Ev oluationary Computation 1. Computational pro cedures patterned after biological ev olution 2. 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 169 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
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 170 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
GA ( F itness; F itness thr eshol d; p; r ; m ) � Initialize: P p random h yp otheses � Evaluate: for eac h h in P , compute F itness ( h ) � While [max F itness ( h )] < F itness thr eshol d h 1. Sele ct: Probabilistic al ly select (1 � r ) p mem b ers of P to add to P . S F itness ( h ) i Pr ( h ) = i P p F itness ( h ) j j =1 r � p 2. Cr ossover: Probabilistic al l y select pairs of 2 h yp otheses from P . F or eac h pair, h h ; h i , 1 2 pro duce t w o o�spring b y applying the Crosso v er op erator. Add all o�spring to P . s 3. Mutate: In v ert a randomly selected bit in m � p random mem b ers of P s 4. Up date: P P s 5. Evaluate: for eac h h in P , compute F itness ( h ) � Return the h yp othesis from P that has the highest �tness. 171 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
Represen ting Hyp otheses Represen t ( O utl ook = O v er cast _ R ain ) ^ ( W ind = S tr ong ) b y O utl ook W ind 011 10 Represen t IF W ind = S tr ong THEN P l ay T ennis = y es b y O utl ook W ind P l ay T ennis 111 10 10 172 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
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 173 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997 00001010101 01101011001 Point mutation: 11101001000 11101011000
Selecting Most Fit Hyp otheses Fitness prop ortionate selection: F itness ( h ) i Pr( h ) = i P p F itness ( h ) j j =1 ... can lead to cr owding T ournamen t selection: � Pic k h ; h at random with uniform prob. 1 2 � 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 174 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
Genetic Programming P opulation of programs represen ted b y trees r 2 sin ( x ) + x + y + sin + x y ^ 182 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997 2 x
Crosso v er + + sin ^ sin 2 + + x x ^ x y y 2 x + + sin ^ sin 2 ^ + x x 2 + x y 183 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997 x y
GP for Classifying Images [T eller and V eloso, 1997] Fitness: based on co v erage and accuracy Represen tatio n: � Primitiv es include Add, Sub, Mult, Div, Not, Max, Min, Read, W rite, If-Then-Else, Either, Pixel, Least, Most, Av e, V ariance, Di�erence, Mini, Library � Mini refers to a lo cal subroutine that is separately co-ev olv ed � Library refers to a global library subroutine (ev olv ed b y selecting the most useful minis) Genetic op erators: � Crosso v er, m utation � Create \mating p o ols" and use rank prop ortionate repro duction 188 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
Biolog i cal Ev olution Lamark (19th cen tury) � Believ ed individual genetic mak eup w as altered b y lifeti me exp erience � But curren t evidence con tradicts this view What is the impact of individual learning on p opulation ev olution? 189 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
Summary: Ev olutionary Program- ming � Conduct randomized, parallel, hill-cl i m bing searc h through H � Approac h learning as optimization problem (optimize �tness) � Nice feature: ev aluation of Fitness can b e v ery indirect { consider learning rule set for m ultistep decision making { no issue of assigning credit/blame to indiv. steps 193 lecture slides for textb o ok Machine L e arning , T. Mitc hell, McGra w Hill, 1997
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