  We consider a coordinated complexity-aware 4D trajectory planning problem in
this paper. A case study of multiple aircraft traversing through a sector that
contains a network of airways and waypoints is utilized to illustrate the model
and solution method. En-route aircraft fly into a sector via certain entering
waypoints, visit intermediate waypoints in sequence along airways and finally
exit the sector via some exiting waypoints. An integer programming model is
proposed as to solve the problem, minimizing the total cost of fuel, delay and
air traffic complexity. Different from most existing literature, this
optimization model explicitly takes air traffic complexity into account in the
4D trajectory planning and can ensure conflict-free at any given time (not only
at discrete time instances). The first-come-first-served (FCFS) heuristics,
commonly adopted in current practice, is also investigated and compared.
Numerical results are included to demonstrate the effectiveness of the model.
