Models for Global Constraint Applications - Cork Constraint ...

2.3.3 Moving planes
Our model so far assumed that planes are parked in the same location for their
entire stay at the airport. In certain situations a plane might be moved by a
tractor to another stand, in order to free up space at the terminal or because the
plane is required at a different position. The tractors are also required to “pushback”
departing flights from the gate, since turbine engines can not be used to
reverse the plane, and also to move planes on the ground more economically. If
additional plane movements are allowed, we gain a degree of freedom in deciding
when the plane should be moved. But this is best decided heuristically before
the constraint model is set-up, since otherwise the non-overlap condition can
no longer be expressed with the given models. We would also have to consider
cumulative resource constraints for the tractors.
2.4 Incremental Resolving
We have assumed that the start and end times of the parking activities are
constants when the model is set-up. In practice, these times are constantly
changing, since planes arrive or depart later than predicted or planes arrive
before their scheduled arrival time. This may invalidate the previous solution,
and we have to re-run the solver. Many elements of the previous solution must
be kept; all planes currently on a stand must continue to stay there in an updated
solution. Some part of the future schedule may be fixed as well: if passengers
already have been sent to a gate, it is quite difficult to reverse that decision.
We also can make our solution more robust by introducing safety margins
in the overlap constraints. We extend each parking period by some margin
before its arrival and/or after its departure and compute solutions using these
extended time intervals. If flight times change only slightly during the day,
then the previous solution will still be feasible. Choosing the right compromise
between cost optimisation and safety margins is an important interactive choice,
which also depends on the current state of operations.
2.5 Search
The choice of an appropriate search routine is essential for solving large scale
problems, even if the constraint model is quite powerful. The problem size
typically prohibits an exhaustive search of all possible assignments to find an
optimal solution, especially since the solving times should be in seconds due to
the rapid change of the underlying data. The search routine was refined in a
number of steps, beginning with a static ordering.
In a first version, the planes are ordered statically by decreasing number of
passengers, and the domains are enumerated such that stands at the terminals
are tested first. This can be done by enumerating the qi variable of a plane
before fixing its yi variable. A feasible solution (often of acceptable quality)
will be found without backtracking, but search for the optimal solution leads to
shallow backtracking.
The next improvement is to choose the stand more wisely. For this, we
statically calculate an indicator demandj which describes how many planes want
to use a given stand j at a terminal. For this calculation we restrict the domains
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