IEEE Computational Intelligence Magazine - May 2021 - 97

0.016
0.014

Path Utility Score

1.2

0.8
0.6
0.4

0.01
0.008
0.006
0.004

0.2
0

0.012

0.002
0:00

6:00
12:00
Departure Time (SFC)
2TD

w/o_R1

18:00

w/o_R2

0:00

w/o_R3

6:00
12:00
Departure Time (NYC)

w/o_R4

18:00

w/o_ss

FIGURE 11 Results of the path utility score under different departure times for 2TD and its variants.

2TD obtains the highest path utility
score for all departure times in the two
cities, compared to the other 5 variants,
with the result shown in Fig. 11. In the
chromosome encoding, we can observe
that each rule is effective in improving
the path utility score but their effectiveness varies. Specifically, Rule 1 and Rule
2 have quite a big impact on the path
utility score, while Rule 3 and Rule 4
have relatively little impact. The path
utility score is even reduced at least by
half when not applying Rule 2.
Compared to 2TD, we can observe
that the path utility score is slightly reduced
without the secondary selection operation.
This is because when the departure time of
the first edge is in the range of critical timezone in the original 2TD, one more edge
will be selected from the edge timetable to
deal with the situation when the first edge
is actually unreachable. In this case, as for the
w/o_ss, there is only one edge selected and
added to the chromosome, resulting in an
invalid chromosome. The diversity of chromosomes would be reduced, which is not
conducive to finding a high-utility path.
C. Case Study: Recommending the
Optimal Patrol Routes

It is well-known that the utility as the
form of scenic score can be useful in
real applications, such as finding the

Police Department

The Plaza

FIGURE 12 The time-dependent optimal patrol route (best viewed in an enlarged digital version).

most beautiful driving routes [1], [22].
In this study, we will showcase the
potential applications of the utility as the
form of risky score based on the NYC
road network. To be more specific, we
aim to suggest time-dependent most
risky patrol routes for policemen. The
application can be very helpful for the
policemen to prevent potential crimes
along the route and make the city safer.
In this study, we set the origin to the
New York City Police Department and the
destination to the Plaza, with locations
shown in Fig. 12. The departure time
and time budget are set to 0:00 and 35
minutes, respectively.

The time-dependent most risky
driving route from the Police Department
to the Plaza obtained by 2TD is plotted
in Fig. 12. To highlight the differences,
we use three colors to label different
utility edges during the trip time. In
more detail, we use red to denote the
high-value utility edge, blue to denote
the median-value utility edge, and black
to denote the non-utility edge, respectively. In addition, for the reference, we
also plot the heat-map of reported
crime events in Fig. 12. The more the
reported crime events in the region, the
darker the color. We can draw the conclusion that the suggested driving route

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IEEE Computational Intelligence Magazine - May 2021

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