Genetic Algorithms [Read Chapter 9] [Exercises 9.1, 9.2, 9.3, 9.4] Ev olutionary computation Protot ypical GA An example: GABIL Genetic Programming Individual learning and p opulation ev olution
Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 7Selecting Most Fit Hyp
theses
Fitness prop
rtionate
selection: Pr(h i ) = F itness(h i ) P p j =1 F itness(h j ) ... can lead to cr
wding
T
urnamen
t selection:
Pic
k h 1 ; h 2 at random with uniform prob.
With
probabilit y p, select the more t. Rank selection:
Sort
all h yp
theses
b y tness
Prob
f
selection is prop
rtional
to rank 174 lecture slides for textb
k
Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 8GABIL [DeJong et al. 1993] Learn disjunctiv e set
f
prop
sitional
rules, comp etitiv e with C4.5 Fitness: F itness(h) = (cor r ect(h)) 2 Represen tatio n: IF a 1 = T ^a 2 = F THEN c = T ; IF a 2 = T THEN c = F represen ted b y a 1 a 2 c a 1 a 2 c 10 01 1 11 10 Genetic
p
erators: ???
w
an t v ariable length rule sets
w
an t
nly
w ell-formed bitstring h yp
theses
175 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 9Crosso v er with V ariable-Length Bit- strings Start with a 1 a 2 c a 1 a 2 c h 1 : 10 01 1 11 10 h 2 : 01 11 10 01 1. c ho
se
crosso v er p
in
ts for h 1 , e.g., after bits 1, 8 2. no w restrict p
in
ts in h 2 to those that pro duce bitstrings with w ell-dened seman tics, e.g., h1; 3i, h1; 8i, h6; 8i. if w e c ho
se
h1; 3i, result is a 1 a 2 c h 3 : 11 10 a 1 a 2 c a 1 a 2 c a 1 a 2 c h 4 : 00 01 1 11 11 10 01 176 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 10GABIL Extensions Add new genetic
p
erators, also applied probabilistic al l y: 1. A ddA lternative: generalize constrain t
n
a i b y c hanging a to 1 2. Dr
pCondition:
generalize constrain t
n
a i b y c hanging ev ery to 1 And, add new eld to bitstring to determine whether to allo w these a 1 a 2 c a 1 a 2 c AA D C 01 11 10 01 1 So no w the learning strategy also ev
lv
es! 177 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 11GABIL Results P erformance
f
GABIL comparable to sym b
lic
rule/tree learning metho ds C4.5, ID5R, A Q14 Av erage p erformance
n
a set
f
12 syn thetic problems:
GABIL
without AA and D C
p
erators: 92.1% accuracy
GABIL
with AA and D C
p
erators: 95.2% accuracy
sym
b
lic
learning metho ds ranged from 91.2 to 96.6 178 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 12Sc hemas Ho w to c haracterize ev
lution
f
p
pulation
in GA? Sc hema = string con taining 0, 1, * (\don't care")
T
ypical sc hema: 10**0*
Instances
f
ab
v
e sc hema: 101101, 100000, ... Characterize p
pulation
b y n um b er
f
instances represen ting eac h p
ssible
sc hema
m(s;
t) = n um b er
f
instances
f
sc hema s in p
p
at time t 179 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 13Consider Just Selection
f
(t) = a v erage tness
f
p
p.
at time t
m(s;
t) = instances
f
sc hema s in p
p
at time t
^
u(s; t) = a v e. tness
f
instances
f
s at time t Probabilit y
f
selecting h in
ne
selection step Pr (h) = f (h) P n i=1 f (h i ) = f (h) n
f
(t) Probabilt y
f
selecting an instance
f
s in
ne
step Pr (h 2 s) = X h2s\p t f (h) n
f
(t) = ^ u(s; t) n
f
(t) m(s; t) Exp ected n um b er
f
instances
f
s after n selections E [m(s; t + 1)] = ^ u(s; t)
f
(t) m(s; t) 180 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 14Sc hema Theorem E [m(s; t+1)]
^
u (s; t)
f
(t) m(s; t) B B @ 1
p
c d(s) l
1
1 C C A (1p m )
(s)
m(s;
t) = instances
f
sc hema s in p
p
at time t
f
(t) = a v erage tness
f
p
p.
at time t
^
u(s; t) = a v e. tness
f
instances
f
s at time t
p
c = probabilit y
f
single p
in
t crosso v er
p
erator
p
m = probabilit y
f
m utation
p
erator
l
= length
f
single bit strings
(s)
n um b er
f
dened (non \*") bits in s
d(s)
= distance b et w een leftmost, righ tmost dened bits in s 181 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 15Genetic Programming P
pulation
f
programs represen ted b y trees sin (x) + r x 2 + y
^ sin x y 2 + x +
182 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 16Crosso v er
^ sin x y 2 + x + ^ sin x y 2 + x + sin x y + x + ^ sin x y 2 + x + ^ 2
183 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 17Blo c k Problem
u i v a n e r s l
Goal: sp ell UNIVERSAL T erminals:
CS
(\curren t stac k") = name
f
the top blo c k
n
stac k,
r
F .
TB
(\top correct blo c k") = name
f
topmost correct blo c k
n
stac k
NN
(\next necessary") = name
f
the next blo c k needed ab
v
e TB in the stac k 184 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 18Primitiv e functions:
(MS
x): (\mo v e to stac k"), if blo c k x is
n
the table, mo v es x to the top
f
the stac k and returns the v alue T . Otherwise, do es nothing and returns the v alue F .
(MT
x): (\mo v e to table"), if blo c k x is somewhere in the stac k, mo v es the blo c k at the top
f
the stac k to the table and returns the v alue T . Otherwise, returns F .
(EQ
x y ): (\equal"), returns T if x equals y , and returns F
therwise.
(NOT
x): returns T if x = F , else returns F
(DU
x y ): (\do un til") executes the expression x rep eatedly un til expression y returns the v alue T 185 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 19Learned Program T rained to t 166 test problems Using p
pulation
f
300 programs, found this after 10 generations: (EQ (DU (MT CS)(NOT CS)) (DU (MS NN)(NOT NN)) ) 186 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 20Genetic Programming More in teresting example: design electronic lter circuits
Individuals
are programs that transform b egining circuit to nal circuit, b y adding/subtracting comp
nen
ts and connections
Use
p
pulation
f
640,000, run
n
64 no de parallel pro cessor
Disco
v ers circuits comp etitiv e with b est h uman designs 187 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 21GP for Classifying Images [T eller and V eloso, 1997] Fitness: based
n
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, Dierence, Mini, Library
Mini
refers to a lo cal subroutine that is separately co-ev
lv
ed
Library
refers to a global library subroutine (ev
lv
ed b y selecting the most useful minis) Genetic
p
erators:
Crosso
v er, m utation
Create
\mating p
ls"
and use rank prop
rtionate
repro duction 188 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 22Biolog i cal Ev
lution
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
f
individual learning
n
p
pulation
ev
lution?
189 lecture slides for textb
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Machine L e arning, T. Mitc hell, McGra w Hill, 1997
SLIDE 23Baldwin Eect Assume
Individual
learning has no direct inuence
n
individual DNA
But
abilit y to learn reduces need to \hard wire" traits in DNA Then
Abilit
y
f
individual s to learn will supp
rt
more div erse gene p
l
{ Because learning allo ws individual s with v arious \hard wired" traits to b e successful
