Branch & bound based algorithm for aircraft VNAV profile reference trajectory optimization

Computing the vertical navigation reference trajectory is investigated as a way to reduce fuel consumption. Future Air Traffic Management functions might be able to allow aircraft to fly at their most economical profiles allowing fuel consumption reduction. The vertical navigation reference trajectory solution is a combination of the possible Indicated Air Speed, Mach number and altitude of the different flight phases. This paper considers these speeds and altitudes as discrete values, which area available in a Performance Database. The possible combinations are modeled as a tree-like graph. The graph was browsed using a mixture of Best-First Search and Depth-First Search method. A Branch & Bound based algorithm was implemented to reduce the number of computations required to find the optimal combination. A bounding function to estimate the cost at each node was developed and a parameter defined as the Optimism Coefficient was introduced to vary the accuracy of the bounding function. Comparing the experimental results to an exhaustive search algorithm proved the optimal solution and the fuel reduction potential of this algorithm. This algorithm tries to calculate the least possible combinations making it a good choice in low processing power devices such as the Flight Management System.

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