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
FD(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
FN(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

No

25.1
Semestre
octubre-febrero

2022
ISSN
electrónico:

2790-5195
ISSN:
1316-3930
131