Plans de vols Pareto-optimaux : coût du carburant vs durée du vol

飞行计划优化必须在燃料成本和飞行时间之间进行权衡。例如，如果航班延误了几分钟，这是经常发生的情况，人们必须确定应该使用多少燃料来提高飞机的速度，从而减少因延误而造成的成本。这种权衡目前是通过最小化燃料成本加上成本指数乘以飞行时间来实现的。这种方法有两个缺点。首先，成本指数必须由计划者确定，通常需要多次尝试才能找到令人满意的值。其次，燃料成本作为飞行时间的函数并不是在所有持续时间值中都是凸的。飞行高度变化、征收关税的区域、禁止的空域或不利的风条件可能会导致时间间隔函数不凸。结果，成本指数的任何值都不可能获得在这样的间隔内的飞行时间。然而，有可能有一个与这个飞行时间相对应的飞行计划。这个项目开发了这个问题的新公式和一种新的求解方法，可以在几秒钟内获得所有持续时间的最优飞行计划。开发了两个系统：一个用于飞行计划，其中需要确定机上携带的燃料数量；另一个用于更新飞行计划，其中，燃料数量是固定的，一个必须在最小燃料供应的时间窗口内通过某些点。除了包括飞行计划优化的基本研究目标外，该项目还旨在使新开发的系统达到高度成熟的水平，以便迅速为工业终端用户使用。

Flight plan optimization has to make a trade-off between fuel cost and flight time. For example, if a flight is delayed by a few minutes, as is often the case, one has to determine how much fuel should be used in order to increase the speed of the aircraft and, thus, reduce the costs resulting from a delayed arrival. This trade-off is currently obtained by minimizing the fuel cost plus the cost index times the flight time. This method has two drawbacks. First, the cost index has to be determined by the planner, and often many attempts are necessary before a satisfactory value is found. Second, fuel cost as a function of flight time is not convex for all duration values. Flight level changes, tariffed zones, prohibited airspace or adverse wind conditions can lead to time intervals where the function is not convex. As a result, no value of the cost index makes it possible to obtain a flight time in such an interval. Yet it is possible to have a flight plan corresponding to this flight time.This project develops a new formulation of this problem and a new solving method with which optimal flight plans can be obtained for all durations in a few seconds. Two systems are developed: one for flight planning, where the quantity of fuel to be taken on board has to be determined, the other one for updating the flight plan, where the quantity of fuel is fixed, and one has to go through some points within a time window with minimum fuel supply.In addition to including the fundamental research objectives on flight plan optimization, this project aims at bringing the new developed systems to a high level of maturity so that they quickly become usable by industrial end users.