Mathematical Problems in Engineering

Volume 2016, Article ID 8738014, 16 pages

http://dx.doi.org/10.1155/2016/8738014

## Multiobjective Simulated Annealing for Collision Avoidance in ATM Accounting for Three Admissible Maneuvers

Decision Analysis and Statistics Group, Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, Boadilla del Monte, 28660 Madrid, Spain

Received 8 January 2016; Accepted 6 June 2016

Academic Editor: Martin J. Geiger

Copyright © 2016 A. Mateos and A. Jiménez-Martín. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Technological advances are required to accommodate air traffic control systems for the future growth of air traffic. Particularly, detection and resolution of conflicts between aircrafts is a problem that has attracted much attention in the last decade becoming vital to improve the safety standards in free flight unstructured environments. We propose using the archive simulated annealing-based multiobjective optimization algorithm to deal with such a problem, accounting for three admissible maneuvers (velocity, turn, and altitude changes) in a multiobjective context. The minimization of the maneuver number and magnitude, time delays, or deviations in the leaving points are considered for analysis. The optimal values for the algorithm parameter set are identified in the more complex instance in which all aircrafts have conflicts between each other accounting for 5, 10, and 20 aircrafts. Moreover, the performance of the proposed approach is analyzed by means of a comparison with the Pareto front, computed using brute force for 5 aircrafts and the algorithm is also illustrated with a random instance with 20 aircrafts.

#### 1. Introduction

Cargo and air traffic (AT) congestion has experienced a general exponential growth throughout the world over the last decade. Every minute of the day, both morning and afternoon, there are about 11,000 aircrafts in the air somewhere in the world, as can be seen in real time at https://www.flightradar24.com/.

2014 was the first year in which 100,000 flights per day were exceeded. Europe’s largest airports handle about 2,000 daily takeoffs and landings. This trend continues to increase gradually and estimates predict bending movements until 2030.

With the systems currently available, the air traffic control agencies are not able to efficiently manage this large increase which is taking place due to several factors as follows:(1)Efficient use of airspace: currently, the airspace is rigidly structured and with a large number of constraints that aircrafts have to comply with. They must fly along predetermined routes through certain waypoints, which are set by the agencies of air traffic control (ATC), something that usually fails to produce optimal results. Aircrafts are not allowed to fly directly to their final destination taking advantage of favorable winds without making changes to their trajectories causing unnecessary fuel costs, which can indirectly cause increases in ticket prices. This problem is particularly evident in transoceanic routes, which are experiencing the greatest growth in demand.(2)Increased ATC workload: AT controllers have, among other functions, to prevent collisions between aircrafts and redirect routes to avoid adverse conditions. In congested areas, such as regions near to airports called* terminal radar approach controls* (TRACONs), AT controllers often simplify their high workloads making aircraft maintain default routes outside these regions, causing delays in landings and takeoffs.(3)Slow communication: communication is restricted to a tedious voice communication between aircraft and AT controllers, causing frequent bottleneck situations.

In view of the problems described, the aviation community has been working in recent years on a concept called* free flight*. This innovative concept allows pilots to choose their own routes, altitude, and velocity to reduce delays and manage the use of aircraft fuel more efficiently. The preferences of the pilots will be restricted only in very congested airspace areas or to prevent unauthorized entry into military areas.

Free flight is potentially possible due to the availability of technologies such as* global positioning systems* (GPS); communications data links such as* automatic dependence surveillance-broadcast* (ADS-B); detection systems and collision avoidance; and powerful computing increasingly being implemented in aircrafts.

In addition, there are several decision support tools that reduce the workload of both AT controllers and pilots and optimize their capacity, for example, the detection and resolution of conflicts in airspace sectors, landings and takeoffs management in airports, and organizational systems of the workload of AT controllers to better organize their tasks to increase productivity.

These technological advances will also allow current ATC systems to accommodate the future growth of air traffic. Algorithms to detect and solve aircraft conflicts are vital to improve the safety standards in free flight unstructured environments. These systems can be used on land by ATC or by the* flight management system* (FMS) of each aircraft.

In this paper, we focus on the development of algorithmic tools for aircraft* conflict detection and resolution* (CDR) problem. We assume that each aircraft is surrounded by cylinder representing a security virtual volume. Conflict between two aircrafts occurs when the respective aircraft security volumes overlap.

Different approaches can be found in literature to deal with collision avoidance accounting for different number and types of admissible maneuvers for aircrafts and with different solution approaches, including the use of exact solvers, simulation techniques, and metaheuristics. The work in [1] present a survey with the most important of these up to the year 2000, whereas [2] focuses on approaches from 2000 up to 2012.

One of the first approaches to deal with collision avoidance was [3]. A path planning problem among given waypoints avoiding all possible conflicts was considered aimed at minimizing the total flight time. Two mixed-integer linear programs were proposed accounting for velocity changes and angle changes as admissible maneuvers, respectively. The work in [4] proposes a three-dimensional formulation as a mixed-integer nonlinear program in which only velocity changes were admissible. CPLEX was used for the resolution in both approaches.

Simulation techniques have also been used to handle CDR problems. For instance, [5] analyzes the economic performance of a specific conflict resolution strategy based on velocity change between two aircrafts in terms of extra time and fuel consumption. The work in [6] also considers a velocity regulation problem, but from a different perspective, distinguishing between* crossing conflicts* (the wider), in which the aircrafts intersect at some point and security cylinders overlap, and* conflicts trail*, caused when an aircraft pursues another, both with different velocities.

*Neural networks* have been also used for performing velocity changes in CDR problems [5, 7, 8].

More recently, [9] focuses on mixed-integer optimization models based on velocity regulation. They propose to accelerate or decelerate during a specified time interval, reverting back to the original velocity once the conflict is avoided. They propose a heuristic procedure where the problem is decomposed and locally exactly solved.

Other less frequent proposals consider turn changes that lead to nonlinear optimization models. For instance, [10] proposes a two-step approach. First, a nonconvex mixed-integer nonlinear optimization is used to minimize the weighted aircraft angle variations. Then, a set of unconstrained quadratic optimization models are considered, where aircrafts are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict with any other. Both an exact and an approximate resolution are proposed. In the second, the turn changes are discretized to reduce the search space.

Different metaheuristics have been proposed for solving CDR models accounting for turn changes, such as* ant colony systems* [11, 12],* genetic algorithms* [13],* variable neighborhood search* [14], and* particle swarm optimization* [15], which uses a series of waypoints the aircrafts can pass through.

A pretty realistic proposal is described in [16], wherein the acceleration variable is added to the model. It intends to solve conflicts discretizing the time remaining until it occurs at different intervals, optimizing acceleration, and velocity that should be assigned to each aircraft. A nonlinear mixed 0-1 model is used to solve the problem, which is iteratively linearized by using Taylor polynomials. This approach is then enhanced in [17], extending control to aircraft outside the aviation sector to manage, that is, taking into account those aircrafts leaving it or entering it. Moreover, they take into account the conflicts that may arise when an aircraft is climbing or descending to change altitude.

The work in [18] improves the velocity change model by adding altitude changes when necessary, for example, in head-to-head conflict situations. A multiobjective perspective is considered including objectives such as velocity variation and total number of maneuvers and forcing to return to the original flight configuration when no aircrafts are in conflict. An exactly solved mixed 0-1 linear optimization model is used, with small computational time for the execution making it suitable for real-time use.

In [19] an innovative point of view based on the choice of different strategies to avoid conflicts is proposed. An original trajectory model using B-splines is introduced together with a new semi-infinite programming formulation of the separation constraint involved in CDR problems.

In this paper we propose using* simulated annealing* to deal with a CDR problem accounting for three admissible maneuvers (velocity, turn, and altitude changes) in a multiobjective context. Specifically, the* archive simulated annealing-based multiobjective optimization algorithm* (AMOSA) has been adapted to the CDR problem accounting for objectives such as minimizing the maneuver number and magnitude, time delays, or deviations in the leaving points.

Both the possibility of performing three types of maneuvers and the multiobjective context make this paper an original contribution regarding previous works on CDR problems.

The paper is structured as follows. The mathematical modeling for the multiobjective problem under consideration is introduced in Section 2, including the identification of parameters, decision variables, and constraints and the description and modelization of the candidate objective functions for analysis. AMOSA and its adaptation to the considered CDR problem are described in Section 3. Section 4 deals with the parameter setting and the performance analysis when 5 aircrafts are considered. The parameter setting for 10 and 20 aircrafts and an example illustrating the flexibility of the proposed algorithm are provided in Section 5. Finally, some conclusions are provided in Section 6.

#### 2. Mathematical Modeling

We assume that in a particular moment there are aircrafts in an* aerial sector*, a cubic volume in the space managed by an AT controller; see Figure 1. We have to decide which maneuvers to perform to avoid possible collisions between them. We also assume that the decision on maneuvers will be effective until aircrafts leave the aerial sector or until a new aircraft enters the aerial sector. At the moment a new aircraft enters the aerial sector, the analysis we propose should be again carried out to identify new maneuvers to avoid new possible collisions caused by the entering aircraft.