Air Traffic Management Problem Research Articles

Creating Executable Agent‐Based Models Using SysML

AbstractSimulation plays an important role in the analysis of alternatives during the early phases of systems engineering activities. This is especially true for endeavors in the system of systems realm where there is even more need for simulation to characterize interdependencies. In this paper, we develop a generic framework to translate a SysML conceptual model to an executable agent‐based simulation model. We demonstrate the translation using a simplified air traffic management problem. Along with the potential advantages, we also identify major challenges and possible mismatches in accomplishing a suitable translation for real‐world systems of systems.

An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution

An exact mixed integer nonlinear optimization (MINO) model is presented for tackling the aircraft conflict detection and resolution problem in air traffic management. Given a set of flights and their configurations, the aim of the problem was to provide new configurations such that all conflict situations are avoided, with conflict situation understood to mean an event in which two or more aircraft violate the minimum safety distances that must be maintained in flight. The proposed model solves the problem using both horizontal (velocity and angle turn change) and vertical (altitude level change) maneuvers. As a special case, another model is presented in which only horizontal maneuvers are used. The models proposed are based on a geometric construction which involves trigonometric functions, so the constraint system is included via a large set of trigonometric and nonconvex inequalities. A multicriteria approach is presented to provide useful information to air traffic control officers about the maneuvers to be performed. The main results of an extensive computational experiment are reported in which the performance of the state-of-the-art nonconvex MINO solver Minotaur is studied.

Multiobjective optimization for aircraft conflict resolution. A metaheuristic approach

The conflict resolution problem in Air Traffic Management is tackled in this paper by using a mixed integer linear approximation to a Mixed Integer Nonlinear Optimization (MINO) model that we have presented elsewhere. The aim of the problem consists of providing a new aircraft configuration such that every conflict situation is avoided, a conflict being an event in which two or more aircraft violate the minimum safety distance that they must keep in flight. The initial information consists of the aircraft configuration in a certain time instant: position, velocity, heading angle and flight level. The proposed approach allows the aircraft to perform any of the three possible maneuvers: velocity, turn angle and flight level changes. The nonlinear model involves trigonometric functions which make it difficult to solve, in addition to the integer variables related to flight level changes, among other auxiliary variables. A multicriteria scheme based on Goal Programming is also presented. In order to provide a good solution in short computing time, a Sequential Mixed Integer Linear Optimization (SMILO) approach is proposed. A comparison between the results obtained by using the state-of-the-art MINO solver Minotaur and SMILO is performed to assess the solution’s quality. Based on the computational results that we have obtained in a broad testbed we have experimented with, SMILO provides a very close solution to the one provided by Minotaur practically for all the instances. SMILO requires a very small computing time that makes the approach very suitable for helping to solve real-life operational situations.

A Variable Neighborhood Search Heuristic for Three-dimensional Conflict Resolution Model

This paper investigates a Variable Neighborhood Search (VNS) for a three-dimensional air traffic conflict resolution model. The conflict resolution problem in Air Traffic Management (ATM) is solved by changing the maneuvering dimensions of aircrafts, such as lateral and vertical maneuvers. Compared with existing methods, such as mixed-integer linear optimization approaches that change one or two dimensions of the velocity vector, our algorithm proposes three neighborhoods for conflict resolution based on changes in all three dimensions of the velocity vector of aircrafts. The approach could resolve both horizontal and vertical conflicts. Simulation studies demonstrate that aircrafts could perform various maneuvers to avoid collisions in a three-dimensional space.

MOCCA-II: A multi-objective co-operative co-evolutionary algorithm

Most real-world problems naturally involve multiple conflicting objectives, such as in the case of attempting to maximize both efficiency and safety of a working environment. The aim of multi-objective optimization algorithms is to find those solutions that optimize several components of a vector of objective functions simultaneously. However, when objectives conflict with each other, the multi-objective problem does not have a single optimal solution for all objectives simultaneously. Instead, algorithms attempt to search for the set of efficient solutions, known as the global non-dominated set, that provides solutions that optimally trade-off the objectives. The final solution to be adopted from this set would depend on the preferences of the decision-makers involved in the process. Hence, a decision-maker is typically interested in knowing as many potential solutions as possible.In this paper, we propose an extension to a previous piece of work on multi-objective cooperative coevolution algorithms (MOCCA). The idea was motivated with a practical problem in air traffic management to design terminal airspaces. MOCCA and a further study that was done on a distributed environment for MOCCA, were found to fit the need for the application. We systematically questioned key components of this algorithm and investigated variations to identify a better design. This paper summarizes this systematic investigation and present the resultant new algorithm: multi-objective co-operative co-evolutionary algorithm II (MOCCA-II).

Risk-Hedged Traffic Flow Management Under Airspace Capacity Uncertainties

This paper presents a novel solution to the problem of air traffic flow management under airspace capacity uncertainty arising from weather or environmental effects. The traffic flow management problem is formulated as a stochastic linear program with multiple available routes between origin–destination pairs, with the weather/environmental factors constraining the probable capacities along these routes. The performance index consists of the delays introduced by deterministic and stochastic capacity constraints. Primary impact of the weather/environmental factors is to require the rerouting of aircraft, causing additional delays. These additional delays require the aircraft to carry additional fuel or to incur costs associated with the failure to meet the schedules in hub-spoke operations. Thus, the variance of delays can be used to define the degree of risk in stochastic traffic flow management, and flow management algorithms that assure the variations in the delay below a specified value can be considered as providing a hedge against uncertain weather or environmental factors. The algorithm developed in this paper produces a risk-hedged decision that results in the least delay at a specified level of acceptable variance. This algorithm represents a dramatic departure from the more traditional stochastic traffic flow management algorithms, which minimize expected value of delays, without attempting to control their variances. The performance of the present stochastic traffic flow management algorithm is demonstrated on a use case representing National Airspace System operations on a regional scale.

The China Air Traffic Flow Management Problem

At present, with the continuous increase in domestic flight number, due to air traffic flow management caused flight delays have occurred from time to time, flow control and flow management caused by other reasons has become one of the main causes of flight delay; therefore, the air traffic flow management is the urgent need to complete the task of civil aviation. This paper points out the existing problem of air traffic flow management, then put forward to strengthen the air traffic flow management measures.

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

A class of problems in air traffic management (ATM) asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs (MIPs), hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the fully routed nominal problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively piecewise linear with finitely many vertices, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.

A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes

The aircraft Conflict Detection and Resolution (CDR) problem in air traffic management consists of finding a new configuration for a set of aircraft such that conflict situations between them are avoided. A conflict situation arises if two or more aircraft violate the safety distances that they must maintain in flight. In this paper we propose a Variable Neighborhood Search approach for solving the CDR by turn changes. This metaheuristic compares favorably with previous best known methods for solving the Mixed Integer Nonlinear Programming (MINLP) model proposed elsewhere. It is worth pointing out the astonishingly short time in which the first feasible solution is obtained. This is crucial for this specific problem, where a response must be provided almost in real time if it is to be useful in a real-life problem. A comparative study between the performance of the new approach, a state-of-the-art MINLP solver and our Sequential Integer Linear Optimization approach proposed elsewhere is reported, using a testbed of instances with up to 25 aircraft.

Introduction to the theory of splines with an optimal mesh. Linear Chebyshev splines and applications

On June 18, 2008 at the Plenary Meeting of the International Conference ``Differential Equations and Topology" dedicated to the 100-th anniversary of L.S. Pontryagin, the report [15] was submitted by Isaev V.K. and Leitmann G. This report in a summary form included a section dedicated to the research of scientists of TsAGI in the field of automation of full life-cycle (i.e. engineering-design-manufacturing, or CAE/CAD/CAM, or CALS-technologies) of wind tunnel models [21]. Within this framework, methods of geometric modeling [1,11] were intensively developed, new classes of optimal splines have been built, including the Pontryagin splines and the Chebyshev splines [12-13,19,37]. This paper reviews some results on the Chebyshev splines. We also give brief remarks about the new applications of Chebyshev splines (outside the usual scope of CALS-technologies in design and manufacturing), namely to the actual problem of air traffic management (ATM) within the Free Flight concept.

Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact solver. Since the problem is very difficult to solve, we also propose a heuristic procedure where the problem is decomposed and it is locally exactly solved. Computational results show that the proposed approach provides satisfactory results.

VNS based algorithm for solving a 0–1 nonlinear nonconvex model for the Collision Avoidance in Air Traffic Management

Abstract A mixed 0–1 nonlinear high nonconvex model is presented for solving the collision avoidance problem in Air Traffic Management. The aim is to give a new configuration for a set of aircraft such that their conflict situations are avoided. A conflict situation happens if two or more aircraft violate the safety distances that they have to keep during the flight. A geometric construction is used for detecting and solving the problem by performing turn changes in the aircraft. Elsewhere [Alonso-Ayuso, A., L.F. Escudero, and F.J. Martin-Campo, On solving the aircraft collision avoidance problem by turn changes. Exact and approximate nonconvex mixed 0–1 nonlinear optimization, to be submitted (2012).], we have presented an approximate algorithm based on Sequential Integer Linear Optimization (SILO, for short) that favorably is compared with different state-of-the-art nonconvex Mixed Integer Nonlinear Optimization (MINLO) engines requiring much smaller computational time with acceptable goodness gap. However, in this work, we computationally compare the SILO approach with the state-of-the-art MINLO metaheuristic approach based on the Variable Neighbourhood Search (VNS) methodology, such that the trigonometric nonconvex functions of our problem are considered among other special characteristics.

Aircraft Trajectory Planning Under Uncertainty by Light Propagation

In the SESAR framework (Single European Sky ATM Research), the need to increase the air traffic capacity motivated the 4D (space + time) aircraft trajectory planning. This paper deals with an important Air Traffic Management (ATM) problem that consists in generating sets of 4D conflict-free trajectories (the tactical planning problem). The Light Propagation Algorithm (LPA) was introduced in [1] to deal with this problem. LPA has recently been shown to manage successfully a full day of traffic over the French airspace, removing all conflicts while satisfying ATM constraints.In this paper, we adapt the LPA to take into account uncertainties in trajectory prediction. We introduce and test a new algorithm called u/LPA (LPA under uncertainty) on the same day of traffic. For some situations, uncertainties reduce so much the search space that the standard algorithm cannot guarantee conflict free situation. As a consequence, one must include some time constraints for few trajectories (so-called RTA points: Real Time of Arrival constraints) in order to remove the remaining conflicts. The goal of RTA points is to impose an aircraft to be at a specified position at some given time. This results into a new optimization formulation of the tactical trajectory planning problem involving the decision as to where/when RTA points should be imposed. In order to solve this new problem, here we are content with a simple heuristic that yields encouraging results.

A New Algorithm of Flight Rerouting Path Planning in Severe Weather

In order to solve the rerouting problem of air traffic management in severe weather areas, a rerouting path planning problem was researched. First, the convex polygon was used to design danger zone. Then, rerouting path planning model was established. After that, a new algorithm used to determine the initial reroute points was proposed. Finally, two examples of the rerouting problem caused by thunderstorms occurring in Southwest China were studied. Compared to the current existing method in real operation, by using this algorithm, the number of reroute points was effectively reduced, and the danger zone was avoided. Additionally, Compared to the geometric algorithm, by using this algorithm, the rerouting path length was reduced by 2.9% and 5% respectively. The results indicate that the algorithm proposed in this paper is effective and practical.

A Flight Plan Rescheduling in Air Traffic Management Problem: A Time Discret Event System Approach

Abstract Motivated by the importance of congestion in air traffic problem and its bad effects on airlines companies and passenger's security, we propose a decision support framework for flight rescheduling in air traffic management based on ground delay, rerouting and flight canceling. This approach is based on using Time Petri Nets (TPN) to model air traffic networks. We introduce a Binary Decision Diagram based tool to represent the state space of Time Petri Nets. This tool, called Time Ordered Binary Decision Diagrams (TOBDDs) is able to represent a large state space of a TPN with a small data structure and enable the efficient manipulation of this set. In what follows, we developed a technique to generate all the rescheduling flights plans taking into account the temporal and spatial constraints.

A mixed 0–1 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM: Velocity changes through a time horizon

In this paper a mixed 0–1 nonlinear model for the Collision Avoidance problem in Air Traffic Management is presented. The aim of the problem consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided where a conflict is the loss of the minimum safety distance that two aircraft have to keep in their flight plans. The optimization model is based on geometric constructions. It requires knowing the initial flight plan (coordinates, angles and velocities in each period). The objective is the minimization of the acceleration variations when the aircraft are forced to return to the original flight plan once there is no aircraft in conflict. A linear approximation by using iteratively Taylor polynomials is presented to solve the problem in mixed 0–1 linear terms. An extensive computational experience for a testbed of large-scale instances is reported.

Minimization of Potential Air Conflicts through Speed Regulation

This paper addresses the speed regulation problem in air traffic management. Because global air traffic volume is continuously increasing, improvement in air traffic control has become a priority. During this decade, European and United States initiatives have been launched to design the future of air traffic management. One of their objectives is to increase air traffic density and optimize flight route plans. This can be achieved through en route deconfliction. Air conflicts have the potential to occur when two or more aircraft are predicted to be below a separation norm in the near future. Such situations affect air traffic controllers' workload; thus, these situations limit controllers' capacity to deal with large numbers of aircraft and induce flight delay. Reducing air traffic controllers' potential workload through speed regulation has been investigated in the En Route Air Traffic Soft Management Ultimate System project. Efficiency of the method has been validated through simulations, including human-in-the-loop experiments, which opens the door to conflict resolution algorithms based on speed regulation. In this paper a formulation for the speed regulation problem is proposed. First, a potential conflict detection and resolution framework is presented. Uncertainty is then introduced in the model, with the aim of reproducing realistic air navigation conditions. A case study of real air traffic instances is described, and results are discussed to assess the potential of the proposed algorithm.

Collision Avoidance in Air Traffic Management: A Mixed-Integer Linear Optimization Approach

This paper tackles the collision-avoidance problem in air traffic management. The problem consists of deciding the best strategy for new aircraft configurations (velocity and altitude changes) such that all conflicts in the airspace, i.e., the loss of the minimum safety distance that has to be kept between two aircraft, are avoided. A mixed 0-1 linear optimization model based on geometric transformations for collision avoidance between an arbitrary number of aircraft in the airspace is developed. Knowing the initial coordinates, angle direction, and level flight, the new configuration for each aircraft is established by minimizing several objective functions, e.g., velocity variation and total number of changes (velocity and altitude), and forcing to return to the original flight configuration when no aircraft are in conflict. Due to the small computational time for the execution, the new configuration approach can be used in real time by using optimization software.

Simulation‐based Bayesian optimal design of aircraft trajectories for air traffic management

AbstractIn this paper, we consider a specific Air Traffic Management problem, where multiple aircraft in a specific region are required to reach a different target zone in the minimum expected time, while maintaining safe separation. The problem is complicated by the presence of random wind disturbances. We propose a realistic policy to automatically generate optimal and safe maneuvres for each aircraft. The parameters of the optimal policy are computed using a sequential Monte Carlo approach. Copyright © 2010 John Wiley & Sons, Ltd.

Dynamic Flow Scheduling in Air Traffic Network Based on Game Theory

Recently, many works have employed deterministic strategies in dealt with flow scheduling problem in Air traffic flow management (ATFM). In practice, however, they are proved unreasonable for omitting airline’s preference in ATFM. In this paper, we develop a novel air traffic flow control model based on game theory to solve this problem in air traffic network. In the flow model, a resource (link/time pair in air traffic network) allocation strategy that uses sequential game method to predict traffic allocation is proposed in resource sharing environment. The problem of multiple airlines competes for an optimal route is formulated as a multi-player dynamic game. Through finding the Nash equilibrium solution of the multi-player dynamic game, the optimal flow scheduling is also formed at the same time. The flow model also incorporates many key characteristics of ATFM, such as competitive airlines, allowing multiply flow control strategies and so on. Numerical simulation results show the feasibility of solving the air traffic flow control problem using game theory on the air traffic network.