Total unimodularity and decomposition method for large-scale air traffic cell transmission model

Strategic flight assignment approach based on multi-objective parallel evolution algorithm with dynamic migration interval

“…8,9 Bertsimas and Patterson presented an efficient deterministic approach with consideration of both the time and route assignment. 10 Sun et al proposed a large-capacity cell transmission model for air traffic flow management [11][12][13] and applied integer program to solve it. Recently, the cooperative co-evolution multi-objective algorithm (CCMA) was introduced to resolve the flight assignment problem in a simplified network.…”

Optimal Traffic Flow Scheduling Using High-Performance Computing

“…It has been shown that the IP has a strong linear program (LP) relaxation [17], allowing for the use of standard LP solvers such as the simplex method, while resulting almost always in binary solutions. Recent work [23,24] has shown that techniques such as the Dantzig-Wolfe (DW) decomposition [25] can exploit the unique block matrix structure of the LP and solve the problem using parallel computation and, in the process, significantly reduce the computation time, even for problems composed of a large number of flights over a large geographical area. Tandale et al [26] have demonstrated an implementation of the decomposition on graphics processing units.…”

A network‐based dynamic air traffic flow model for short‐term en route traffic prediction

“…Thus, in practice, it is difficult to make sound online air traffic control strategies based on the trajectory-based model due to the short forecast horizon and the expensive computational cost.Efficient ATFM requires reasonable prediction of the whole traffic flow situations in the specified airspace, rather than the temporal-spatial information of individual aircraft. Therefore, the aggregate air traffic flow models are introduced recently, which focus on the overall distribution of the air traffic flow in the airspace volumes of interest [5][6][7][8][9][10][11][12][13][18][19][20][21][22][23][24]. Because the aircrafts in the airspace volumes are spatially aggregated, the dimension of the aggregated model depends solely on the number of airspace volumes rather than the total number of aircrafts in the airspace, which will reduce the computational cost significantly.…”

“…Because the aircrafts in the airspace volumes are spatially aggregated, the dimension of the aggregated model depends solely on the number of airspace volumes rather than the total number of aircrafts in the airspace, which will reduce the computational cost significantly. In addition, because the behaviour of the individual aircraft is not taken into account in the aggregated model, it is less sensitive to the uncertainty factors related to individual aircraft, such as the departure delay and the weather, and thus, a longer forecast time horizon with less prediction errors can be achieved.Recently, the aggregated approach is widely discussed in the literatures [5][6][7][8][9][10][11][12][13][18][19][20][21][22][23][24]. A stochastic framework with linear dynamic system model was developed by Sridhar et al, where the dimension of the model depends on the number of control volumes by introducing split parameters to describe the air traffic flow distribution in neighbouring airspace.…”

“…To resolve the diffusion problem of air traffic flow transforming between neighbouring airspace due to the introduction of the split parameters, Sun et al proposed a Eulerian-Lagrangian model, which uses the real origin-destination information from the flight plan instead of the constant split parameters derived from the historical data [20][21][22]. Wei et al and Cao et al further explored the Eulerian-Lagrangian model for air traffic flow prediction and management decision-making optimization [23,24]. The main limitation of the current method is the assumption that the speed of air traffic is considered to be constant within a specified en route airspace, which means the time-invariant aggregate air traffic model ignores not only the dynamics of air traffic flow both in time and space but also the uncertainty factors like the weather and the traffic conditions.Aimed at modelling and predicting the traffic flow in en route airspace with full consideration of the dynamics and uncertainty of the air traffic, this paper proposes a novel dynamic air traffic flow model based on the network of en route traffic flow.…”