Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
V
o
l.
3, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 20
1
~
21
1
I
S
SN
: 208
9-4
8
5
6
2
01
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRA
Controlling Bloat in Genetic
Programming for Sloving Wall
Following Problem
Na
vid B
a
z
r
ka
r, M
o
s
t
a
f
a
Ne
mati,
Rez
a
Sal
i
mi
Com
puter S
c
ien
ce Dep
a
rtm
e
nt
,
Ta
bar
i
Univ
ersity
, Babo
l, Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 5, 2013
Rev
i
sed
Jun
20,
201
4
Accepte
d
J
u
l 15, 2014
The go
al in
auto
m
a
tic progr
am
ming is to g
e
t
a
co
m
puter to per
f
or
m
a task
b
y
telling it what
needs to be do
ne, ra
ther than b
y
explicitly
pr
ogramming
it.W
ith
consider
s the task of
aut
o
m
a
tica
l
l
y
gen
e
r
a
ting
a com
puter
program
to
enable an
autono
mous mobile robot to
p
e
rform the task of followin
g the wall
of an irregular s
h
aped room. During th
e evolutio
n of solutions using genetic
program
m
i
ng (GP
)
there is
gener
a
ll
y an in
cre
a
s
e
in averag
e tre
e
s
i
ze withou
t
a corresponding
increase in fitn
ess-
a phenomenon commonly
referred to as
bloat. Man
y
diff
erent blo
a
t contr
o
l me
thods have been proposed.
This paper
review,
evalu
a
te, implementatio
n
and
comparison of these methods in wall
following problem and the most appropriate method for solving bloat
problem is prop
osed.
Keyword:
Aut
o
m
a
ti
c pr
o
g
ram
m
i
ng
Co
n
t
ro
llin
g b
l
oat
Genet
i
c
pr
o
g
ra
m
m
i
ng
Wall fo
llo
wi
n
g
prob
lem
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Mostafa Nem
a
ti,
C
o
m
put
er Sci
e
nce
Depa
rt
m
e
nt
, Taba
ri
U
n
i
v
e
r
si
t
y
M
a
nji
l
,
B
a
har
Ave
,
P:
67
, Ta
b
a
ri
B
a
b
o
l
,
Ira
n
Em
a
il: Mo
stafa.m
a
n
j
il@g
m
a
il.co
m
1.
INTRODUCTION
Gen
e
tic Prog
rammin
g
(GP) is th
e au
to
m
a
ted
learn
i
ng
o
f
co
m
put
er pro
g
r
a
m
s [2, 3]
. The
o
ret
i
cal
l
y
, i
t
can solve any problem
whose candi
da
te solutions can be
m
easured a
nd c
o
m
p
ared,
m
a
king it a
widely
appl
i
cabl
e
t
e
c
h
ni
q
u
e. F
u
rt
he
r
m
ore, t
h
e sol
u
t
i
ons
fo
u
nd
by
GP a
r
e us
ual
l
y
pr
o
v
i
d
e
d
i
n
a
fo
rm
at
t
h
at
users can
u
n
d
e
rstand
and
m
o
d
i
fy to their n
e
ed
s. Bu
t
its h
i
gh
v
e
rsatili
ty is also
the cau
se of some d
i
fficu
lties. Users
m
u
st
set
a nu
m
b
er of
param
e
t
e
rs rel
a
t
e
d
t
o
seve
ral
aspe
ct
s o
f
t
h
e
ev
ol
ut
i
ona
ry
p
r
oce
ss,
som
e
of
whi
c
h m
a
y
influe
nce the
search
proce
s
s
so stro
n
g
l
y as to
actu
a
lly p
r
ev
en
t an
o
p
ti
m
a
l so
lu
tio
n to
b
e
foun
d, if set
incorrectly.
And e
v
en whe
n
a reasona
b
le m
a
tch betw
een
p
r
ob
lem
a
n
d par
a
m
e
ter
s
is ach
i
ev
ed
,
a m
a
j
o
r
pr
o
b
l
e
m
rem
a
ins,
o
n
e t
h
at
ha
s bee
n
st
udi
e
d
fo
r m
o
re t
h
a
n
a
deca
de:
c
ode
gr
owt
h
[1]
.
The sea
r
ch s
p
ace of
GP is
virtually unlimited a
nd program
s
tend to grow
i
n
size
during the
evol
ut
i
ona
ry
p
r
oces
s. C
o
de g
r
o
w
t
h
i
s
a heal
t
h
y
resul
t
of
g
e
n
e
tic o
p
e
rato
rs in
search
of better so
lu
tio
ns, b
u
t
it
also
perm
its the appeara
n
ce
of
pieces
of re
dunda
n
t c
ode
that increase
the
size of
progra
m
s
without im
proving
t
h
ei
r fi
t
n
ess. m
a
ny
di
ffe
rent
b
l
oat
co
nt
r
o
l
m
e
t
h
o
d
s
ha
ve
bee
n
pr
o
pose
d
.
Thi
s
pape
r re
v
i
ew, e
v
al
uat
e
,
im
pl
em
ent
a
t
i
o
n a
nd c
o
m
p
ari
s
on
o
f
t
h
e
s
e
m
e
t
hods i
n
wa
l
l
fol
l
o
wi
n
g
pr
o
b
l
e
m
.
The
next
sect
i
o
n
d
eal
s wi
t
h
bl
oat
,
de
scri
bi
n
g
t
h
e m
a
i
n
t
h
eori
e
s
re
gar
d
i
n
g
w
h
y
i
t
occu
rs.
Se
ct
i
on
3
d
e
scri
b
e
s th
e
Dyn
a
m
i
c Li
mi
ts in
d
e
tail, wh
ile Sect.
4 de
scri
bes V
a
ri
at
i
ons
on si
ze an
d de
pt
h p
r
obl
e
m
s and
Sect
i
on
6
rep
o
r
t
s
t
h
e
res
u
l
t
s
of t
h
e c
o
m
p
ari
s
on
s am
ong t
h
e di
f
f
ere
n
t
t
ech
ni
q
u
es,
w
h
i
l
e
Sect
. 6
di
sc
uss
e
s t
h
em
and
pr
esent
s
s
o
m
e
consi
d
e
r
at
i
ons
o
n
t
h
e
usa
g
e o
f
l
i
m
i
t
restri
ct
i
ons i
n
GP
.
Fi
nal
l
y
, Sect
. 7
concl
ude
s an
d
Sect
.
8 pr
o
v
ides
i
d
ea
s
f
o
r f
u
tu
re wo
rk
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
20
1 – 21
1
20
2
2.
BLOAT
Whe
n
Koza
p
ubl
i
s
hed t
h
e fi
rst
b
o
o
k
on
G
P
[
3
]
,
m
o
st
of t
h
e ev
ol
ve
d
p
r
o
g
ram
s
t
h
erei
n co
nt
ai
ne
d
pieces of c
o
de
that did not cont
ribute to the sol
u
tion a
n
d could be
re
m
oved w
ithout altering the results
pr
o
duce
d
. B
e
si
des i
m
posi
n
g
a de
pt
h l
i
m
it
to t
h
e t
r
ees cre
a
t
e
d by
c
r
os
so
ver t
o
pre
v
ent
spe
ndi
ng
com
put
e
r
resources
on e
x
trem
ely large program
s
, Koza also
rou
tin
ely ed
ited
th
e so
lu
tions
provided at t
h
e e
n
d of eac
h
ru
n t
o
si
m
p
l
i
f
y som
e
exp
r
essi
ons
w
h
i
l
e
rem
ovi
ng
t
h
e
re
du
nda
nt
c
ode
.
Tw
o y
ears l
a
t
e
r,
An
gel
i
n
e
re
m
a
rked
o
n
t
h
e
ubi
qui
t
y
o
f
t
h
e
s
e re
du
n
d
ant
c
ode
se
gm
ent
s
and
,
base
d o
n
a slig
h
t
b
i
o
l
og
i
cal si
milarity,
called
th
e
m
in
t
r
on
s [7
]. In
sp
ite o
f
classifyin
g
th
em
as
ex
tran
eou
s
, u
n
n
e
cessary
and
s
upe
rfl
uo
us,
A
n
gel
i
n
e
not
e
d
t
h
at
t
h
e
y
pr
o
v
i
d
e
d
c
r
oss
ove
r
wi
t
h
s
y
nt
act
i
cal
l
y
redu
n
d
ant
co
nst
r
uct
i
o
n
s
wh
ere sp
littin
g
co
u
l
d
b
e
p
e
rfo
rm
ed
witho
u
t
alterin
g
th
e
se
m
a
n
tics o
f
the swapp
e
d
su
b trees. Referri
n
g
t
o
so
m
e
stu
d
i
es
wh
ere th
e in
tro
d
u
c
tion
o
f
artificial
in
tro
n
s was h
e
lp
fu
l o
r
ev
en
essen
tial to
th
e su
ccess o
f
g
e
n
e
tic alg
o
rith
m
s
, An
g
e
lin
e rev
e
ls in
th
e fact th
at
i
n
t
r
on
s em
erge nat
u
r
a
l
l
y
from
t
h
e
dy
nam
i
cs of GP. He
even goes as
far as to state that ‘‘it is im
porta
nt th
e
n
t
o
not
i
m
pede t
h
i
s
em
ergent
p
r
ope
rt
y
as i
t
m
a
y
be
crucial to the
s
u
ccess
f
ul
de
velopm
ent of
genetic program
s
’’ [7].
It is po
ssib
l
e t
h
at in
tro
n
s m
a
y p
r
o
v
i
d
e
so
me b
e
nef
its.
A no
n-in
t
u
itiv
e effect th
at in
tron
s
m
a
y h
a
v
e
in
GP is co
d
e
co
m
p
ression
and
parsim
o
n
y
.
It is no
t th
e
blo
a
ted
co
d
e
full o
f
redu
nd
ant a seg
m
en
t t
h
at is
parsi
m
oni
o
u
s,
but
t
h
e e
ffect
i
v
e c
ode
t
h
at
r
e
m
a
i
n
s aft
e
r
r
e
m
ovi
n
g
t
h
e
i
n
t
r
ons
.
Un
de
r
speci
fi
c c
o
n
d
i
t
i
ons,
part
i
c
ul
a
r
l
y
i
n
t
h
e
pr
esence
of
dest
ruct
i
v
e
cross
o
ver
,
t
h
ere is evi
d
e
n
ce t
h
at the
ex
istence of i
n
tron
s in
the
p
opu
latio
n
resu
lts in
shorter
an
d
less co
m
p
lex
effectiv
e
solu
tio
n
s
.Co
m
p
act so
lu
tion
s
are tho
ugh
t to
be
m
o
re
ro
b
u
st
an
d
ge
neral
i
ze
bet
t
e
r [8]
.
I
n
t
r
o
n
s a
l
so d
o
seem
t
o
pr
ovi
de s
o
m
e
pr
ot
ect
i
o
n a
g
ai
nst
t
h
e
de
st
ruct
i
v
e
effect
s o
f
cr
oss
ove
r an
d ot
her
genet
i
c
o
p
erat
ors [
9
,
8]
al
t
h
o
u
g
h
t
h
i
s
m
a
y not
al
way
s
be h
e
l
p
f
u
l
.
The
usa
g
e o
f
ex
p
licitly d
e
fined
artificial in
tron
s
h
a
s yield
e
d
g
e
n
e
rally
g
o
o
d
resu
lts in
lin
ear
GP
[10
,
11
], bu
t in
tree
b
a
sed
GP i
t
us
ual
l
y
d
e
gra
d
e
d
t
h
e
pe
rf
orm
a
nce o
f
t
h
e sea
r
ch
p
r
oc
ess [
13]
.
R
e
gar
d
l
e
ss
of
i
t
s
possi
bl
e be
nefi
t
s
t
o
GP
, t
h
e si
de
effects o
f
in
tro
n
pro
lifer
atio
n ar
e
ver
y
ser
i
ou
s.
C
o
m
put
at
i
onal
reso
urc
e
s m
a
y
be t
o
t
a
l
l
y
exha
ust
e
d i
n
t
h
e st
ora
g
e, e
v
al
uat
i
on a
n
d sw
appi
ng
o
f
co
d
e
t
h
at
co
n
t
ribu
tes no
t
h
ing
to
t
h
e fi
nal so
lu
tion
,
p
r
ev
en
ting
GP
fr
o
m
perf
orm
i
ng t
h
e
ef
fec
tive s
earch
nee
d
ed to fi
nd
bet
t
e
r s
o
l
u
t
i
o
n
s
. B
l
oat
i
s
n
o
w
wi
del
y
rec
o
gn
i
zed as a
per
n
i
c
i
ous
p
h
en
om
eno
n
t
h
at
pl
ag
u
e
s m
o
st
pro
g
re
ssi
ve
search t
ech
ni
q
u
es base
d o
n
d
i
scret
e
vari
abl
e
-l
en
gt
h re
prese
n
t
a
t
i
ons a
nd u
s
i
ng fi
xe
d eval
u
a
t
i
on fu
nct
i
o
ns
[14
,
15]
. B
l
oat
co
n
t
rol
ha
s bec
o
m
e
a ve
ry
act
i
v
e researc
h
a
r
ea
in GP, alrea
d
y
subject t
o
d
i
fferen
t th
eoretic and
anal
y
t
i
c
st
udi
e
s
[
10]
.
Se
veral
t
h
eo
ri
es c
o
nce
r
ni
ng
w
h
y
bl
o
a
t
occu
rs
ha
ve
been
ad
va
nce
d
, an
d m
a
ny
di
f
f
ere
n
t
bl
oat
c
ont
rol
m
e
t
h
o
d
s ha
ve be
en pr
o
pose
d
.
Lu
ke o
b
ser
v
e
d
t
h
at
un
de
rl
y
i
ng cau
ses of
code bl
oat
i
n
g co
nt
ai
ns Hi
t
c
hhi
ki
ng
, De
f
e
nse agai
nst
C
r
oss
o
ver,
R
e
m
oval
B
i
as, Fi
t
n
ess C
a
uses B
l
oat
an
d M
odi
f
i
cat
i
on P
o
i
n
t
Dept
h.
The
n
i
t
coi
n
e
d
t
h
at
t
h
e co
de
b
l
o
a
ting
i
n
evo
l
u
tion
a
ry com
p
u
t
atio
n
field
is i
d
en
tified with th
e C
-
valu
e Paradox
in
th
e b
i
o
l
og
y [1
2
]
.
There
f
ore, i
f
n
o
any
re
st
ri
ct
i
ons a
d
di
n
g
t
o
genet
i
c
o
p
e
r
at
i
ons
, co
de
bl
oa
t
i
ng i
s
i
n
e
v
i
t
a
bl
e i
n
G
P
. J
u
s
t
l
i
k
e
Luke said in [6], “In a ve
ry real sense, bl
oating
m
a
kes genetic programming a race against tim
e
,
to find the
best
s
o
l
u
t
i
o
n p
o
ssi
bl
e
bef
o
re
bl
oat
put
s a
n
e
ffect
i
v
e st
o
p
t
o
t
h
e sear
ch
.” F
o
r
f
u
rt
he
r i
n
f
o
r
m
at
i
on o
n
bl
oa
t
see
[1
6]
.
3.
D
YNA
M
I
C
DEPTH
LIM
I
T
Dy
nam
i
c M
a
xim
u
m
Tree De
pt
h
[
4
]
i
s
a
bl
oat
c
ont
r
o
l
t
e
c
hni
que
i
n
s
p
i
r
e
d
by
t
h
e
t
r
a
d
i
t
i
onal
st
at
i
c
l
i
m
i
t
.
It
al
so i
m
poses a de
pt
h l
i
m
i
t
on t
h
e
i
ndi
vi
dual
s
acc
ept
e
d i
n
t
o
t
h
e
po
p
u
l
a
t
i
on,
b
u
t
t
h
i
s
one
i
s
dy
nam
i
c,
mean
in
g
th
at it can
b
e
ch
an
g
e
d
du
ri
n
g
t
h
e run
.
Th
e d
y
n
a
m
i
c li
mit is in
it
ial
l
y set with
a lo
w v
a
l
u
e,
b
u
t
at
least
as h
i
gh
as th
e
m
a
x
i
m
u
m
d
e
p
t
h
o
f
th
e i
n
itial ran
d
o
m
tre
e
s. An
y n
e
w in
d
i
v
i
du
al wh
o b
r
eak
s
th
is limit
is
rej
ecte
d
and re
placed
by one
of its pa
re
nts instead (as with th
e traditional static
li
mit), unless it is the best
i
ndi
vi
dual
f
o
u
n
d
s
o
far.
I
n
t
h
i
s
case, t
h
e
dy
n
a
m
i
c l
i
m
i
t
i
s
rai
s
ed t
o
m
a
t
c
h t
h
e
dept
h
of
t
h
e
ne
w
best
-
o
f
-
r
u
n a
n
d
allo
w it in
to
the p
opu
latio
n
.
Fig
u
re 1
sh
ows
th
e p
s
eu
do
co
de of this
proce
d
ure. T
h
e res
u
l
t
is a succession of
limit risings, as
the
best s
o
luti
on be
c
o
m
e
s
more
accurate a
n
d m
o
re c
o
m
p
le
x.
Dynam
i
c Maxi
m
u
m
Tree Depth does not
necessar
ily replace the
tra
d
itional
de
pth li
m
i
t
:
bot
h
dy
nam
i
c and fi
xed l
i
m
i
t
s
can be
used at
t
h
e sam
e
t
i
m
e
(n
ot
sh
ow
n i
n
Fi
gu
re 1
)
.
When t
h
i
s
hap
p
e
n
s, t
h
e
d
y
n
a
m
i
c li
mit
always lies somewh
ere b
e
t
w
een
th
e in
itial tree
d
e
p
t
h
an
d th
e fi
x
e
d
d
e
p
t
h
li
mit. Th
e simp
licit
y
of
Dy
nam
i
c M
a
xi
m
u
m
Tree Dept
h m
a
kes i
t
easy
t
o
use
wi
t
h
any
set
o
f
p
a
ram
e
t
e
rs and/
or c
o
upl
e
d
wi
t
h
ot
her
tech
n
i
qu
es
fo
r co
n
t
ro
lling
b
l
oat.
The dy
nam
i
c lim
it
m
a
y
al
so
be use
d
f
o
r a
n
ot
he
r p
u
r
p
o
s
e besi
des c
ont
ro
l
l
i
ng bl
oat
.
I
n
real
wo
rl
d
appl
i
cat
i
o
ns,
o
n
e m
a
y
not
be i
n
t
e
rest
ed
or a
b
l
e
t
o
i
n
vest
a l
a
rge am
ount
o
f
t
i
m
e
i
n
achi
e
vi
n
g
t
h
e
best
p
o
ssi
bl
e
solution, partic
ularly
in
approxim
a
tion proble
m
s
. Instead, one m
a
y
consider a solution to be acceptable
only
if it is su
fficien
tly si
m
p
le to
b
e
u
n
d
e
rstoo
d
, ev
en
if
its accu
r
acy is
k
nown
to
b
e
worse
than t
h
e acc
uracy of
o
t
h
e
r m
o
re com
p
lex
so
lu
tio
ns. Plu
s
, sh
orter so
lu
tion
s
ten
d
to
g
e
n
e
ralize
better (Sect.
2
)
.
On
e
way to
avo
i
d
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
C
ont
r
o
l
i
n
g
Bl
o
a
t
i
n
Ge
net
i
c
P
r
og
ra
m
m
i
n
g F
o
r
Sl
ovi
n
g
Wal
l
Fol
l
o
w
i
n
g
P
r
obl
e
m
(
N
avi
d
Bazrk
ar)
20
3
o
v
e
r-sp
ecializatio
n
of th
e so
l
u
tio
ns fo
und
by GP is to
cho
o
s
e term
in
ati
o
n
criteria th
at will n
o
t
fo
rce th
e
ev
o
l
u
tio
n
a
ry
pro
cess to
go
on
ind
e
fi
n
itely in
search
o
f
a p
e
rfect so
lu
tio
n.
A less stri
n
g
e
n
t
stop
cond
itio
n
yields a s
o
m
e
what i
n
acc
ura
t
e solutio
n
,
bu
t on
e th
at is also
sim
p
ler
and
ho
p
e
fu
ll
y g
e
n
e
ralizes
b
e
tter.
Howev
e
r, settin
g th
e ri
g
h
t
sto
p
co
nd
itio
n
may b
e
a m
a
j
o
r ch
alleng
e in
itself, as
one canno
t pred
ict th
e
com
p
lexity needed to achie
ve a ce
rtain le
ve
l of acc
uracy
.
By startin
g th
e search
with a l
o
w d
y
n
a
m
i
c li
mit fo
r
tree de
pth, the
search is force
d
to conce
n
trat
e on sim
p
le
solu
tio
n
s
first. Th
e lim
i
t
is th
en
raised
wh
en
a n
e
w
solution is
found t
h
at is m
o
re com
p
lex, but also m
o
re accurate, t
h
a
n
the pre
v
ious
one. As t
h
e e
vol
ution
procee
ds, the l
i
m
i
t is repeatedly raised as
m
o
re a
n
d
m
o
re co
m
p
lex
so
lu
tio
ns ach
iev
e
in
creasing
l
y h
i
gh
er
levels of accuracy. Regardless of the st
op c
o
ndition,
the
Dynam
i
c Maxi
m
u
m
Tree Depth tec
hni
que
can i
n
fact
pr
ovi
de a seri
es of s
o
l
u
t
i
ons
of i
n
creasi
ng c
o
m
p
l
e
xi
t
y
and acc
uracy
,
from
whi
c
h t
h
e use
r
s m
a
y
cho
o
se
the one m
o
st a
d
equate to thei
r
needs
.
Fi
gu
re
1.
Pse
u
do
co
de
o
f
t
h
e
basi
c
Dy
nam
i
c M
a
xi
m
u
m
Tree De
pt
h
p
r
oce
d
ure
(
w
i
t
h
no
st
at
i
c
l
i
m
i
t
)
4.
VA
RI
ATIO
N
S
O
N
SIZ
E
A
N
D
DEPT
H
The origi
n
al Dynamic Maxim
u
m Tree De
pth
was s
o
on
ex
tend
ed
t
o
inclu
d
e
ad
d
itional v
a
rian
ts: a
heavy
dynam
i
c lim
i
t, called heavy
b
eca
use
it falls back t
o
lower
values
whe
n
e
v
er all
o
wed, and a
dy
namic
limit on size instead
of
de
pth. Fi
gure 2 s
h
ows t
h
e ge
neral acceptance
proce
d
ure (inc
luding all the varia
n
ts,
u
s
ing
no
static li
mit) th
at a
ll n
e
wly created
in
d
i
v
i
du
als
m
u
st p
a
ss b
e
fore b
e
ing
accep
ted
in
to
th
e n
e
w
gene
rat
i
o
n. T
h
i
s
i
s
an e
x
t
e
nsi
o
n o
f
t
h
e
p
r
oce
d
ure i
n
Fi
gure 1. Only the s
h
aded pa
rt
s are com
p
le
tely n
e
w.
Bo
th
th
e n
e
w cod
e
an
d
t
h
e sm
all
d
i
fferen
ces in
th
e co
mm
o
n
co
d
e
will b
e
exp
l
ain
e
d
i
n
th
e
n
e
x
t
section
s
.
An
y
indivi
dual that does
not m
eet the si
ze/dept
h/fitness re
qui
re
m
e
nts of the
Dynam
i
c Lim
its
m
e
thod
will not be
accepted by t
h
is proce
d
ure
,
but instead
replac
ed by
one of
its
pa
rents
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
20
1 – 21
1
20
4
Figure
2. Pse
u
do code
of the
gene
ral
Dynamic Lim
its acceptance procedure
(all va
riants,
no static lim
i
t).
Th
is is an
ex
ten
s
ion
o
f
th
e
pro
cedure in Figu
re
1.
On
ly th
e sh
ad
ed
co
d
e
is co
m
p
letely n
e
w
5.
HEAV
Y DYN
AM
IC
LIM
I
T
Dy
nam
i
c M
a
xim
u
m
Tree D
e
pt
h i
s
ca
pa
bl
e of
wi
t
h
st
a
n
d
i
ng a c
o
nsi
d
e
r
abl
e
am
ount
o
f
pa
rsi
m
ony
p
r
essure, as
p
r
o
v
e
n
b
y
th
e resu
lts ob
tain
ed
b
y
in
itializin
g
th
e d
y
n
a
m
i
c li
mit with
th
e lo
west po
ssib
l
e
v
a
lue,
t
h
e m
a
xim
u
m
dept
h o
f
t
h
e i
n
i
t
i
a
l
rand
om
t
r
ees [4]
(
S
ect
.
3.
1.
2)
. S
o
t
h
er
e s
e
em
s t
o
be n
o
reaso
n
why
t
h
e
l
i
m
i
t
sh
ou
l
d
no
t b
e
allo
wed
t
o
fall back
to
lower
valu
es in
case the d
e
p
t
h
of th
e
n
e
w
b
e
st ind
i
v
i
d
u
a
l
b
eco
m
e
s l
o
wer
th
an
t
h
e cu
rrent li
mit, an
o
c
cu
rren
ce wh
ich
is actu
a
lly
ver
y
com
m
on. So
t
h
e fi
rst
va
ri
at
i
on i
n
t
r
od
uce
d
t
o
t
h
e
ori
g
inal Dyna
mic
Maxim
u
m Tree Dept
h is the Heavy dy
nam
i
c
limit, one that acco
mpanies the de
pt
h of the
b
e
st in
d
i
v
i
du
al, u
p
o
r
d
o
wn
,
with
th
e so
le co
n
s
t
r
ain
t
of not g
o
i
ng
lo
wer th
an
its in
itializ
atio
n
v
a
l
u
e [5
]
.
An
ad
d
ition
a
l v
a
ri
atio
n
is th
e VeryHeav
y li
mit,
si
m
i
lar to
th
e
h
eav
y v
a
rian
t
b
u
t
allo
wed
to
fall b
ack
ev
en
b
e
low
its in
itializat
io
n
v
a
lu
e. Bo
t
h
t
h
ese
v
a
rian
ts are c
o
v
e
red in
t
h
e secon
d
sh
aded
b
l
o
c
k
o
f
Figu
re 2.
As exp
ected, wh
en
ev
er th
e
li
mit falls b
a
c
k
to
a l
o
we
r val
u
e, s
o
m
e
indi
viduals already in the
po
p
u
l
a
t
i
on i
m
m
e
di
at
el
y
break t
h
e
new l
i
m
it
, becom
i
ng ‘i
l
l
egals’. T
h
ere
was a va
st range of options t
o
deal
with
th
em
, th
e
m
o
re drastic
b
e
ing
th
eir im
med
i
ate re
m
o
val fro
m
th
e pop
u
l
ation
,
po
ssi
b
l
y rep
l
acing
t
h
em
b
y
n
e
w
ran
d
o
m
in
d
i
v
i
du
als.
How
e
v
e
r, si
n
ce these n
e
w
‘
illeg
a
ls’ cou
l
d
b
e
the o
n
e
s who
m
a
n
a
g
e
d
to produce th
e
new
best
i
n
di
v
i
dual
,
el
i
m
i
n
ati
ng t
h
em
coul
d be
ha
rm
ful
for t
h
e searc
h
pr
ocess
.
A m
u
ch s
o
ft
er
o
p
t
i
o
n wa
s
ad
op
ted
:
th
e
‘illeg
a
ls’ are allowed
to
rem
a
in
in
th
e po
pu
la
tio
n
as if th
ey
were no
t b
r
eak
i
ng
th
e li
m
it, b
u
t
wh
en
bree
ding, t
h
eir childre
n ca
nnot be
dee
p
er t
h
an t
h
e
d
eepe
s
t pare
nt. T
h
is
naturally and gra
d
ually places the
p
opu
latio
n
wit
h
in
limits ag
ai
n
.
Th
e first shad
ed
b
l
o
c
k
of Fig
u
re 2
d
eals with
cho
o
s
i
n
g th
e rig
h
t
limit
(my
li
mit i) to
u
s
e for th
e
n
e
w i
n
d
i
v
i
du
al,
d
e
pen
d
i
n
g
on
wheth
e
r it h
a
s illeg
a
l p
a
ren
t
s.
Th
e
first co
m
p
ariso
n
i
n
v
o
l
v
i
n
g t
h
e
vari
a
b
l
e
dy
na
m
i
c l
i
m
i
t
i
n
Fi
gu
re
1 (i
f si
ze
_i
<= dy
nam
i
c_l
i
m
i
t
)
i
s
no
w
per
f
o
rm
ed usi
n
g
t
h
e
v
a
riab
le m
y
_
l
i
m
it_
i in
Figu
re 2
( if size_
i <= my_
l
i
m
i
t
_
i
)
.
6.
DY
N
A
MI
C SI
Z
E
LIMIT
Eve
n
t
h
o
u
g
h
bl
oat
i
s
kn
o
w
n t
o
a
ffect
m
a
ny
ot
her
search
pr
oce
sses usi
n
g
va
ri
abl
e
l
e
n
g
t
h
rep
r
ese
n
t
a
t
i
ons
(Sect
.
2)
,
dept
h l
i
m
i
t
s
cannot
be
use
d
o
n
n
o
n
t
r
ee
-base
d
G
P
sy
st
em
s. Ext
e
ndi
ng
t
h
e i
d
e
a
of
a
dy
nam
i
c
l
i
m
i
t
t
o
ot
he
r dom
ai
ns m
u
st
begi
n wi
t
h
t
h
e rem
oval
of t
h
e co
n
cept
of de
pt
h, repl
aci
n
g
i
t
wi
t
h
t
h
e
conce
p
t
of
si
ze. The
sec
o
n
d
vari
at
i
o
n
on
t
h
e o
r
i
g
i
n
al
D
y
nam
i
c M
a
xi
m
u
m
Tree Dept
h i
s
t
h
e
usa
g
e
of a
dy
nam
i
c si
ze lim
it
, where si
ze i
s
t
h
e num
ber o
f
n
ode
s [
5
]
.
If a st
at
i
c
l
i
m
i
t
i
s
t
o
be
use
d
al
on
g wi
t
h
t
h
is
dy
nam
i
c l
i
m
i
t
,
i
t
sho
u
l
d
al
so
be
on
si
ze,
no
t
dept
h. T
h
e
v
a
ri
abl
e
dep
t
h
_
i
of t
h
e
pseu
d
o
c
ode i
n
Fi
gu
re 1
i
s
n
o
w called
siz
e
_i
in
Figu
r
e
2, alth
ou
gh
it can
refe
r to
eithe
r
size
or
de
pth
.
Tree in
itializat
io
n
in
tree-b
a
sed
GP also
typ
i
cally relies o
n
th
e con
cep
t
o
f
d
e
p
t
h. Th
is is th
e case
with the popul
a
r Grow, Full, and
Ram
p
ed Half-a
nd-Half
initialization
m
e
thods [3]. Both Grow and Full
m
e
thods
creat
e trees
by adding
ra
ndom
node
s
until a m
a
xim
u
m
specified de
pth. T
h
e
Grow m
e
thod adds
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
C
ont
r
o
l
i
n
g
Bl
o
a
t
i
n
Ge
net
i
c
P
r
og
ra
m
m
i
n
g F
o
r
Sl
ovi
n
g
Wal
l
Fol
l
o
w
i
n
g
P
r
obl
e
m
(
N
avi
d
Bazrk
ar)
20
5
i
n
t
e
rnal
or t
e
r
m
i
n
al
nodes
,
e
x
cept
at
t
h
e m
a
xi
m
u
m
dept
h,
whe
r
e t
h
e c
h
oi
ce i
s
rest
ri
ct
ed t
o
t
e
rm
i
n
als. Thi
s
creates trees
with differe
n
t s
h
apes
a
n
d sizes. The
Full m
e
thod creates
bala
n
ced trees, wit
h
all term
in
al n
o
d
e
s
at
t
h
e
m
a
xim
u
m
dept
h. It
d
o
e
s t
h
i
s
by
addi
ng ra
n
dom
i
n
ternal
n
o
d
e
s ex
cept
at
t
h
e
m
a
xi
m
u
m
dept
h,
whe
r
e i
t
selects only term
inals. The Ra
m
p
ed Half-and-Half m
e
th
o
d
is a co
m
b
in
atio
n
of
th
e two
,
wh
ere h
a
lf
th
e
p
opu
latio
n
is i
n
itialized
with Grow, and
the o
t
h
e
r
h
a
lf
w
ith
Fu
ll.
In each
h
a
lf tr
ees are created
with
d
e
p
t
h
li
mits ran
g
i
ng
fro
m
2
to
a
sp
ecified
m
a
x
i
m
u
m
v
a
lu
e, en
su
ri
n
g
a
v
e
ry
d
i
v
e
rse in
itial p
opu
latio
n
.
Whe
n
usi
n
g t
h
e dy
nam
i
c si
ze l
i
m
i
t
,
i
t
m
a
kes no
sense t
o
keep
usi
ng
de
pt
h as a
rest
ri
c
t
i
on o
n
t
r
ee
in
itializat
io
n
.
So
a m
o
d
i
fied v
e
rsi
o
n
o
f
t
h
e Ra
m
p
ed
Hal
f-an
d
-Half in
itializatio
n
m
e
t
h
od
was creat
ed
[5
],
wh
ere an
equ
a
l
n
u
m
b
e
r o
f
indiv
i
d
u
a
ls are in
i
tialized
with
si
zes rang
ing
b
e
t
w
een
2
and
th
e in
itial
v
a
lu
e of th
e
d
y
n
a
m
i
c size li
mit. Fo
r each
size, h
a
lf or th
e in
d
i
v
i
du
als are in
itialized
wi
th
th
e
Grow m
e
th
od
, and
th
e
o
t
h
e
r
hal
f
wi
t
h
t
h
e F
u
l
l
m
e
t
hod, t
h
a
t
have al
so bee
n
m
odi
fi
ed t
o
f
i
t
t
h
e si
ze const
r
ai
nt
s onl
y
.
I
n
t
h
e
m
odi
fi
ed
Gr
o
w
m
e
thod, the i
ndi
vidual grows by ad
dition of ra
ndom
nodes (i
nterna
l or
term
inal) withou
t excee
ding the
m
a
xim
u
m
specified size; the
m
odified
F
u
ll
m
e
thod choos
e
s only interna
l
node
s until the size is close to the
sp
ecified, and
o
n
l
y th
en
choo
ses term
in
als. Un
lik
e th
e
o
r
ig
in
al Fu
ll m
e
th
od
, it
m
a
y n
o
t b
e
ab
le to
create
i
ndi
vi
dual
s
wi
t
h
t
h
e e
x
act
si
z
e
speci
fi
e
d
,
bu
t
onl
y
cl
ose
(a
nd
ne
ver e
x
ce
edi
n
g)
. Fi
g
u
r
e
3 s
h
o
w
s t
h
e
p
s
eu
do
co
d
e
of
bo
th
m
e
th
od
s.
Fig
u
re
3
.
Pseud
o
cod
e
of th
e
m
o
d
i
fied
Grow and
Fu
ll in
itializatio
n
m
e
th
o
d
s
7.
WALL FOLLOWING PROBLEM
M
a
t
a
ri
c [1
7]
d
e
scri
be
d t
h
e
p
r
obl
em
of c
o
nt
r
o
l
l
i
ng a
n
a
u
t
o
n
o
m
ous m
obi
l
e
ro
b
o
t
t
o
per
f
o
r
m
t
h
e t
a
sk
o
f
fo
ll
o
w
i
n
g
t
h
e walls
o
f
an irregu
lar
ro
om
. Th
e rob
o
t
i
s
cap
ab
le of ex
ecu
ting
t
h
e fo
llo
wi
n
g
fiv
e
p
r
im
it
iv
e
m
o
t
o
r funct
i
o
n
s
:
m
ovi
ng f
o
r
w
ar
d by
a con
s
t
a
nt
di
st
ance,
m
ovi
ng bac
k
w
a
rd by
a con
s
t
a
nt
di
st
ance, t
u
r
n
i
n
g
r
i
gh
t b
y
30
d
e
gr
ees, t
u
rn
ing
lef
t
b
y
30
d
e
gr
ees, an
d stop
p
i
ng. Th
e
r
obo
t h
a
s 12
son
a
r senso
r
s wh
ich r
e
por
t th
e
di
st
ance t
o
t
h
e
nea
r
est
w
a
l
l
.
Each s
o
nar
se
n
s
or
co
ve
rs a
3
0
deg
r
ee s
ect
or
ar
ou
n
d
t
h
e
r
o
bot
.
I
n
a
d
di
t
i
on, t
h
ere
was a sens
or
f
o
r t
h
e S
T
OP
P
E
D co
n
d
i
t
i
on
of t
h
e
ro
b
o
t
.
F
i
gu
re 4 s
h
o
w
s
an i
rre
gul
a
r
l
y
sha
p
ed r
o
om
and t
h
e
di
st
ances
rep
o
r
t
e
d by
t
h
e
1
2
s
ona
r se
ns
ors
.
The
ro
b
o
t
i
s
sh
ow
n at
poi
nt
(
1
2
,
16
)
near t
h
e cent
e
r
o
f
t
h
e
ro
om
.
The
n
o
rth
(t
op
)
wall an
d
west
(left)
wall are
e
ach
27.6 feet l
o
ng.
Fi
gu
re
4.
I
rre
g
u
l
a
r
ro
om
wi
t
h
r
o
b
o
t
wi
t
h
12
son
a
r s
e
ns
o
r
s l
o
cat
ed
nea
r
m
i
ddl
e
o
f
t
h
e
r
o
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
20
1 – 21
1
20
6
8.
EX
P
E
R
I
M
E
NT
S
Al
l
t
h
e e
x
peri
m
e
nt
s we
re
pe
rf
orm
e
d o
n
t
r
e
e
-base
d
GP
us
i
ng m
y
java
c
ode
[
?
?
]
Wal
l
f
o
l
l
o
wi
ng
p
r
ob
lem
was ch
o
s
en to
test, an
d th
is is a first research
o
f
b
l
o
a
t pro
b
l
em
in
wall fo
llo
wi
n
g
.
8.
1.
Process
of W
o
rk:
Th
e
p
r
ob
lem
is
so
l
v
ed u
s
i
n
g a GP.
Gene:
A
Sche
me program
that is represe
n
te
d
by a T
r
ee
(Li
k
e a c
o
m
p
iler AST
)
.
(a)
Term
inals: {SS0
…SS
1
1,
EDG
,
S
S
, M
S
D}
EDG
==
2.
3,
S
S
==m
i
n
im
u
m
of
al
l
sens
or
s,
M
S
D ==
2.
0.
SS0
..S
S1
1 a
r
e
t
h
e sens
o
r
s i
n
a 30
de
gree i
n
t
e
rval
, a
n
d eac
h
ret
u
rn
s th
e
distan
ce to
th
e
first in
tersected wall.
(b) F
u
nctions:
{PLUS
,
IFLT
E, PR
OGN2, T
L
, TR, MB, M
F
}
All th
e fun
c
tion
s
are tak
e
n
fro
m
th
e article, ex
cep
t
PL
US
th
at tak
e
s
2
arg
u
m
en
ts and
retu
rn
th
eir sum
.
TL,
TR, MB, MF – m
oves the robot and ret
u
rns the m
i
nim
u
m
of SS
2 and
SS3. IF
LTE -
equals t
o
"if less the
n
equal
t
h
en el
s
e
". PR
O
G
N
2
t
a
kes 2 a
r
gum
ent
s
eval
uat
e
s
bot
h
of t
h
em
and
ret
u
r
n
s t
h
e sec
o
n
d
.
Al
l
t
h
e
fun
c
tion
s
th
at
mak
e
th
e
robo
t m
o
v
e
tak
e
on
e ti
m
e
step
.
Fitn
ess fun
c
tion
:
Th
e fitn
ess functio
n
is th
e
n
u
m
b
er o
f
tiles (o
u
t
o
f
56
) th
at
th
e ro
bo
t m
o
v
e
s th
ro
ugh
th
em. Each
robo
t
h
a
s 400
ti
m
e
s
t
ep
s to
si
m
u
lat
e
, an
d
if th
ere is n
o
ch
ang
e
fro
m
th
e last ev
alu
a
tio
n
we
will sto
p
th
e ev
alu
a
tion
l
o
o
p
. Sel
ect
i
o
n
m
e
t
hod:
Fi
t
n
ess pr
op
ort
i
on f
unct
i
o
n,
usi
n
g ro
ul
et
t
e
wheel
sam
p
l
i
ng. Pop
u
l
a
t
i
on si
ze = 50
0
.
Num
of
ge
nera
t
i
ons =
5
1
.
C
r
o
sso
ver:
P
c
=
0.
9.
The cr
oss
o
v
er
i
s
do
ne bet
w
e
e
n su
b t
r
ees
, t
h
e sub t
r
ee i
s
pi
cked
ra
nd
om
l
y
. M
u
t
a
t
i
on:
Pm
= 0.
01
. I
n
o
u
r
case
the m
u
tation obj
ective is to reduce t
r
ee size
. It will pi
c
k
a
sub tree a
nd
replace it with a ne
w sub tre
e
of
dept
h 1.
Steps /
Process
:
1
.
In
itial pop
u
l
ation
calcu
lated
rand
o
m
ly,
all th
e trees are co
m
p
lete in
dep
t
h
of
2
.
2.
1
Fi
t
n
e
ss c
a
l
c
ul
at
i
on.
2.
2
ap
pl
y
dy
n
a
m
i
c dept
h
m
e
t
h
o
d
[1]
2.
3
ap
pl
y
hea
v
y
m
e
t
hod
(si
ze/
dept
h
)
[1]
2.
4
ap
pl
y
fal
l
s bac
k
m
e
t
hod
(l
o
w
er
val
u
e
s
)
[1]
3.
Selection.
4.
C
r
oss
o
ve
r a
n
d
m
u
t
a
t
i
on.
5.
M
o
vi
ng
t
o
next
ge
nerat
i
on
.
On
e
o
f
t
h
e pro
b
l
em
s in
GP is th
at th
e Tree –
Cod
e
h
a
v
e
th
e tend
en
cy to
g
r
o
w
t
h
ro
ugh
ou
t th
e
gene
rations.
We tried to m
o
derate the probl
e
m
usi
ng tree
m
e
thod a
nd m
u
tation
fu
nction (with proba
bility of
Pm
=0.01
)
,
we
repl
ace
d a
ra
n
dom
su
b t
r
ee
wi
t
h
a
ne
w t
r
e
e
o
f
si
ze
1.
T
h
i
s
s
h
o
u
l
d
ca
u
s
e t
h
e t
r
ee
– c
ode
t
o
reduce its size. The
Fitness
function do
es
n'
t
take i
n
t
o
acc
ou
nt
t
h
e l
e
ngt
h
of
t
h
e
pat
h
,
an
d
n
u
m
b
er o
f
t
i
m
e
st
eps
neede
d
to com
p
lete "collecting" all
the tiles.
So we tried to
replace the
Fitness functi
on
with a new Function.
F1
=
(Tiles step
p
e
d
o
n
) +
facto
r
/(Tim
e
step
s) +
f
actor /(W
a
ll
co
llision
s
). Wh
ere
Tiles
step
p
e
d
on
-
th
e
n
u
m
b
e
r
of
Tiles th
at th
e r
obot "p
ick
e
d
"
d
u
r
i
n
g
t
h
e ru
n. Time step
s –
th
e n
u
m
b
e
r
of
time step
s th
at t
o
ok
th
e
robo
t to
co
m
p
l
e
te th
e
missio
n
(
m
ax
4
0
0
)
.Wall co
llisio
n
s
–
th
e n
u
m
b
e
r of walls th
at th
e ro
bo
t co
llid
ed
du
ri
n
g
t
h
e r
u
n. T
h
e
ne
w fi
t
n
ess
fu
nct
i
on
ha
d
no
ef
fe
ct
on
t
h
e e
v
ol
u
t
i
on
pr
o
g
ressi
o
n
, s
o
we
deci
d
e
d t
o
d
r
op
t
h
e i
d
ea.
You ca
n also s
ee the des
p
ite the fact that the robot
di
dn
't t
a
k
e
th
e ab
ov
e
d
a
ta it f
o
und
a v
e
r
y
shor
t w
a
y t
o
solve the
proble
m
. You ca
n see clear
ly the increa
sing value
of the a
v
era
g
e and be
st fitness duri
ng the
gene
rat
i
o
ns.
It
con
f
i
r
m
s
t
h
e cor
r
ect
ness
o
f
u
s
i
ng
GP t
o
sol
v
e t
h
i
s
pr
obl
e
m
. In t
h
e si
m
u
lat
e
d pl
ot
of
ge
nerat
i
o
n
3
0
, 40
, 51
you can
see an
in
ter
e
stin
g
b
e
h
a
vio
r
at th
e b
e
g
i
n
n
i
n
g
o
f
th
e rob
o
t
p
a
t
h
, it d
o
es so
m
e
u
n
e
x
p
lain
ed
lo
op
s.
W
e
witnessed
t
h
e sam
e
b
e
h
a
v
i
o
r
in
Ko
za's article.
9.
RESULTS
Th
is sectio
n
p
r
esen
ts th
e results o
f
all th
e ex
p
e
rim
e
n
t
s. Sev
e
ral p
l
o
t
s and th
eir b
r
ief and Best Tree
Dept
h f
o
r bl
ot
descri
pt
i
o
n
s
ar
e prese
n
t
e
d. Fi
gu
re 5 s
h
o
w
s
a bo
xpl
ot
of t
h
e best
fi
t
n
ess o
f
ru
n an
d sh
o
w
s t
h
e
evol
ut
i
o
n
o
f
t
h
e best
fi
t
n
ess a
l
on
g t
h
e
r
u
n.
An
d C
o
m
p
are
cano
n
i
cal
G
P
wi
t
h
new
m
e
t
h
od
i
n
st
a
n
dar
d
ro
om
and ne
w
room
are
prese
n
ted.
A.
1
out
put
i
n
c
a
no
ni
cal
G
P
i
n
st
an
dar
d
ro
om
B
e
st
i
ndi
vi
du
al
:
49
B
e
st
Tree
Dept
h:
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
C
ont
r
o
l
i
n
g
Bl
o
a
t
i
n
Ge
net
i
c
P
r
og
ra
m
m
i
n
g F
o
r
Sl
ovi
n
g
Wal
l
Fol
l
o
w
i
n
g
P
r
obl
e
m
(
N
avi
d
Bazrk
ar)
20
7
(IF
LTE (PR
O
GN2 (IFLTE
S06 (PROGN2
(PR
O
GN2
M
F
S
1
1) (PR
O
GN2 S11
M
F
))
(PROGN2 MB
S10
)
(PRO
G
N
2
S
0
4
S0
9)
) M
F
)
(P
ROG
N
2
(
I
FLT
E
ED
G
TL TR
M
B
) M
S
D) M
F
TR)
Fi
gu
re
5.
1.
Ou
t
put
i
n
can
o
n
i
c
al
GP
Fi
gu
re 5.
2.
O
u
t
put
i
n
ca
no
ni
ca
l
A.
2
out
put
wi
t
h
new
m
e
t
hods
i
n
st
a
nda
rd
r
o
om
B
e
st
i
ndi
vi
du
al
:
50
B
e
st
Tree
Dept
h:
3
(IF
LTE
(IFLT
E
MF MF
MF
S00) (IFLTE
S
0
8 MB S
0
5 T
R
) (IFLT
E
TL
MF MF MF
)
(PROGN2
(IF
L
TE TR
S1
0 S
0
2 M
F
)
M
F
))
Fi
gu
re 6.
1.
Ou
t
put
wi
t
h
new
m
e
t
hod
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
20
1 – 21
1
20
8
Fi
gu
re 6.
2.
O
u
t
put
wi
t
h
ne
w m
e
t
hod
B
1
.
o
u
t
p
ut
i
n
c
a
no
ni
cal
G
P
i
n
ne
w
ro
om
1
B
e
st
i
ndi
vi
du
al
:
54
B
e
st
Tree
Dept
h:
6
(IF
LTE (IFL
T
E
S00 MF (PROGN2 (P
LUS (PROGN2
S01 (IFL
TE MF
MF MF MF))
(PROGN2
(PR
O
GN2
TR MB)
MB))
S02
)
M
F
)
S08
MF MF)
Fi
gu
re
7.
1.
O
u
t
put
i
n
ca
no
ni
ca
l
GP
Fi
gu
re
7.
2.
O
u
t
put
i
n
ca
no
ni
ca
l
GP
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
C
ont
r
o
l
i
n
g
Bl
o
a
t
i
n
Ge
net
i
c
P
r
og
ra
m
m
i
n
g F
o
r
Sl
ovi
n
g
Wal
l
Fol
l
o
w
i
n
g
P
r
obl
e
m
(
N
avi
d
Bazrk
ar)
20
9
B
2
. o
u
t
p
ut
wi
t
h
new
m
e
t
hod
i
n
new
r
o
om
1
B
e
st
i
ndi
vi
du
al
:
54
B
e
st
Tree
Dept
h:
4
(IF
LTE (IFLT
E
MB (IFLTE
S00 MB MB MB) (IFLTE
MB EDG MB MB) MB) (
I
FLTE MB MB MB
(IF
LTE TL MB MB
MB)) (IFLTE MF S10 TR (IFLTE
E
DG MB MB
MB)) (IFLTE
MF TR (IFLT
E S00
M
B
(IFL
TE M
S
D
S0
9 M
F
T
R
) M
B
) TR
Fi
gu
re 8.
1.
O
u
t
put
wi
t
h
ne
w m
e
t
hod
Fi
gu
re 8.
2.
O
u
t
put
wi
t
h
ne
w m
e
t
hod
C
1
.
o
u
t
p
ut
i
n
c
a
no
ni
cal
G
P
i
n
ne
w
ro
om
2
B
e
st
i
ndi
vi
du
al
:
33
B
e
st
Tree
Dept
h:
6
(PROGN2
(IF
LTE S09 (IFL
TE (IF
LTE M
F
(IF
LTE S
09
MF (IFL
TE T
R
SS MB MB
) MF) (IFLT
E
TR SS
M
B
M
B
) (PR
O
G
N
2
S
S
S
0
7
0
)
)
M
F
(I
FLT
E
(I
FLTE
S
0
9
MF (
I
FLTE TR SS MB MB) MF)
MF (I
FLTE TR
SS MB MB) (IFLTE S
09 MF
(IFL
TE TR S
S
MB MB) MF)) MF
) (IFLT
E
(IF
LTE (IFL
TE S09 MF (IFLTE
TR SS MB MB) (PROGN2
S05 S03)
) MF
(IFLT
E TR SS MB MB) MF) (IFLTE S
0
9 MF (IF
LTE
TR SS
MB MB) MF) (IFLT
E S09 (IFLTE S
0
9 MF (IFL
TE TR
SS MB MB)
S09) (IFL
TE TR SS MB MB) MF)
(IF
LTE (IFLT
E
(IFLT
E S09 MF (IFLTE
TR SS MB MB
) (PROGN2
S05 S03))
MF (IFLTE TR S
S
MB
MB) MF) (IFL
TE S09 MF
(IFLTE TR S
S
MB MB)
MF) (IF
LTE S
0
9 (IFLTE
S09 M
F
(IFLTE TR
SS MB
MB) S09) (IF
LTE TR SS
MB MB) MF) MF))
(PROGN2
(IF
LTE
S09 MF
(IF
L
TE TR SS M
B
MB)
(PROGN2 SS
S070)) MF
)) (IFLTE (IFLTE
(IF
LTE S09 MF
(IFL
TE TR SS MB MB) (PROGN2 S05
S03))
MF (IFLTE T
R
SS MB MB) MF)
(IFLTE
S09 MF (IF
L
T
E
TR SS MB
MB) (IFLTE
S09 (IFLT
E
S
09 M
F
(IF
LTE TR
SS
MB MB) (PROGN2 S
S
S
070))
(IF
LTE TR
SS MB MB)
MF)) M
F
MF
))
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
20
1 – 21
1
21
0
Fi
gu
re
9.
1.
O
u
t
put
i
n
ca
no
ni
ca
l
GP
Fi
gu
re
9.
2.
O
u
t
put
i
n
ca
no
ni
ca
l
GP
C
2
.
o
u
t
p
ut
wi
t
h
new
m
e
t
hod
i
n
new
r
o
om
2
B
e
st
i
ndi
vi
du
al
:
30
B
e
st
Tree
Dept
h:
2
(IF
LTE
(IFLT
E
MF S
0
9 S
06 MF) MF
(PL
U
S MB TR
) S
0
2)
Fi
gu
re
1
0
.
1
.
O
u
t
p
ut
wi
t
h
ne
w
m
e
t
hod
Evaluation Warning : The document was created with Spire.PDF for Python.