Computational Intelligence - November 2014 - 59

B. Traffic with TMA

To avoid the N(N-1)/2 time-consuming pair-wise
Since it is not possible to modify the shape
of the trajectories in the TMA, the TMAcomparisons, which are prohibitive in our continentraffic is much more constrained than the
talscale application context, we propose a grid-based
en-route traffic. Indeed, the interactions
interaction detection scheme which is implemented
occurring in en-route airspace can be separated in space and in time, while the interin a so-called hash table.
actions occurring in the TMA can only be
separated by acting in the time domain. In
tions. Moreover, the algorithm has to modify more trajectoorder to take into account the trajectory segments that
ries in order to solve all the interactions.
belong to the TMA, we first set the size of the minimum
One observes that the computation time required to
separation N hTMA to 3 NM. The trajectory set consists of
obtain the interaction-free solution depends on the size of
N = 30, 695 trajectories which yields U tot,initial = 235, 632
the solution space. As expected, with the same setting
initial interactions.
The input parameters of the optimization algorithm are,
d i = 0.12 and maximum time shift, -d ia = d id = 60 minutes
here again, empirically set. Two different values for the maxi(case 1), the algorithm requires significantly more computamum departure time shift (- d ia, d id) and for the maximum
tion time for solving the scenario with TMA traffic than to
solve the scenario involving only en-route traffic. However,
route length extension (d i) are used, and their values are given
the required computation time decreases significantly when
in Table 3. The simulation is carried out 10 times for each of
the solution space is relaxed (i.e., when more candidate soluthe three cases in Table 3. Again, the proposed algorithm is
tions are considered; case 2 and case 3).
able to find interaction-free solutions ^U tot,final = 0h for the
given traffic situation involving the high-density traffic
occurring in the TMA. The computation time and the numC. Taking into Account Uncertainty
ber of modified trajectories relevant to each case of the optiIn this subsection, we consider the uncertainty of aircraft posimization constraints are compared in Figure 19.
tion in the horizontal plane. Simulations were performed on
Remark that the initial interaction when taking into
both the en-route traffic scenario, and on the traffic scenario
account the air-traffic in the TMA is significantly higher than
involving the TMA. The uncertainty margin in en-route is set
when considering only en-route traffic. This is due to the
to R enroute = 3 NM. The uncertainty margin in the TMA is not
high density of the traffic in the TMA. In addition, our intertaken into account ^R TMA = 0h, since during this phase of
action-detection method cannot distinguish aircraft using
flight, aircraft are usually required to follow a given path with
parallel runways from actual interaction. This leads to some
very high precision. The user-defined input parameters of the
false-positive contributions to the interactions. This larger
optimization algorithm are empirically set as follows. The maxproblem instance is more difficult to solve, and requires lonimum departure time shift is -d ia, d id = 120 minutes, and the
ger computation time to converge to interaction-free solumaximum route length extension d i is 0.25. The number of
1400
Number of Modified Trajectories (%)

Computation Time (minutes)

1200
1000
800
600
400
200
0

Case 1

Case 2
(a)

Case 3

Modified Routes
Modified Departure Times

80
70
60
50
40
30
20
10
0

Case 1

Case 2

Case 3

(b)

Figure 19 (a) Impact of the size of the solution space on the computation time. (b) Impact of the size of the solution space on the number of
modified routes and the number of modified departure times.

november 2014 | Ieee ComputatIonal IntellIgenCe magazIne

Table of Contents for the Digital Edition of Computational Intelligence - November 2014