The increasing demand for environmentally friendly and passenger-favored flight operation requires a systematic scheme of sustainable trajectory optimization for the aircraft cruise. This paper achieves it by proposing an innovative performance framework based on the comprehensive benefit to the society considering both economic and noneconomic ones, following which the sustainable trajectory optimization problem is modeled by discretization. A method combining forward recurrence and memoization operation, called memoization dynamic programming, is developed to solve the model with computational efficiency. Working with real-world operational data of a typical flight route, we demonstrate the effectiveness of the proposed scheme at different levels and explore the difference in its performance due to meteorological conditions, aircraft type, and time horizon. The scheme is proved to perform robustly in comprehensive performance with a stable benefit rate of about 8% through sensitivity analysis, by which we find that it is relatively better for the flights cruising on business route with a load factor of 85%. Tradeoff results suggest that the systematic consideration of both the economic and noneconomic performance contributes to improved integrated sustainability. In particular, the optimal comprehensive performance at a monthly level can be obtained when accepting an additional $26,500 economic cost.

中文翻译：

---

基于综合社会效益的飞机巡航可持续航迹优化方案

对环境友好和乘客青睐的飞行运营的需求不断增长，需要为飞机巡航制定可持续的轨迹优化系统方案。本文通过提出一个基于社会综合效益的创新绩效框架来实现这一目标，同时考虑经济和非经济因素，然后通过离散化对可持续轨迹优化问题进行建模。开发了一种结合前向递推和记忆化操作的方法，称为记忆化动态规划，以计算效率来求解该模型。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 使用典型航线的真实运营数据，我们在不同层面证明了所提出方案的有效性，并探讨了其性能因气象条件、飞机类型、和时间范围。通过敏感性分析，证明该方案综合性能稳健，受益率稳定在8%左右，我们发现该方案在客座率85%的公务航线上巡航相对较好。权衡结果表明，系统地考虑经济和非经济表现有助于提高综合可持续性。尤其是在接受额外的 26,500 美元经济成本的情况下，可以获得每月级别的最佳综合性能。权衡结果表明，系统地考虑经济和非经济表现有助于提高综合可持续性。尤其是在接受额外的 26,500 美元经济成本的情况下，可以获得每月级别的最佳综合性能。权衡结果表明，系统地考虑经济和非经济表现有助于提高综合可持续性。尤其是在接受额外的 26,500 美元经济成本的情况下，可以获得每月级别的最佳综合性能。