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Solving air traffic conflict problems via local continuous optimization. (English) Zbl 1339.90356
Summary: This paper first introduces an original trajectory model using B-splines and a new semi-infinite programming formulation of the separation constraint involved in air traffic conflict problems. A new continuous optimization formulation of the tactical conflict-resolution problem is then proposed. It involves very few optimization variables in that one needs only one optimization variable to determine each aircraft trajectory. Encouraging numerical experiments show that this approach is viable on realistic test problems. Not only does one not need to rely on the traditional, discretized, combinatorial optimization approaches to this problem, but, moreover, local continuous optimization methods, which require relatively fewer iterations and thereby fewer costly function evaluations, are shown to improve the performance of the overall global optimization of this non-convex problem.

MSC:
90C90 Applications of mathematical programming
90B90 Case-oriented studies in operations research
90C59 Approximation methods and heuristics in mathematical programming
65K05 Numerical mathematical programming methods
90C34 Semi-infinite programming
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