IEEE Computational Intelligence Magazine - May 2021 - 94
varying departure time except that we fix
the departure time to 0:00.
In terms of the path utility score, for
all three algorithms, the path utility
score increases as the utility edge gets
denser in the road network. Again, 2TD
achieves the best performance under all
utility densities. We can further observe
that the increment of the path utility
score becomes marginal if increased from
a bigger utility density. This is because all
three algorithms iteratively select and
insert " best " utility edges in the path and
fill the gaps between the inserted utility
edges based on the shortest path-finding
algorithms. Therefore, two parts contrib-
ute the final path utility score, i.e., all
inserted utility edges and all utility edges
contained by the gap-filling paths. It is
easy to understand that the second part
would dominantly contribute the total
path utility score if the utility density
gets big. In addition, with the increase of
utility density, compared to MA, the
advantage of 2TD becomes not obvious. This is because the first part of the
final path utility score is the main
improvement of 2TD.
In terms of the running time, quite
different from the previous studies, SRN
needs the least running time under
almost all utility densities except when
1,200
1.8
2TD
MA
SRN
1.6
1,000
Running Time (s)
Path Utility Score
1.4
1.2
1
0.8
0.6
0.4
800
600
8
7
2TD
MA
SRN
6
5
4
3
2
400
1
5
200
0.2
5
30
55
80
Utility Density (%)
utility density is 5%. Both 2TD and
MA algorithms require a longer running time as the utility edge gets denser.
Worse still, the running time of MA
grows exponentially with the utility
density. For example, the average running time is up to 630 seconds, which
cannot be acceptable. This is because the
number of chromosomes generated by
MA increases exponentially with the
number of utility edges. For 2TD, on
one hand, as discussed, the reachability
timetable building operation accelerates
the population generation; on the other
hand, 4 new utility edges at most can be
inserted at one iteration in most cases
100
5
30
30
55
(%)
80
100
55
80
Utility Density (%)
100
FIGURE 7 Results of the path utility score and running time under different utility densities for all three algorithms.
1.8
50
2TD
MA
SRN
1.6
40
Running Time (s)
Path Utility Score
1.4
1.2
1
0.8
0.6
0.4
2TD
MA
SRN
30
20
10
0.2
1
1.5
2
2.5
Driving Distance (km)
3
1
1.5
2
2.5
Driving Distance (km)
FIGURE 8 Results of the path utility score and running time under different driving distances for all three algorithms.
94
IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2021
3
IEEE Computational Intelligence Magazine - May 2021
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