Genetic Algorithms �Read Chapter �� �Exercises ���� ���� ���� ���� � Ev olutionary computation � Protot ypical GA � An example� GABIL � Genetic Programming � Individual learning and p opulation ev olution ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Ev oluationary Computation �� Computational pro cedures patterned after biological ev olution �� Searc h pro cedure that probabilisti cal l y applies searc h op erators to set of p oin ts in the searc h space ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Biological Ev olution Lamarc k and others� � Sp ecies �transm ute� o v er time Darwin and W allace� � Consisten t� heritable v ariation among individuals in p opulation � Natural selection of the �ttest Mendel and genetics� � A mec hanism for inheriting traits � genot yp e � phenot yp e mapping ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
GA � F m � itness� F itness thr eshol d� p� r � � � random h yp otheses Initialize� P p � for eac h in � compute itness � h � Evaluate� h P F � While �max itness � h �� F � F itness thr eshol d h �� Probabilistic al ly select �� � � p Sele ct� r mem b ers of to add to � P P S itness � h � F i Pr � h � � i p itness � h � F P �� j j r � p �� Probabilistic al l y select pairs of Cr ossover� � h yp otheses from � F or eac h pair� h h i � P � h � � pro duce t w o o�spring b y applying the Crosso v er op erator� Add all o�spring to � P s �� In v ert a randomly selected bit in Mutate� � random mem b ers of m p P s �� � Up date� P P s �� for eac h in � compute Evaluate� h P itness � h � F � Return the h yp othesis from that has the P highest �tness� ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Represen ting Hyp otheses Represen t � O � � ain � � � W � � utl ook O v er cast R ind S tr ong b y O utl ook W ind ��� �� Represen t IF � THEN � W ind S tr ong P l ay T ennis y es b y O utl ook W ind P l ay T ennis ��� �� �� ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Op erators for Genetic Algorithms Initial strings Crossover Mask Offspring Single-point crossover: 11101001000 11101010101 11111000000 00001010101 00001001000 Two-point crossover: 11101001000 11001011000 00111110000 00001010101 00101000101 Uniform crossover: 11101001000 10001000100 10011010011 00001010101 01101011001 Point mutation: 11101001000 11101011000 ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Selecting Most Fit Hyp otheses Fitness prop ortionate selection� itness � h � F i Pr� h � � i p itness � h � F P �� j j ��� can lead to cr owding T ournamen t selection� � Pic k at random with uniform prob� h � h � � � With probabilit y p � select the more �t� Rank selection� � Sort all h yp otheses b y �tness � Prob of selection is prop ortional to rank ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
GABIL �DeJong et al� ����� Learn disjunctiv e set of prop ositional rules� comp etitiv e with C��� Fitness� � itness � h � � � cor ect � h �� F r Represen tatio n� IF � � a � THEN � � IF � THEN � a T F c T a T c F � � � represen ted b y a a c a a c � � � � �� �� � �� �� � ��� Genetic op erators� � w an t v ariable length rule sets � w an t only w ell�formed bitstring h yp otheses ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Crosso v er with V ariable�Length Bit� strings Start with a a c a a c � � � � � �� �� � �� �� � h � � �� �� � �� �� � h � �� c ho ose crosso v er p oin ts for � e�g�� after bits �� � h � �� no w restrict p oin ts in to those that pro duce h � bitstrings with w ell�de�ned seman tics� e�g�� h � � � i � h � � � i � h � � � i � if w e c ho ose h � � � i � result is a a c � � � �� �� � h � a a c a a c a a c � � � � � � � �� �� � �� �� � �� �� � h � ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
GABIL Extensions Add new genetic op erators� also applied probabilistic al l y� �� lternative � generalize constrain t on b y A ddA a i c hanging a � to � �� opCondition � generalize constrain t on b y Dr a i c hanging ev ery � to � And� add new �eld to bitstring to determine whether to allo w these a a c a a c AA D C � � � � �� �� � �� �� � � � So no w the learning strategy also ev olv es� ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
GABIL Results P erformance of comparable to sym b olic GABIL rule�tree learning metho ds C��� � ID�R � A Q�� Av erage p erformance on a set of �� syn thetic problems� � without and op erators� ����� GABIL AA D C accuracy � GABIL with AA and D C op erators� ����� accuracy � sym b olic learning metho ds ranged from ���� to ���� ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Sc hemas Ho w to c haracterize ev olution of p opulation in GA� Sc hema � string con taining �� �� � ��don�t care�� � T ypical sc hema� ������ � Instances of ab o v e sc hema� ������� ������� ��� Characterize p opulation b y n um b er of instances represen ting eac h p ossible sc hema � m � s� t � � n um b er of instances of sc hema in s p op at time t ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Consider Just Selection � � � t � � a v erage �tness of p op� at time f t � m � s� t � � instances of sc hema in p op at time s t � u � s� � t � � a v e� �tness of instances of at time s t Probabilit y of selecting in one selection step h � h � f Pr � h � � n � h � f P i i �� � h � f � � � t � n f Probabilt y of selecting an instance of in one step s � h � f Pr � h � s � � X � � t � n f h � s � p t u � s� � t � � m � s� t � � � t � n f Exp ected n um b er of instances of after selections s n u � s� � t � � m � s� � ��� � m � s� t � E t � � t � f ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Sc hema Theorem � � s� t � d � s � u � � o � s � � m � s� t ���� � m � s� t � � � �� � p � E p B C � c m B C � t � � � f l � A � m � s� t � � instances of sc hema in p op at time s t � � � t � � a v erage �tness of p op� at time f t � u � s� � t � � a v e� �tness of instances of at time s t � � probabilit y of single p oin t crosso v er p c op erator � � probabilit y of m utation op erator p m � � length of single bit strings l � o � s � n um b er of de�ned �non ���� bits in s � d � s � � distance b et w een leftmost� righ tmost de�ned bits in s ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
Genetic Programming P opulation of programs represen ted b y trees r � sin � x � � � x y + sin + x y ^ 2 x ��� lecture slides for textb o ok Machine L e arning � T� Mitc hell� McGra w Hill� ����
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