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In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss-Lobatto direct collocation method and is then solved using a nonlinear-programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.

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In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

Abstract. Aviation aims to reduce its climate impact by adopting trajectories, that avoid those regions of the atmosphere where aviation emissions have a large impact. To that end, prototype algorithmic climate change functions can be used, which provide spatially and temporally resolved information on aviation’s climate impact in terms of future near-surface temperature change. These alogorithmic climate change functions can be calculated with meteorological input data obtained from e.g. numerical weather prediction models. We here present an open-source Python Library, an easy to use and flexible tool which efficiently calculates both the individual algorithmic climate change functions of water vapour, nitrogen oxide (NOx) induced ozone and methane, and contrail-cirrus and also the merged non-CO2 algorithmic climate change functions that combine all individual contributions. These merged aCCFs can be only constructed with the technical specification of aircraft/engine parameters, i.e., NOx emission indices and flown distance per kg burnt fuel. These aircraft/engine specific values are provided within CLIMaCCF version V1.0 for a set of aggregated aircraft/engine classes (i.e. regional, single-aisle, wide-body). Moreover, CLIMaCCF allows by a user-friendly configuration setting to choose between a set of different physical climate metrics (i.e. average temperature response for pulse or future scenario emissions over the time horizons of 20, 50 or 100 years). Finally, we demonstrate the abilities of CLIMaCCF by a series of example applications.