Authors: Alonso-Ayuso, Antonino
Escudero, Laureano
Martín-Campo, Javier
Mladenović, Nenad 
Title: VNS based algorithm for solving a 0-1 nonlinear nonconvex model for the Collision Avoidance in Air Traffic Management
Journal: Electronic Notes in Discrete Mathematics
Volume: 39
First page: 115
Last page: 120
Issue Date: 1-Dec-2012
ISSN: 1571-0653
DOI: 10.1016/j.endm.2012.10.016
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. Martín-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. © 2012 Elsevier B.V.
Keywords: Collision avoidance | Mixed integer nonlinear nonconvex optimization | Sequential mixed integer optimization | Variable neighbourhood search
Publisher: Elsevier

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