Maintaining the Diversity of Genetic Programs

��

��

� ��

��

� �� !�� " �� #$%$�$ &'� !��

��

�� (�� $ )�� *�� (�� (� ��+ �� (�� $ ,� ��-�� (�� .'/$ ,� �� 0�� -�� $ ,� �� 1�� $

� ��

�� !�� "#$� % ��

&�� "#$ �� ' � �� &�� ' �� (�� %� � ��' ��

)� �� *�� +�� ",$� )� �� +�� +�� +�� -�� )� �� -� ��

�� -� �� +��

�� !�� . �� *� �� !�� , �� ' �� !�� / �� )� �� !�� # �� )� �� !�� 0 ��

� � ��

�� 1�� +�� Æ �� Æ�� ( ��

�� ' �� "22� 2/� 2#$� %�� "2/$ �� "22$�� ".$� �� "0� 2.$� 1�� -�� "2$ ��

)� �� *�� +�� 3 �� ",$� �� (

2� ��

.� &�� +��

,� �� +�� (

�� 4

�� 3

��

��

�� +�� 2 �� +�� +��

� 3 2� -� �� +�� +��

)� �� !�� /��

�� 5�� "0$ �� * �� 6 �� ' �� +�� * ��

� ��

% �� 6�� *�� +�� 6��

&�� "/$ ��

�� *�� +��

7�� "8$ �� 9�� :� ;�� "2<$�� ' � �� +�� - � �� 7��6�� "=$ ��

>�� "2,$ �� - � �� !�� +�� +��

7�� -�� "?$ �� +�� 1��

� ��

��

�� (

�� 4.

�� 2�

��

��

��

�� ( ��

%�� *�� )� �� ( �� 4 "�� < � � � �� 4 "��3�� 4 "<� �� )� �� *�� +�� % ��

� ��+�� 2 �� +�� @�� +�� 4 #��

��

�� 4�

��

��

�� (

�� 4.��

�� 2��

��

�� A � �� ' � ��

�� +�� ' ��

� ��

-� �� +�� "#$ �� !�� 0�� 6�� *�� (

� �� B ��

� ��

�� Æ �� +�� +�� (

� �� ' �� B

� ��

)��

)� �� #�� !�� 0�(

��

��

!�� )�� )� ��

� !��" #� �"� �� $��%�" #��

��%"��

)� �� =�� "�2� 2$ �� "�2� 2$ �� &�� #< �� "�2� 2$�� +�� +�� 2� !�� .� #� �� =� ��

� �� .�� / �� (� �� 1�� +�� -�� (�� 2�3 4 5$ 6� �7��

��

%(8�� 9�� 7�� .�� / ��

�� 7� �� (� � � .�� /6�� :� �� 6�� 2� �� 3 � 4 �5 �� 2�� 3�

;� �� 4 ��2�� : 5�'3;� �� 4 2��:5��3�2��5��32�� :5��32��5�<3;' �� 4 2��:5�=32��5�=32��5�&3�2��:5�"3

2�� : 5�'32�� : 5�>3�� 4 �5 �� 4 �5 ��

�� 0� ��

��+ -�� ?��-��

��

�

��

��22��3� ��3�� 2��3 (�� 1

� �� #�� ?� �55� �� (�(�� =5@# �(�(�� #�� )�� 5@�� ?� �5)�7�� (� �� 55 ��?�� !�� !��A�� 9��

)� �� &�� #< � �� <�<,# �� <�<2= �� 4 2< �� 4 <�2� &�� +�� - � �� )� �� &�� 2 ��

A�� <�<2 �� /8�� )�� +�� 4 <�#� �� <�, �� #?�� +��

�� (

2� �� @�� )��

�� 2�3 4 5 �� (�� ; � �� 5��5&� +�� (� �� 5�55=$

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100

Ave

rage

dis

tanc

e of

two

indi

vidu

als

Generation

Original GPFitness sharing, sigma=0.1Fitness sharing, sigma=0.5Fitness sharing, sigma=1.0

�� #�� -�� 2� 4�53 �� (�� ; �

��

.� )�� 4 <�2� �� <�2=� �� <�<2/� �� <�</. �� ##�� )�� Æ �� 4 2� �� 2�,� �� <�<0� �� <�8,? �� 2<<�� 4 <�#�� <�8==� �� <�<2/� �� <�0?. �� /.��

��

)� ��

!�� )� �� #�� C�� * � ��

�� 2� �� 2�

)� �� 2� � ��(

�� 4 ��

�� 4 ��

�� !�� # ��(

�� <�2�� 4 �

��

��

�� 2�� 4 � � ��

��

D�� +��

�� &�� .� �� (

� �� B

� �� B ��

�� &�� . �� &�� ,�= �� "2<$� ��

�� 6 �� . �� E�� #<� ��

& '��"� ��

)� �� +�� )� �� +��

0

0.5

1

1.5

2

0 20 40 60 80 100

Wei

ghte

d av

erag

e di

stan

ce o

f tw

o in

divi

dual

s

Generation

Original GPFitness sharing, sigma=0.5

Adaptive fitness sharing

�� #�� (�� ; �

�� 8�� ?�

B�� 5$&�5&�5 5$�<"''� 5$5&'�>5 5$5'>5�5 5$55=>&5 5$55�5<5 5$55�'"5 5$555>

�� "#$� A � ��

!�� (

� ��

� ��

�� +�� ;�� "2<$�

)� �� &�� +�� +��

#��

�$ ,$ ��?�� #$ C� �� $ 9$ �� 6$ A$ 6 ��

�� )� �� =="$�$ �$ ��(��D� �$ !� �E�� $ , �(�� - ��1� �� 1

�� !��

�� $� A$ #�� >>& �� !"�� $ &�F<=$ � �� 1G� ��2�=="3$

'$ �$ 9DE� � �� $ H$ CE�� -�� #$%& �'�(((� ��$� �$ #�� ,$ ��?�� ,$ �$ I�� J$ )�� #$ C� �� $ 6�� "5� �� !")*� $ ��=F�<5$ � �� 1G� ��2�5553$

>$ �$ 6�� +� � �� $ �$ � $ �=&�� 2�=="3$

�$ A$ 9$ B��(� �� *��+ &��,��+ �� -�� !��.

�� 1,�� ="=$&$ �$ �� $ �� K�� 1

�� -�� #))&.//� ��

�� # ��0 )�� )�� $� ,$ ��?�� J$ A��$ 9$ 9�(�� )$ !$ B� ?�� G$ !�� )$ J�D�� $ 9$ �� $ �5&�F�5&"� 2�===3$

<$ )�� 8?� � 9Æ�� $� #�� J$ �� 9$ ��1�� =F�<"� ) � # �� 2�==&3$

"$ �$ 9$ �� ,$ ��?�� 97�� A� �� 2�==>3$

=$ J�� $ ��?�� &� �� )�� 0 -��

�� "�� *�� ) � # �� ==�$�5$ ,�� $ I�� 1�� *�� .

�� 2 1�� *�� 3 �� 4� ��+� �� =="$��$ �$1L$ I� �� 1��1� �� ###

�� -�� 2�3� ��=F��>� 2�=<=3$��$ ��1)�� %M��

�� !�� 5�� //6 �� )��.

�� $� J�� $ ��?�� $ �==F�5&� 2�==<3$�'$ J$ #$ �� B�� 7�� +� �� 1

�� )�� # ��0 ��.

�� $ <�=F<'&� 2�==�3$�>$ �$ )$ ��D�+� �� 1��1� �� (�� !��

2&3� �">F�"&� 2�=<<3$��$ �$1�$ �� 1��1� �� (�� 7�� )-� �2'3� >��F

>''� 2�=<=3$

Maintaining the Diversity of Genetic Programs

Documents

Transcript of Maintaining the Diversity of Genetic Programs