Solving the European Air Traffic Flow Management Problem with Kernel Search Matheuristics and Machine Learning

The Air Traffic Flow Management (ATFM) problem has the goal of planning flights within a set of constraints representing both capacity limits of the air space and airline company needs, consisting in a delay and a preference assigned to each trajectory; several mathematical linear programming models exist to solve this problem, and the main issue is their size, since they may contain up to millions of variables for real instances. As a consequence, the computational effort required to solve the model to optimality is huge, and not suitable for practical use. This thesis presents a heuristic method based on Kernel Search. The goal of Kernel Search is to solve the model using only an initial subset of variables, called kernel, and dividing the remaining variables into small groups called buckets, ordered by "promising impact on the solution", that is computed from variable information obtained through the resolution of the linear relaxation of the problem. Each iteration of the Kernel Search method consists in solving a small subproblem given by variables from the kernel and from a single bucket, whose size allows to solve it to optimality in a small amount of time; furthermore, in this thesis, Machine Learning techniques have been used in the process of defining the "quality" of each variable, in order to see if such modification in the bucket defining procedure can lead to more efficient or effective methods. The developed algorithms have been implemented and tested on real instances obtained from European data repositories, showing their ability to find optimal or very close to optimal solutions.The Air Traffic Flow Management (ATFM) problem has the goal of planning flights within a set of constraints representing both capacity limits of the air space and airline company needs, consisting in a delay and a preference assigned to each trajectory; several mathematical linear programming models exist to solve this problem, and the main issue is their size, since they may contain up to millions of variables for real instances. As a consequence, the computational effort required to solve the model to optimality is huge, and not suitable for practical use. This thesis presents a heuristic method based on Kernel Search. The goal of Kernel Search is to solve the model using only an initial subset of variables, called kernel, and dividing the remaining variables into small groups called buckets, ordered by "promising impact on the solution", that is computed from variable information obtained through the resolution of the linear relaxation of the problem. Each iteration of the Kernel Search method consists in solving a small subproblem given by variables from the kernel and from a single bucket, whose size allows to solve it to optimality in a small amount of time; furthermore, in this thesis, Machine Learning techniques have been used in the process of defining the "quality" of each variable, in order to see if such modification in the bucket defining procedure can lead to more efficient or effective methods. The developed algorithms have been implemented and tested on real instances obtained from European data repositories, showing their ability to find optimal or very close to optimal solutions

Incorporating User Preferences Within an Optimal Traffic Flow Management Framework

The effectiveness of future decision support tools for Traffic Flow Management in the National Airspace System will depend on two major factors: computational burden and collaboration. Previous research has focused separately on these two aspects without consideration of their interaction. In this paper, their explicit combination is examined. It is shown that when user preferences are incorporated with an optimal approach to scheduling, runtime is not adversely affected. A benefit-cost ratio is used to measure the influence of user preferences on an optimal solution. This metric shows user preferences can be accommodated without inordinately, negatively affecting the overall system delay. Specifically, incorporating user preferences will increase delays proportionally to increased user satisfaction

Enhanced Demand and Capacity Balancing based on alternative trajectory options and traffic volume hotspot detection

Nowadays, regulations in Europe are applied at traffic volume (TV) level consisting in a reference location, i.e. a sector or an airport, and in some traffic flows, which act as directional traffic filters. This paper presents an enhanced demand and capacity balance (EDCB) formulation based on constrained capacities at traffic volume level. In addition, this approach considers alternative trajectories in order to capture the user driven preferences under the trajectory based operations scope. In fact, these alternative trajectories are assumed to be generated by the airspace users for those flights that cross regulated traffic volumes, where the demand is above the capacity. For every regulated trajectory the network manager requests two additional alternative trajectories to the airspace users, one for avoiding the regulated traffic volumes laterally and another for avoiding it vertically. This paper considers that the network manager allows more flexibility for the new alternative trajectories by removing restrictions in the Route Availability Document (RAD). All the regulated trajectories (and their alternatives) are considered together by the EDCB model in order to perform a centralised optimisation minimising the the cost deviation with respect to the initial traffic situation, considering fuel consumption, route charges and cost of delay. The EDCB model, based on Mixed-Integer Linear Programming (MILP), manages to balance the network applying ground delay, using alternative trajectories or both. A full day scenario over the ECAC area is simulated. The regulated traffic volumes are identified using historical data (based on 28th July of 2016) and the results show that the EDCB could reduce the minutes of delay by 70%. The cost of the regulations is reduced by 11.7%, due to the reduction of the delay, but also because of the savings in terms of fuel and route charges derived from alternative trajectories.Peer ReviewedPostprint (published version

Fair task allocation in transportation

Task allocation problems have traditionally focused on cost optimization. However, more and more attention is being given to cases in which cost should not always be the sole or major consideration. In this paper we study a fair task allocation problem in transportation where an optimal allocation not only has low cost but more importantly, it distributes tasks as even as possible among heterogeneous participants who have different capacities and costs to execute tasks. To tackle this fair minimum cost allocation problem we analyze and solve it in two parts using two novel polynomial-time algorithms. We show that despite the new fairness criterion, the proposed algorithms can solve the fair minimum cost allocation problem optimally in polynomial time. In addition, we conduct an extensive set of experiments to investigate the trade-off between cost minimization and fairness. Our experimental results demonstrate the benefit of factoring fairness into task allocation. Among the majority of test instances, fairness comes with a very small price in terms of cost

A Distributed Framework for Traffic Flow Management in the Presence of Unmanned Aircraft

The integration of unmanned aircraft systems (UAS) into the airspace system is a key challenge facing air traffic management today. An important aspect of this challenge is how to determine and manage 4-dimensional trajectories for both manned and unmanned aircraft, and how to appropriately allocate resources among different aircraft. An integrated approach requires solving the traditional Air Traffic Flow Management (ATFM) problem to balance the capacity and demand of airport and airspace resources, but at a significantly larger scale. In doing so, aircraft connectivity constraints of commercial flights must be satisfied. In addition to these and the resource capacity constraints, geofencing constraints for unmanned aircraft that keep them within or outside a certain region of the airspace, must also be incorporated. This paper presents a distributed implementation of an integer programming approach for solving large-scale ATFM problems in the presence of unmanned aircraft. Given desired mission plans and flight-specific operating and delay costs, the proposed approach uses column generation to determine optimal trajectories in space and time, in the presence of network and flight connectivity constraints, airport and airspace capacity constraints, and geofencing constraints. Using projected demand for the year 2030 from the United States with approximately 48, 000 passenger flights and 29, 000 UAS operations (on a wide range of missions) per day, we show that our implementation can find nearly-optimal trajectories for a 24-hour period in less than 4 minutes. Furthermore, a rolling horizon implementation (with 6-8 hour time windows) results in run times of less than a minute. In addition to being the largest instances of the ATFM problem solved to date, these results represent the first effort to incorporate UAS trajectories into airspace and airport resource sharing problems.United States. National Aeronautics and Space Administration (Small Business Innovative Grant

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons

Flight flexibility in strategic traffic planning: visualisation and mitigation use case

The concept of strategic traffic planning that takes into account changing airspace configurations, their capacity, and allows the quantification of flight flexibility is presented in this paper: the visualization of the results and an example of possible use. The concept is implemented through two deterministic optimization models. Here, we focus on the output of the models, which identifies the departure times, trajectories, flight flexibility and the list of saturated sector-hours throughout the day, based on the configurations used during the day. In order to make the output understandable to various stakeholders, we use a visualization tool and a set of performance indicators. The information on the saturated sectors, and their impact on flexibility (criticality index) is taken as an input in the example of mitigation action application by Air Navigation Service Providers, aimed at improving the situation. A mitigation strategy of increasing capacity of saturated airspace is implemented, and results show that the improvements in flexibility can be achieved

The Price of Fairness

In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.National Science Foundation (U.S.) (grant DMI- 0556106)National Science Foundation (U.S.) (grant EFRI-0735905

Air traffic flow management slot allocation to minimize propagated delay and improve airport slot adherence

In Europe, one of the instruments at the Network Manager’s (NM) disposal to tackle demand-capacity imbalance is to impose ground, i.e. Air Traffic Flow Management (ATFM), delays to flights. To compensate for anticipated delays and improve on-time performance, Aircraft Operators usually embed a buffer time in their schedules. The current practice for allocating ATFM delays does not take into account if flights have any remaining schedule buffer to absorb ATFM delay and reduce delay propagation to subsequent flights. Furthermore, the policy presently employed is to minimize ATFM delays, an order of magnitude of half a minute per flight, while propagated delays are approximately ten times higher. In this paper, we explore the possibility to control ATFM delay distribution in a way so as to minimize delay propagated to subsequent flights, but also to increase flights’ adherence to airport slots at coordinated airports. To this aim, we propose a two-level mixed-integer optimization model to solve en-route demand-capacity imbalance problem and further improve airport slot adherence. The rationales behind the research are drawn from practical experience, while the model proposed is compatible with the one currently being used by the NM, making it easy to implement. We test the model on two real-world case studies and conduct ex post analysis to test the effects of violation of model assumptions on results. The results show that it is possible to use the proposed methodology to lower delay propagated to subsequent flights and at the same time to improve airport slot adherence. In addition, they suggest that the current regulatory settings aiming to minimize ATFM delay minutes, as well as operational implementation thereof, are neither necessarily fully aligned with the desires and operating goals of Aircraft Operators, nor they improve the predictability of operations in the network