
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
0 $ 7 / $ % * $ 7 R R O E R [
? & D Q L P S O H P H Q W * $ ? V G L U H F W O \ L Q 0 $ 7 / $ %
? 1 R W R I I L F L D O O \ S D U W R I 2 S W L P L ] D W L R Q 7 R R O E R [
? % X W K D Y H X V H U F R Q W U L E X W H G W R R O E R [ L Q * $ 7 R R O E R [
7 K H
P D L Q J H Q H W L F D O J R U L W K P 0 I L O H L V J H Q H W L F P
GENETIC tries to maximize a function using a simple genetic algorithm.
X=GENETIC('FUN',X0,OPTIONS,VLB,VUB) uses a simple (haploid)
genetic algorithm to find a maximum of the fitness function
FUN (usually an M-file: FUN.M).
' H P R X V L Q J D V L P S O H I X Q F W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
* $ L Q L 6 , * + 7
? * $ L V D Y D L O D E O H L Q L 6 , * + 7
? $ O J R U L W K P W X Q L Q J S D U D P H W H U V F D Q E H V H W
? ' H P R Q V W U D W L R Q X V L Q J W K H ) H Q F H H [ D P S O H
? V H H ) U L G D \ O D E V H V V L R Q
& R P S D U H E H K D Y L R U R I J U D G L H Q W V H D U F K W H F K Q L T X H
Y H U V X V J H Q H W L F D O J R U L W K P V $
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
7 D E X 6 H D U F K 7 6
? $ W W U L E X W H G W R * O R Y H U
? 6 H D U F K E \ D Y R L G L Q J S R L Q W V L Q W K H G H V L J Q V S D F H W K D W Z H U H
S U H Y L R X V O \ Y L V L W H G 3 W D E X ′
? $ F F H S W D Q H Z 3 S R R U H U ′ V R O X W L R Q L I L W D Y R L G V D V R O X W L R Q W K D W
Z D V D O U H D G \ L Q Y H V W L J D W H G
? , Q W H Q W $ Y R L G O R F D O P L Q L P D
? 5 H F R U G D O O S U H Y L R X V P R Y H V L Q D 3 U X Q Q L Q J O L V W ′ P H P R U \
? 5 H F R U G U H F H Q W Q R Z I R U E L G G H Q P R Y H V L Q D 3 W D E X ′ O L V W
? ) L U V W 3 G L Y H U V L I L F D W L R Q ′ W K H Q 3 L Q W H Q V L I L F D W L R Q ′
? $ S S O L H G W R F R P E L Q D W R U L D O R S W L P L ] D W L R Q S U R E O H P V
? * O R Y H U ) D Q G / D J X Q D 0 7 D E X 6 H D U F K L Q 0 R G H U Q
+ H X U L V W L F 7 H F K Q L T X H V I R U & R P E L Q D W R U L D O 3 U R E O H P V & 5
5 H H Y H V H G L W R U - R K Q : L O H \ 6 R Q V , Q F
? Z Z Z W D E X V H D U F K Q H W
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
7 D E X 6 H D U F K P L Q L P L ] D W L R Q
Given a feasible solution x* with objective
function value J*, let x := x* with J(x) = J*.
Iteration:
while stopping criterion is not fulfilled do
begin
? select best admissible move that transforms x
into x' with objective function value J(x')
and add its attributes to the running list
(2) perform tabu list management: compute moves
(or attributes) to be set tabu, i.e., update
the tabu list
(3) perform exchanges: x := x', J(x) = J(x'); if
J(x) < J* then J* := J(x), x* := x
endif
endwhile
Result: x* is the best of all determined
solutions, with objective function value J*.
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
7 D E X 6 H D U F K ' H P R
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
6 H O H F W L R Q R I $ O J R U L W K P V
? / L Q H D U L W \ D Q G V P R R W K Q H V V R I - [ D Q G R U R I
W K H F R Q V W U D L Q W V J [ K [
? 7 \ S H R I G H V L J Q Y D U L D E O H V [ U H D O L Q W H J H U ?
? 1 X P E H U R I G H V L J Q Y D U L D E O H V Q
? ( [ S H Q V H R I H Y D O X D W L Q J - [ ± > & 3 8 ) O R S V @
? ( [ S H Q V H R I H Y D O X D W L Q J J U D G L H Q W R I - [
? 1 X P E H U R I R E M H F W L Y H V ]
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
1 R Q O L Q H D U L W \
& U X P S O H G 3 D S H U $ Q D O R J \ W R 6 K R Z 1 R Q O L Q H D U L W \
8 V H D V K H H W R I S D S H U W R U H S U H V H Q W W K H U H V S R Q V H V X U I D F H R I
- I [
[
, I W K H S D S H U L V F R P S O H W H O \ 3 I O D W ′ Z L W K R U Z L W K R X W V O R S H W K H Q L V D / L Q H D U ) X Q F W L R Q Z K L F K F D Q E H U H S U H V H Q W H G D V
\ F F
[
F
[
, I W K H S D S H U L V W Z L V W H G V O L J K W O \ Z L W K V R P H F X U Y D W X U H W K H Q L W E H F R P H V
D Q R Q O L Q H D U I X Q F W L R Q / R Z Q R Q O L Q H D U L W \ O L N H W K L V P D \ E H D S S U R [ L P D W H G
E \ D 4 X D G U D W L F I X Q F W L R Q O L N H
\ F F
[
F
[
F
[
F
[
F
[
[
& U X P S O H W K H S D S H U D Q G V O L J K W O \ I O D W W H Q L W W K H Q L W E H F R P H V D 3 Y H U \ Q R Q O L Q H D U ′
I X Q F W L R Q 2 E V H U Y H W K H L U U H J X O D U W H U U D L Q D Q G G H W H U P L Q H Z K H W K H U L W L V S R V V L E O H W R
D S S U R [ L P D W H W K H L U U H J X O D U W H U U D L Q E \ D V L P S O H T X D G U D W L F I X Q F W L R Q
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
$ O J R U L W K P 6 H O H F W L R Q 0 D W U L [
/ L Q H D U 1 R Q O L Q H D U
- D Q G J D Q G K - R U J R U K
& R Q W L Q X R X V U H D O 6 L P S O H [ 6 4 3
[ D O O % D U U L H U 0 H W K R G V
F R Q V W U D L Q H G
1 H Z W R Q
X Q F R Q V W U D L Q H G
' L V F U H W H 0 , / 3 * $
[ D W O H D V W R Q H % U D Q F K D Q G 6 $ 7 D E X 6 H D U F K
% R X Q G
3 6 2
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
Copyright ? 2002-2005, GE Company
Practical Engineering Optimization, Aero Engg. M.I.T., Boston, Mass. Hauhua.Lee@ge.com 3/13/2002 p.2
Hybrid Optimization Algorithms:
Use a Combination of “Clubs” to Search Optimum to Leverage the
Strength of Individual Club.
I
r
o
n
C
lu
b
s
W
o
o
d
C
lu
b
s
Heuristics-Based:
Rules-Guided Search
P
u
t
t
e
r
Stochastic-Based:
Simulated Annealing,
Genetic Algorithms.
Gradient-Based:
SLP, SQP, MMFD, Conjugate Gradient,
Exterior Penalty,...
Golf Clubs Analogy
Courtesy of Howard Lee, General Electric. Used with permission.
Copyright ? 2002-2005, GE Company
Practical Engineering Optimization, Aero Engg. M.I.T., Boston, Mass. Hauhua.Lee@ge.com 3/13/2002 p.1
More Computers
+ Hybrid
Optim
.
Utopia
Practical Optimization Strategy
? Obtain Near Optimum ASAP.
(Assess Uncertainty Margin By Sound
Engineering Judgement)
? Then Search for Possible Alternative
Optimum if Time/Resource Permits.
Practical Optimization Strategy
? Obtain Near Optimum ASAP.
(Assess Uncertainty Margin By Sound
Engineering Judgement)
? Then Search for Possible Alternative
Optimum if Time/Resource Permits.
Hybrid Optim.
Genetic Algorithms
Manual Based
Gradient Based
DOE Based
Time (hours, days, weeks)
Design Performance
Optimum
(Analytical
vs. True)
Near
Optimum
(Fidelity: Low / High / True? )
Fidelity
Limits
Hyb
rid
Op
tim
izat
ion
Alg
orit
hm
sA
llow
to F
ind
Bet
ter
Des
igns
in L
essT
ime
.
Practical Optimization Strategy
Courtesy of Howard Lee, General Electric. Used with permission.
L 6 , * + 7 2 S W L P L ] D W L R Q 3 O D Q $ G Y L V R U
5 D Q N L Q J
R I
D O J R U L W K P V
D F F R U G L Q J
W R W K H L U
V X L W D E L O L W W R W K H
3 U R E O H P
D W K D Q G
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
6 X P P D U \
? * U D G L H Q W 6 H D U F K 7 H F K Q L T X H V
± ( I I L F L H Q W U H S H D W D E O H X V H J U D G L H Q W L Q I R U P D W L R Q
± : H O O V X L W H G I R U Q R Q O L Q H D U F R Q W L Q X R X V Y D U L D E O H V
± & D Q H D V L O \ J H W W U D S S H G D W O R F D O R S W L P D
? + H X U L V W L F 7 H F K Q L T X H V
± 8 V H G I R U F R P E L Q D W R U L D O D Q G G L V F U H W H Y D U L D E O H S U R E O H P V
± 8 V H E R W K D U X O H V H W D Q G U D Q G R P Q H V V
± G R Q ? W X V H J U D G L H Q W L Q I R U P D W L R Q V H D U F K E U R D G O ± $ Y R L G O R F D O R S W L P D E X W D U H H [ S H Q V L Y H
? + \ E U L G $ S S U R D F K H V
± 8 V H H I I H F W L Y H F R P E L Q D W L R Q V R I V H D U F K D O J R U L W K P V
? 0 D V V D F K X V H W W V , Q V W L W X W H R I 7 H F K Q R O R J \ 3 U R I G H : H F N D Q G 3 U R I : L O O F R [
( Q J L Q H H U L Q J 6 \ V W H P V ' L Y L V L R Q D Q G ' H S W R I $ H U R Q D X W L F V D Q G $ V W U R Q D X W L F V
| 课件名称： | 麻省理工学院：Multidisciplinary System |
| 课件分类： | 航空航天 |
| 课件类型： | 教学课件 |
| 文件大小： | 13.87MB |
| 下载次数： | 0 |
| 评论次数： | 0 |
| 用户评分： | 0 |
- 1. 麻省理工学院：Multidisciplinary System：l10a_sa
- 2. 麻省理工学院：Multidisciplinary System：l10b_sa
- 3. 麻省理工学院：Multidisciplinary System：l12_ga2_020705
- 4. 麻省理工学院：Multidisciplinary System：l13_msdo_pso
- 5. 麻省理工学院：Multidisciplinary System：l15_gpiso
- 6. 麻省理工学院：Multidisciplinary System：l16_moo1
- 7. 麻省理工学院：Multidisciplinary System：l18_dso
- 8. 麻省理工学院：Multidisciplinary System：l19_approx
- 9. 麻省理工学院：Multidisciplinary System：l20_gmfenyes_1
- 10. 麻省理工学院：Multidisciplinary System：l20_gmfenyes_2
- 11. 麻省理工学院：Multidisciplinary System：l20_gmfenyes_3
- 12. 麻省理工学院：Multidisciplinary System：l21_robustdesign