Evolving Crossover¸ Mutation and Training rates in a Population of

 ! ! "# $ % & '
( )
* + $ +
$ & ,-. -./ 0 ,. +$ .,/ +
$ 1 ,,, ,2 3
4 5 6 % )
7 & 1 0
! 8 0
" 0
. 1 0
9 " #$%# &'
# $ !# "#
0 0 .# 3
6 6
6
& 9 - 2# 6
:
; ' ( 3
+ < ,#
% 1 $ : $ % $ 6 3
$ =
$ 1 6 '
( 3
> * 0
!6 , #-.#+#%$ %#
##+%
3
+
$ .,, .,, ?
* 3 5 ; ,, ,
; 3 5 * ,. ,
3 5 * ,. ,, 3
, ,! 0.75
0.7
0.65
0.6
Fitness
( %)%$ $)# *+$%
0.55
0.5
0.45
0.00 Crossover
0.25 Crossover
0.50 Crossover
0.75 Crossover
1.00 Crossover
0.4
0.35
0
50
100
150
200
250
300
Generations
350
400
450
500
5 +
$ '( & ? + % ,. 6
, ,-. ,. ,-. +
$ ," +
& 6 %
,,/ @ ,,/
0
$ A ,, $ B
,, % / #0$%1 %#
##+%
0.7
0.65
Fitness
0.6
0.55
0.5
0.45
0.4
0.00 Mutation
0.02 Mutation
0.04 Mutation
0.06 Mutation
0.35
0
50
100
150
200
250
300
350
400
450
500
Generations
,,, ,, ,, ,,"
,( 1
0.9
Fitness
0.8
0.7
0.6
0.5
0.4
0 Training Cycles
50 Training Cycles
100 Training Cycles
0.3
0
10
20
30
40
50
60
70
80
90
100
Generations
& ! % A % .,
$ ,< !, ,, % $ 9, = -. ., % ., % & $ , 6 ,, 96 + + 3
+$ & $ 3 )
C & C .,,
& & D '
( 0
$ /! #2
.,, !6 ,,
,. ,, , 3
, ,". 6 :
+ A
8
A
,,. & 1
<, ,, .
,, 6 ,," 0.68
0.66
0.64
Crossover Rate
0.62
0.6
0.58
0.56
0.54
/, # 0.52
0.5
0.48
10
20
30
40
50
Generations
60
70
80
90
45
/" # " ,"2 :
,99 B
,.25,.< $ 5 % ' ,. ,-.( /( # + 0.5
0.45
0.4
Mutation Rate
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
50
100
40
50
60
70
80
90
100
Generations
1 . $ Training Rate
0
40
35
30
25
0
10
20
30
40
50
Generations
60
70
80
90
100
0
+ 9 - % $ ,<. , )
$ // .
#
& - " ,9 . ,, ,,
#)###*
1
0.9
Fitness
0.8
0.7
0.6
0.5
Determined Rates
Evolved Rates
0.4
0
10
20
30
40
50
Generations
60
70
80
90
100
',.<( ',, .( ." E ,, , B ,, 6 3 $*
+
: % 1 %'&$# #+#*
% >
*
0
3 ! " # $
% &#
'()*'+,-' %
..+
/ 0 1& 2% 3 3 " $
&#* 4 & $
2 ! 5 %
% 6 " ','+7 $8% & % ../
9 1 5 "% %* %
2 !
"#
-9,
-9' ../
+ % ## : $
% &# "$
7(9,+)*.',/;. ..'
' 8 " % 2 ! % 1 6 %& ! " %$
9-7,9<+
= ..' 2 - >? 5 @ $
2 ' ( $
$))*)*)& '
+& 342 !&% /;;/
7 >? > @$
2 A& B 5 %
"
,$- . /, )**01 4% >: 4 0
/;;9
< >? @ $
# = 2 %
)**0 $
" / "$ 2*01
22 --',--< 5 B 3 4" /;;9
. A 0 &# & % 2 "# 3 345$
364 ..;
; ! 6 " 4 A $
&# 2 %
" 7
97.,9<+ .<.