An Extension of the Nested Partitions Method
EBERT BREA
Table II.
Summary of the MINP, in which just 1 sample
reached 163 cumulative iterations
f
(
z
)
N
(2
,
2
,
2)
L
(2
,
2
,
2)
Q
(2
,
2
,
2)
Mean
-95.30
5512.32
25.18
1.69e-5
SSD
524.23
4191.62
9.22
2.99e-5
Min
-453.59
2016
1.45
1.25e-6
Q1
-306.94
2808
20.84
5.49e-6
Q2
-215.29
4272
25.05
9.25e-6
Q3
-108.82
6672
32.23
1.45e-5
Max
4265.34
28032
44.54
1.99e-4
From
Figure
13
it
may
be
inferred
that
less
than
10
%
of
the
reported
replications
identified
solutions
to
a
distance
to
the
true
point
less
than
10.
10
20
30
40
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
.
0
0
F
D
(
d
)
d
Figure 13.
Empirical CDF of the DTP for the W
function problem
Figure
14
shows
cumulative
distribution
function
of
the
NE
when
the
MINP
method
is
used
for
globally
solving
the
W
function
problem.
Note
that
the
MINP
at
least
required,
in
this
case,
about
28,000
objective
function
evaluations.
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
.
0
0
5000
10000
15000
20000
25000
F
N
(
η
)
η
Figure 14.
Empirical CDF of the NE for the W
function problem
c
.
ICEBERG
PROBLEM
The
third
problem
of
optimization
is
based
on
an
unpub-
lished
objective
function,
whose
mathematical
expres-
sion
is
given
in
Appendix
A.
Table III.
Summary of the MINP, in which just 1 sample
reached 101 cumulative iterations
f
(
z
)
N
(3
,
2
,
2)
L
(3
,
2
,
2)
Q
(3
,
2
,
2)
Mean
-2649.00
SSD
4441.92
7.448
2.41e-4
583.91
3256.11
2.987
7.41e-4
Min
-3773.35
1440
0.005
6.07e-6
Q1
-3041.65
1920
6.135
2.32e-5
Q2
-2598.08
3504
8.368
4.07e-5
Q3
-2188.85
5736
9.472
7.99e-5
Max
-1326.02
16608
13.03
5.02e-3
Table
III
shows
a
statistical
summary
of
the
random
variables:
N
(3
,
2
,
2)
,
L
(3
,
2
,
2)
and
Q
(3
,
2
,
2)
.
As
can
be
seen
from
the
table,
the
MINP
method
reported
good
enough
solutions,
because
the
25
%
of
replications
identified
solutions
to
the
true
point
less
than
6.135,
and
that
can
be
verified
from
Figure
15,
which
illustrates
the
empirical
CDF
of
the
DTP
for
our
problem.
Revista
TEKHNÉ
N
o
25.1
Semestre
octubre-febrero
2022
ISSN
electrónico:
2790-5195
ISSN:
1316-3930
131