Sequence Assignment Model for the Flight Conflict Resolution Problem

Abstract

E ach and every day, certain air route traffic control centers receive a large number of requested flight plans, each detailing the level, track, and entry time for the flight to enter the oceanic airspace. Because each airline independently optimizes its own flight plans, it is common that the requested flight plans result in an unbalanced usage of level and track capacities and a conflicting schedule that violates the Federal Aviation Administration (FAA) safety standards. In such a situation, the flight conflict resolution problem is to provide a schedule that minimizes the total penalty cost of delay, level change, and track change while maintaining the FAA separation standards. In this paper, we propose a flight sequence assignment model (FSAM) that selects an optimal set of flight sequences to minimize the total penalty cost. We develop a column generation framework with a bilinear pricing subproblem to solve the linear relaxation of the FSAM, and use a branch-and-price method to find the integer optimal solution. The proposed model is tested on 10 simulated instances randomly constructed based on a real data set. The results show that the FSAM outperforms all other methods in all test instances. We also extend the FSAM to incorporate equity of flight plans among airlines. The computational results show that the equity constraints marginally increase the overall schedule disruption.

Daily berth planning in a tidal port with channel flow control

“…Similar observations have been reported in many other applications using set-partitioning based model, such as crew pairing problem (Barnhart et al, 2003), aircraft routing problem (Barnhart et al, 1998), aircraft conflict resolution problem (Liang et al, 2014), parallel machine scheduling problem (van den Akker et al 1999), to name but a few.…”

“…Therefore, we propose a column generation algorithm to generate good vessel plans. Column generation algorithm has been widely and successfully applied to many large-scale, real-life optimization problems in the areas such as transportation (Barnhart et al, 1998, Baldacci et al, 2011, Liang et al 2014, Meng et al 2015, machine scheduling (Van den Akker et al 1999, Chen et al 1999, bioinformatics (Chou et al, 2015), to name but a few. In column generation, when the number of variables in a LP model is too large to enumerate explicitly, a subset of feasible variables is constructed first.…”

Aircraft Deconfliction via Mathematical Programming: Review and Insights

“…First, it is performed on the earliest planning of the flights. This is known as strategic deconfliction and usually occurs before departure; however, it is not limited to a priori actions, in particular when the duration of flights is long, see Rios (2018), Liang et al (2014). The following stage involves tactical deconfliction, which usually takes place during flight, generally from five to thirty minutes before conflicts occur.…”

An integer optimization framework for future air traffic flow management

“…A mixed integer optimization model was proposed in that work, and solutions demonstrated a counter-intuitive result that in Europe, airborne holding delay sometimes can reduce total delay cost even it is much more expensive than ground delay. Liang et al (2013) developed a sequence assignment model to pick the optimal flight sequence based on the tracks in the oceanic airspace. One distinguishing feature of the model is that it could guarantee conflict-free between flights and a branch-and-price algorithm was presented to compute the integer optimal solution under the framework of column generation.…”