Air traffic flow management under uncertainty using chance-constrained optimization

In order to efficiently balance traffic demand and capacity, optimization of Air Traffic Flow Management (ATFM) relies on accurate predictions of future capacity states. However, these predictions are inherently uncertain due to factors, such as weather. This paper presents a novel computationally efficient algorithm to address uncertainty in ATFM by using a chance-constrained optimization method. First, a chance-constrained model is developed based on a previous deterministic Integer Programming optimization model of ATFM to include probabilistic sector capacity constraints. Then, to efficiently solve such a large-scale chance-constrained optimization problem, a polynomial approximation-based approach is applied. The approximation is based on the numerical properties of the Bernstein polynomial, which is capable of effectively controlling the approximation error for both the function value and gradient. Thus, a first-order algorithm is adopted to obtain a satisfactory solution, which is expected to be optimal. Numerical results are reported in order to evaluate the polynomial approximation-based approach by comparing it with the brute-force method. Moreover, since there are massive independent approximation processes in the polynomial approximation-based approach, a distributed computing framework is designed to carry out the computation for this method. This chance-constrained optimization method and its computation platform are potentially helpful in their application to several other domains in air transportation, such as airport surface operations and airline management under uncertainties.