A method is presented to extend current graph-based Air Traffic Management optimization frameworks. In general, Air Traffic Management is the process of guiding a finite set of aircraft, each along its pre-determined path within some local airspace, subject to various physical, policy, procedural and operational restrictions. This research addresses several limitations of current graph-based Air Traffic Management optimization methods by incorporating techniques to account for stochastic effects, physical inertia and variable arrival sequencing. In addition, this research provides insight into the performance of multiple methods for approximating non-differentiable air traffic constraints, and incorporates these methods into a generalized weighted-sum representation of the multi-objective Air Traffic Management optimization problem that minimizes the total time of flight, deviation from scheduled arrival time and fuel consumption of all aircraft. The methods developed and tested throughout this dissertation demonstrate the ability of graph-based optimization techniques to model realistic air traffic restrictions and generate viable control strategies
