An Extension of the Nested Partitions Method
EBERT BREA
Procedure Sampling
of

Surrounding

and

Promising

Region

and

the

Measuring

of

the

Objective

Function

(Part

i)
Let ˆi ←−
0;
if k ≥−
1

then
for ℓ ←−
0

to 2n −−

2

do
for ℓ¯←−
0

to 2m −−

2

do
(b(n−1),
.

.

.

, b(0))2 ←−

c(ℓ);
(¯b(m−1),
.

.

.

,¯b(0))2 ←−

c(ℓ);¯
for r ←−
1

to Ns do
for j ←−
1

to n do
if b(j−1) =
0

then
x(j) ←−u(ˇx(2,j), xˇ(3,j), s)
else
x(j) ←−w(ˇx(1,j), xˇ(2,j), xˇ(3,j), xˇ(4,j), s)
for j ←−
1

to m do
if ¯b(j−1) =
0

then
y(j) ←−u(ˇ¯
y(2,j), yˇ(3,j), s)
else
y(j)
w(ˇy(1,j), yˇ(2,j), yˇ(3,j), yˇ(4,j), s)
Let zst ←−
(x(1),

.

.

.

, x(n)
|
{z
}
n
;
y(n+1),

.

.

.

, y(n+m)
|
{z
}
m
)
Measure the
objective

function

by

f(z)|z
if f(zs)
s
< fˆ(ˆz)

then
Let fˆ(ˆz)
←−

f(zs);
Let zˆ
←−

zs;
Let ˆi ←−Mσ +
1;
for d ←−
1

to 2

do
switch d do
case d=1 do
Let ℓ =
2n −−

1;
Let ℓ¯=
2m −−

2;
case d=2 do
Let ℓ =
2n −−

2;
Let ℓ¯=
2m −−

1;
(b(n−1),
.

.

.

, b(0))2 ←−

c(ℓ);
(¯b(m−1),
.

.

.

,¯b(0))2 ←−

c(ℓ);¯
for r ←−
1

to Ns do
for j ←−
1

to n do
if b(j−1) =
0

then
x(j) ←−u(ˇx(2,j), xˇ(3,j), s)
else
x(j) ←−w(ˇx(1,j), xˇ(2,j), xˇ(3,j), xˇ(4,j), s)
for j ←−
1

to m do
if ¯b(j−1) =
0

then
y(j) ←−
¯u(ˇy(2,j), yˇ(3,j), s)
else
y(j)
w(ˇy(1,j), yˇ(2,j), yˇ(3,j), yˇ(4,j), s)
Let zst ←−
(x(1),

.

.

.

, x(n)
|
{z
}
n
;
y(n+1),

.

.

.

, y(n+m)
|
{z
}
m
)
Measure the
objective

function

by

f(z)|z
if f(zs)
s
< fˆ(ˆz)

then
Let f(ˆˆ
z)

←−

f(zs);
Let zˆ
←−

zs;
Let ˆi ←−Mσ +
1;
Figure 20.
Sampling procedure, part i
Revista
TEKHNÉ

No

25.1
Semestre
octubre-febrero

2022
ISSN
electrónico:

2790-5195
ISSN:
1316-3930
137