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

Abstract

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.