Geoscience Reference
In-Depth Information
problems: the radius R, the minimal distance in (
6.20
), and the number of knots r.
As stopping criterion, the algorithm, stopped when the gap was smaller than 10
2
:
In order to reduce the random variability of the results, for each choice of radius
R; minimal distance and number of knots r; three independent instances were
generated and solved. The results presented in the tables correspond to the median
out of the three values obtained.
In Table
6.1
running times in seconds are shown for the problem of locating one
facility with a smaller and a larger radius (R
D
1:8 and R
D
2:4). It is not surprising
that the computational time grows with the number of knots, as for all knots we need
to do at least one integration.
Running times in seconds are reported in Table
6.2
for the problem of locating
two facilities. Again, the values presented are the median value of the three runs
performed. When at least two out of the three instances could not reach the desired
accuracy in 8 h, the message “>8h” is reported. The results clearly show that,
the higher the number of knots or the radius, the higher the running times. The
connection between the elapsed time and the minimal distance is not so evident.
One can find cases where either smaller or higher minimal distance can be solved
faster, so it looks rather problem dependent.
A second experiment was done in order to analyze the impact of the radius,
displaying the Pareto frontier if one maximizes the radius and minimizes the
coverage. In Fig.
6.3
the Pareto front is displayed for a problem with a mixture
of 50 bivariate gaussian distributions setting minimal distance
D
R, and radii
R
D
0:45;0:6;:::;1:65;1:8. The pdf of such mixture of gaussians was shown in
Tabl e 6. 1
Results for
single-facility problems
(p D 1) with different
minimal distances
r
R D 1:8
R D 2:4
10
3.6
1.9
20
11.8
38.0
50
143.7
244.0
100
675.5
897.6
Tabl e 6. 2
Results for
two-facility problems
(p D 2) with different
minimal distances
r Minimal distance R
D
1:2 R
D
1:8
10 R
110.5
186.1
1:5R
182.8
124.7
2R
178.1
83.4
20 R
114.0
2714.5
1:5R
95.7
2593.5
2R
86.4
2543.9
50 R
3926.2
12282.9
1:5R
3754.7
18167.5
2R
3675.1
>8h
100 R
20026.1 >8h
1:5R
>8h
>8h
2R
>8h
>8h
