F. Javier Martín-Campo

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.

A mixed 0-1 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM

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.

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.

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 lexicographical dynamic flow model for relief operations

Emergency management is a highly relevant area of interest in operations research. Currently the area is undergoing widespread development. Furthermore, recent disasters have highlighted the importance of disaster management, in order to alleviate the suffering of vulnerable people and save lives. In this context, the problem of designing plans for the distribution of humanitarian aid according to the preferences of the decision maker is crucial. In this paper, a lexicographical dynamic flow model to solve this problem is presented, extending a previously introduced static flow model. The new model is validated in a realistic case study and a computational study is performed to compare both models, showing how they can be coordinated to improve their overall performance.

Exact and Approximate Solving of the Aircraft Collision Resolution Problem via Turn Changes

The aircraft conflict detection and resolution problem in air traffic management consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided. A conflict situation occurs if two or more aircraft do not maintain the minimum safety distance during their flight plans. A two-step approach is presented. The first step consists of a nonconvex mixed integer nonlinear optimization MINLO model based on geometric constructions. The objective is to minimize the weighted aircraft angle variations to obtain the new flight configuration. The second step consists of a set of unconstrained quadratic optimization models where aircraft are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict with any other. The main results of extensive computation are reported by comparing the performance of state-of-the-art nonconvex MINLO solvers and an approximation by discretizing the possible angles of motion for solving a sequence of integer linear optimization SILO models in an iterative way. Minotaur, one of the nonconvex MINLO solvers experimented with, gives better solutions but requires more computation time than the SILO approach, which requires only a short time to obtain a good, feasible solution. Its value in the objective function has a reasonable goodness gap compared with the Minotaur solution. Given the need to solve the problem in almost real time, the approximate SILO approach is favored because of its short computation time and solution quality for the testbeds used in the experiment, which include both small-and real-sized instances. However, Minotaur is useful in this particular case for simulation purposes and for calibrating the SILO approach.

Multi-criteria optimization for last mile distribution of disaster relief aid: Test cases and applications

Abstract Humanitarian organizations transport large quantities of aid for distribution in the aftermath of disasters. Transportation for last mile distribution includes multiple, and often conflicting, performance criteria that include time (deprivation), cost, coverage, equity and security. We build a compromise programming model for multi-criteria optimization in humanitarian last mile distribution. Regarding security, ours is the first multi-criteria model able to produce an actual vehicle schedule while forcing vehicles to form convoys in humanitarian operations research. We illustrate the multi-criteria optimization using a realistic test case based on the Pakistan floods, 2010. We standardize and share this case as well as cases based on the Niger famine, 2005 and the Haiti earthquake, 2010. By sharing test cases, we encourage basic scientific tasks such as replicability and model comparison within the humanitarian operations research community.

On the aircraft conflict resolution problem: A VNS approach in a multiobjective framework

Abstract The aircraft conflict resolution problem needs to provide response to such situation in which two or more aircraft violate the safety distances that must be kept during the flight. Then, given the aircraft trajectories, the aim consists of finding a new configuration such that every conflict situation must be avoided. To deal with conflict avoidance an aircraft may change velocity, heading angle and altitude level. Due to nonlinearities involved in the exact model and the need of an almost real-time response, a Variable Neighborhood Search approach is presented within the multiobjective environment.