2
D
5
4
5
4
100
.
000
2005
137
0
,
66
M ev
60
γ
α
β
2
D
3
D
2005
467
.
440
1
.
000
2000
10
2005
467
.
440
43
.
330 17
.
110
49
.
470
20
.
690
2005
2005
229
.
610
2005
237
.
830
100
.
000
2000
10
53%
902
543
1
20
05
0
20000
40000
60000
80000
100000
120000
140000
Outras localidades
Pele Melanoma
Cavidade Oral
Leucemias
Esofago
Colon e Reto
Prostata
Colo do Ultero
Estomago
Traqueia, Bronquio e Pulmao
Mama Feminina
Pele nao Melanoma
Quantidade de casos estimados para 2005
Feminino
Masculino
50
−
1775
200
100%
•
•
•
•
•
•
2
5
5
10
25%
320
−
400
nm
280
−
320
nm
50%
•
α
214
Po
7
,
6
10
9
α
α
α
β γ
1896
α
α
2
+2
4
α
3
.
000
30
.
000
Km/s
2
8
cm
α
α
α
1911
1
a
α
α
α
X
A
Z
Q
a
α
A
Z
X
−→
A
−
4
Z
−
2
X +
α
+ Q
α
226
(88 = 86 + 2)
(226 = 222 + 4)
β
β
70
.
000
300
.
000
Km/s
1
cm
1
mm
50
100
α
3
m
β
β
2
a
β
β
β
A
Z
X
−→
−
0
1
β
+
Z
+1
A
X
210
83
Bi
−→
−
0
1
β
+
210
84
P o
γ
γ
λ
= 0
,
01
0
,
001
γ
(300
.
000
Km/s
)
γ
α
β
γ
20
cm
5
cm
γ
γ
α
β
γ
γ
γ
A
Z
X
−→
A
Z
X
+
γ
60
27
Co
−→
60
27
Co
+
γ
α
β
γ
t
= 0
s
N
0
λ
t >
0
s
N
λN
N
−
dN
dt
λN
N
N
0
t
−
dN
dt
=
λN
dN
N
=
−
λdt
N
N
0
dN
N
=
−
λ
t
t
0
dt
ln(
N
)
−
ln(
N
0
) =
−
λ
(
t
−
0)
ln
N
N
0
=
−
λt
e
−
λt
=
N
N
0
N
=
N
0
e
−
λt
−
dN
dt
=
A
=
λN
T
=
t
0
−→
λN
0
=
A
0
T
=
t
−→
λN
=
A
A
A
0
=
λN
λN
0
N
N
0
A
A
0
=
e
−
λt
A
=
A
0
e
−
λt
Bq
= 1
s
−
1
1
g
0
,
05
5
pm
10
nm
400
nm
800
nm
Catodo
Anodo
A
Energia: E2
Energia: E1
Nucleo
Eletrons
Lacuna provocada
pela retirada de eletron
Emissao
Foton com energia (E2 − E1)
B
C
γ
μ
−
1
Fonte Radioativa
Material
Colimador
μ
= 0
,
10
−
1
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
Intensidade transmitida relativa
Distancia em Cm
x
dx
dI
I
dI
=
−
μIdx
dI
I
=
−
μdx
dI
I
=
−
μ
dx
ln
I
−
ln
I
0
=
−
μ
(
x
−
x
0
)
ln
I
I
0
=
−
μ
(
x
−
0)
ln
I
I
0
=
−
μx
I
I
0
=
e
−
μx
I
=
I
0
e
−
μx
I
1
I
2
=
d
2
d
1
2
γ
1
3
0
,
001293
Δ
Q
Δ
m
X
=
Δ
Q
Δ
m
[
X
] =
C
Kg
1
R
= 2
,
58
.
10
−
4
C
kg
100
0
,
01
Δ
E
Δ
m
D
=
Δ
E
Δ
m
Gy
=
1
J
k
m
m
K
=
Δ
N
Δ
a
.hf.μ
k
/ρ
μ
k
/ρ
=
μ
hf ρ
E
k
Δ
N
Δ
a
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
Ionizacao relativa
137
Cs
60
Co
137
0
,
66
M ev
60
γ
1
,
17
M ev
1
,
33
M ev
espalhado
espalhado
foton
incidente
eletron
livre
a
b
266
1896
20
1930
130
2
D
2
D
2
D
3
D
15
−
30
4
D
4
D
3
D
1646
−
1716
1707
−
1783
1736
−
1813
1805
−
1865
1842
−
1919
1878
−
1909
1871
−
1945
1848
−
1923
ℜ
2
(1
,
1)
T
(3
,
3)
T
(1
,
3)
T
(3
,
1)
T
x
∗
∈
S
x
∈
S
f
i
(
x
)
f
i
(
x
)
≤
f
i
(
x
∗
)
∀
i
= 1
, . . . , k
f
j
(
x
)
< f
j
(
x
∗
)
j
z
∗
∈
Z
z
∈
Z
z
i
≤
z
i
∗
∀
i
= 1
, . . . , k
z
j
< z
j
∗
a, b
∈ ℜ
n
a
≻
b
↔
a
i
≥
b
i
∧ ∃
j
|
(
a
j
> b
j
)
a
⊁
b
↔
a
i
=
b
i
∨
(
∃
j
|
(
a
j
> bj
)
∧ ∃
k
|
(
a
k
< b
k
))
j, i
= 1
, . . . , n
;
i
=
j
;
i
=
k
;
n
≥
2
(2
,
2)
T
(3
,
1)
T
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
objetivo 2
objetivo 1
LS
T
D
N
D
S
LS
LN
x
D
T
D
N
D
S
F
p
n
3
xn
3
ℜ
3
n
F
p
n
max
D
T
(
X, F
n
p
) =
D
(
x
T
, F
n
p
)
min
D
N
(
X, F
n
p
) =
D
(
x
N
, F
n
p
)
min
D
S
(
X, F
n
p
) =
D
(
x
S
, F
n
p
)
s.t.
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
D
T
(
X, F
n
p
)
< LS
T
D
T
(
X, F
n
p
)
> LI
T
D
N
(
X, F
n
p
)
≤
D
S
(
X, F
n
p
)
< LS
S
X
=
⎛
⎜
⎜
⎝
x
T
x
N
x
S
⎞
⎟
⎟
⎠
F
p
D
T
D
S
D
N
Tumor
Silhueta
Estruturas
Nobres
Feixe
Tumor
Silhueta
Estruturas
Nobres
Feixe
Colimador
Fonte Radioativa
ℜ
2
ω
∈ ℜ
ψ
∈ ℜ
P
∈ ℜ
2
ψ
E
∈ ℜ
2
U
∈ ℜ
2
ψ
ω
Tumor
E
U
F
P
2
D
X
F
p
n
2
D
2
D
3
D
3
D
2
D
E
P
=
E
H
x
x
P
H
e
−
μx
P
3
D
7
6
5
4
3
2
1
I
H
G
F
E
D
C
B
A
l
=
⌊
√
d
∗
v
2
⌋
c
=
⌊
h
v
⌋
e
=
a
l.c
160
mm
F
p
n
Sadios
Tumor
Nobres
Sadios
E
P
P
E
H
μ
(
cm
−
1
)
x
(
cm
)
H
P
x
H
x
P
(
x
P
+
Silhueta do Paciente
P
Tumor
Acelerador
Linear
Feixe
X
+
H − Equilibrio Eletronico
Espessura de Equilibrio Eletronico
I
P
=
I
H
e
−
μx
P
E
P
T
P
.x
P
=
E
H
T
H
.x
H
e
−
μx
P
T
H
=
T
P
E
P
x
P
=
E
H
x
H
e
−
μx
P
E
P
=
E
H
x
P
x
H
e
−
μx
P
D
= [
d
ij
]
(
L,C
)
L
2
D
2
D
D
E
P
=
E
H
x
P
x
H
e
−
μx
P
d
ij
=
k
b
=1
E
H
.
(
b,i,j
)
x
P
x
H
e
−
μ
(b,i,j)
x
P
d
ij
=
E
H
x
H
k
b
=1
(
b,i,j
)
x
p
e
−
μ
(b,i,j)
x
P
E
P
E
H
P
H
x
P
x
H
P
H
μ
−
1
k
b
P
i
j
f
obj
2
D
D
corpo
B
p
d
S
n
n
ℜ
2
S
n
{
d, i, j, m, n, o, p
∈
N
∗
}
S
n
=
{
(
v
1
, . . . , v
n
)
|
v
i
∈ ℜ
2
}
T umor
∈
S
m
T ecidos
∈
S
o
Orgoes
∈ {
S
α
,
S
β
,
S
γ
, . . .
}
B
p
d
=
{
(
b
1
, . . . , b
p
)
| ∀
b
i
∈
S
d
}
D
corpo
= (
T umor, Orgoes, T ecidos
)
Area
:
S
n
→ ℜ
S
T
=
i
≤
L
i=1
i∈T umor
j
≤
C
j=1
j∈T umor
1
S
O
=
i
≤
L
i=1
i∈Orgoes
j
≤
C
j=1
j∈Orgaos
1
S
S
=
i
≤
L
i=1
i∈T ecidos
j
≤
C
j=1
j∈T ecidos
A
T
=
Area
i
≤
p
i
=1
T umor
∩
(
i
)
B
p
d
A
O
=
Area
i≤p
j≤m
i=1
j=1
(
j
)
Orgoes
∩
(
i
)
B
p
d
A
S
=
Area
i
≤
p
i
=1
T ecidos
∩
(
i
)
B
p
d
A U B
A
B
A B
U
D
T
=
i
≤
L
i=1
i∈T umor
j
≤
C
j=1
j∈T umor
D
ij
D
O
=
i
≤
L
i=1
i∈Orgoes
j
≤
C
j=1
j∈Orgoes
D
ij
D
S
=
i
≤
L
i=1
i∈T ecidos
j
≤
C
j=1
j∈T ecidos
D
ij
(
δ
T
)
2
=
i
≤
L
i=1
i∈T umor
j
≤
C
j=1
j∈T umor
D
ij
−
D
S
T
T
2
LC
−
1
(
δ
O
)
2
=
i
≤
L
i=1
i∈Orgoes
j
≤
C
j=1
j∈Orgoes
D
ij
−
D
A
O
O
2
LC
−
1
(
δ
S
)
2
=
i
≤
L
i=1
i∈T ecidos
j
≤
C
j=1
j∈T ecidos
D
ij
−
D
A
S
S
2
LC
−
1
O
T
O
T
δ
T
O
O
O
S
O
T
=
A
T
(
S
T
)
2
.
D
T
1 +
δ
T
O
O
=
−
1
A
O
.D
O
.
(1 +
δ
O
)
O
S
=
−
1
A
S
.D
S
.
(1 +
δ
S
)
f
obj
: (
D
corpo
,
B
p
d
)
→
(
O
T
, O
O
, O
S
)
3
2
D
1960
10
ψ
0
,
5
0
,
3
0
,
2
i
+1
i
+1
mlc
i
+1
mlc
=
min
(
linha, coluna
)
plinha
i
+1
= ((
rand
()
mod mlc
) +
plinha
i
)
mod linha
pcoluna
i
+1
= ((
rand
()
mod mlc
) +
pcoluna
i
)
mod coluna
anglo
i
+1
= (
anglo
i
+ (
rand
()
mod
15 + 1))
mod
360
P
(
F
; 8)
ψ
(
F
; 8)
β
ψ
ψ
P
Q
(
F
; 8)
(
H
; 8)
(
F
; 9)
R
α
corrente
←
genesis
()
elite
←
φ
(
tempo
()
< T EMP O
)
f ilho
←
φ
paretoRank
(
corrente
)
(
i
←
0;
i <
|
corrente
|
/
2;
i
←
i
+ 1)
a
←
roleta
(
corrente
)
b
←
roleta
(
corrente
)
cruzamento
(
ab, ba, a, b
)
(
j
←
0;
j < MUT ACOES
;
j
←
j
+ 1)
(
mutAnglo
(
ab
)
≻
ab
)
(
mutP ontaria
(
ab
)
≻
ab
)
(
j
←
0;
j < MUT ACOES
;
j
←
j
+ 1)
(
mutAnglo
(
ba
)
≻
ba
)
(
mutP ontaria
(
ba
)
≻
ba
)
c
1
←
torneioBinario
(
a, ab
)
c
2
←
torneioBinario
(
b, ba
)
f ilho
←
f ilho
{
c
1
, c
2
}
corrente
←
f ilho
elite
←
elite
paretoSet
(
f ilho
)
saida
←
paretoSet
(
elite
)
10% 20% 30%
40%
50 100 150 200
10%
70%
10
150
20%
70%
150
30%
20
30% 50%
150
20
30
40%
0 100 200 300 400 500 600
0 5 10 15 20 25 30
Solucoes Melhoradas Decadas
10%
0 50 100 150 200 250 300 350 400 450 5000 5 10 15 20 25 30 35
Solucoes Melhoradas Decadas
20%
0 50 100 150 200 250 300 350 400 450 5000 5 10 15 20 25 30 35
Solucoes Melhoradas Decadas
30%
0 50 100 150 200 250 300 350 400 450 5000 2 4 6 8 10 12 14 16 18 20
Solucoes Melhoradas
Decadas
0 100 200 300 400 500 600
0 5 10 15 20 25
Solucoes Melhoradas Decadas
50
0 100 200 300 400 500 600 700 800 900 10000 2 4 6 8 10 12 14
Solucoes Melhoradas Decadas
100
0 200 400 600 800 1000 1200 1400 16000 1 2 3 4 5 6 7
Solucoes Melhoradas Decadas
150
0 200 400 600 800 1000 1200 1400 1600 1800 20000 1 2 3 4 5
Solucoes Melhoradas
Decadas
genesis
←
genesis
()
local
←
φ
(
tempo
()
< T EMP O
)
(
i
←
0;
i <
|
repositorio
|
;
i
←
i
+ 1)
melhor
←
NADIR
sol
i
←
genesis
[
i
]
(
c
←
0;
c < MOV IMENT O
;
c
←
c
+ 1)
solT abu
←
getListaT abu
()
solLivre
←
x
|
x
∈ {{
vizinho
(
sol
i
)
}
ListaT abu
}
ListaT abu
←
ListaT abu
{
solLivre
}
|
ListaT abu
|
> T AMANHO LIST A
ListaT abu
←
ListaT abu
{
getListaT abu
()
}
vencedor
←
(
solT abu
≻
solLivre
?
solT abu
:
solLivre
)
!(
melhor
≻
vencedor
)
(
vendedor
=
solT abu
)
ListaT abu
←
ListaT abu
{
solT abu
}
(
vencedor
≻
melhor
)
melhor
←
vencedor
local
←
local
{
vencedor
}
destruir
(
vencedor
)
10
360
,
720
,
1080
1800
0 5 10 15 20 25 30 35 40 45 50
0 5 10 15 20 25 30
Solucoes Melhoradas Solucoes Processadas
360
0 5 10 15 20 25 30 35 40 450 5 10 15 20 25 30
Solucoes Melhoradas Solucoes Processadas
720
0 5 10 15 20 25 30 35 40 45 500 5 10 15 20 25 30
Solucoes Melhoradas Solucoes Processadas
1080
0 10 20 30 40 50 60 700 5 10 15 20 25 30
Solucoes Melhoradas
Solucoes Processadas
1800
720
P
=
exp
−
Δ
E
K
B
.T
T
Δ
E
K
B
Δ
E
T
a
b
P
=
exp
−
cos(
a, b
)
T
P
ψ
P
n
.x
=
P
n
−
1
.x
+
T.
[0 : 1]
P
n
.y
=
P
n
−
1
.y
+
T.
[0 : 1]
ψ
n
= (
ψ
n
−
1
+
T.
[0 : 1](
))(
)
cos(
a, b
)
[
]
ℜ
n
[0; 1]
0
1
(
rand
[0
,
1]
< e
P
′
)
cos(
a,b
) =
a.
b
repositorio
←
genesis
()
local
←
φ
(
tempo
()
< T EMP O
)
(
i
←
0;
i <
|
repositorio
|
;
i
←
i
+ 1)
T emp
←
T EMP MAX
S
0
←
repositorio
[
i
]
(
T emp > T EMP MIN
)
(
t
←
0;
t < T ENT AR
;
t
←
t
+ 1)
S
←
vizinho
(
S
0
)
(
S
≻
S
0
)
∨
(
rand
[0
,
1]
< P
)
S
0
←
S
(
S
≻
S
0
)
local
←
local
{
S
}
T emp
←
esquemaAnnealing
(
T emp
)
saida
←
paretoSet
(
local
)
α
T
α
[0
,
8; 0
,
99]
β
1
m
T
i
=
T
i
−
1
1 +
βT
i
−
1
β
=
1
m
.
T
0
−
T
m
T
0
T
m
≪
T
0
40
60
80
100
120
140
160
180
200
0
5
10
15
20
25
30
Solucoes Melhoradas
Solucoes Processadas
α
= 0
,
99
0
100
200
300
400
500
600
0
1
2
3
4
5
6
Solucoes Melhoradas
Solucoes Processadas
30
C
(
A, B
) = 1
B
A
C
(
A, B
) = 0
A
B
C
(
A, B
) =
|{
Z
∈
B
} ∃
z
∈
A
:
z
≻
z
|
|
B
|
3
4
5
3
4
5
3
4
5
3
4
5
0
,
113557
5
-12
-10
-8
-6
-4
-2
0
2
4
0
200
400
600
800
1000
1200
Objetivos
Solucoes
6
7
-1.5
-1
-0.5
0
0.5
1
1.5
0
10
20
30
40
50
60
70
80
90
100
Objetivos
Solucoes
2
2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0
1
2
3
4
5
6
7
8
9
Objetivos
Solucoes
2
2
2
2
0 0.5 1 1.5 2 2.5 3-1.8 -1.6 -1.4-1.2 -1-0.8 -0.6-0.4 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 Sadios Tumor Nobres Sadios
0 0.2 0.4 0.6
0.8 1 1.2 1.4
1.6 1.8-1.8-1.6 -1.4-1.2 -1-0.8 -0.6-0.4 -0.2 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Sadios Tumor Nobres Sadios
0.2 0.4 0.6 0.8 1
1.2 1.4 1.6 1.8 2
0 0.5 1
1.5 2 2.5
3 3.5 4 -2 -1.8-1.6 -1.4-1.2 -1-0.8 -0.6-0.4 -0.2 -1.1-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Sadios Tumor Nobres Sadios 0 0.5 1 1.5 2
2.5 3
3.5-4.5-4 -3.5-3
-2.5-2 -1.5-1
-0.5 0 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 Sadios Tumor Nobres Sadios 0 0.5 1 1.5 2 2.5-1.1-1
0 0.5 1
1.5 2 2.5
3 3.5 4-1.8 -1.6-1.4 -1.2-1 -0.8-0.6 -0.4-0.2 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Sadios Tumor Nobres Sadios 0 0.5 1 1.5 2 2.5 3-2.5 -2 -1.5 -1 -0.5 0 -1.1-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Sadios Tumor Nobres Sadios
0.2 0.4 0.6 0.8 1
1.2 1.4 1.6 1.8 2
2.2-1.1-1 -0.9-0.8 -0.7-0.6 -0.5-0.4 -0.3-0.2 -0.1 -1.2 -1.1-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Sadios Tumor Nobres Sadios 0 0.5 1 1.5 2 2.5 3-1.6 -1.4-1.2 -1-0.8 -0.6-0.4
