To achieve system resilience, one can leverage high-level design features (e.g., redundancies and fail-safes), adjust operational profiles (e.g., load or trajectory), and use appropriate contingency management (e.g., emergency procedures) to mitigate potential hazards. For example, in the design of a novel drone, one would optimize the rotor and battery pack architectures (design), flight-plan (operations), and flight reconfiguration plans (contingency management) to maximize operational value while minimizing failure risk. In this work, the integrated resilience optimization formulation of the resilient design problem is defined, in which the system design, operational profile, and contingency management are optimized in a single framework. To understand how best to leverage this framework in early design exploration, sequential, all-in-one, and bilevel optimization architectures on the exhaustive search of a discrete-variable drone model are then compared in terms of their effectiveness and computational performance. This comparison shows that using a bilevel or all-in-one optimization architecture can lead to better solutions than sequential architectures in design problems where the levels are coupled. Additionally, for this problem, a bilevel structure has lower computational cost than the all-in-one architecture, especially when the lower-level resilience optimization problem is decomposed into independent subproblems for each set of fault modes.

为了实现系统弹性，可以利用高级设计功能（例如，冗余和故障保险），调整操作配置文件（例如，负载或轨迹）以及使用适当的应急管理（例如，应急程序）来减轻潜在危害。例如，在新型无人机的设计中，将优化旋翼和电池组的架构（设计），飞行计划（操作）和飞行重新配置计划（应急管理），以在最大程度地降低故障风险的同时最大化运营价值。在这项工作中，定义了弹性设计问题的综合弹性优化公式，其中在单个框架中优化了系统设计，操作配置文件和应急管理。要了解如何在早期设计探索，顺序，多合一，然后在穷举搜索离散变量无人机模型方面比较了两级优化架构的有效性和计算性能。这种比较表明，在将各个级别耦合在一起的设计问题中，使用双层或多合一优化体系结构可以比顺序体系结构提供更好的解决方案。此外，针对此问题，双层结构的计算成本低于多合一体系结构，尤其是在针对每组故障模式将较低级别的弹性优化问题分解为独立的子问题时。这种比较表明，在将各个级别耦合在一起的设计问题中，使用双层或多合一优化体系结构可以比顺序体系结构提供更好的解决方案。此外，针对此问题，双层结构的计算成本低于多合一体系结构，尤其是在针对每组故障模式将较低级别的弹性优化问题分解为独立的子问题时。这种比较表明，在将各个级别耦合在一起的设计问题中，使用双层或多合一优化体系结构可以比顺序体系结构提供更好的解决方案。此外，针对此问题，双层结构的计算成本低于多合一体系结构，尤其是在针对每组故障模式将较低级别的弹性优化问题分解为独立的子问题时。