发表机构
Karlsruhe Institute of Technology; Katholische Universität Eichstätt-Ingolstadt（卡尔斯鲁厄理工学院; 艾希施泰特-因戈尔施塔特天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一般两阶段网络流多准则优化模型，将回弹、抵抗、损失和最大性能退化作为独立准则，证明问题难解并开发包络启发式算法，强调弹性决策需显式考虑多准则权衡而非单一标量指标。
AI 中文摘要
弹性是系统准备、抵抗、吸收并从不利事件中恢复的能力。因此，从定义上讲，弹性包含多个可能相互冲突且可能规定不同决策的准则。重要的是，系统还必须在日常运行中保持其有效性，并适当调整其对不利事件的准备程度。尽管弹性本质上是多准则的，但现有模型往往侧重于单一准则，并未明确分析潜在冲突、相关权衡及其对决策的影响。我们将回弹、抵抗、损失和最大性能退化分别作为独立的弹性准则，纳入一个一般性的两阶段网络流多准则优化模型中，该模型整合了准备、有效性和响应。我们证明，一般而言，此类多准则优化模型是难以处理的，并开发了一种基于包络的启发式方法来逼近非支配集。我们的计算结果表明，不同的准备工具和激活时机与不同的弹性准则相关联，且相应的权衡具有强烈的实例特异性。因此，应从明确的多准则视角来处理弹性问题，而非通过一个通用的、与偏好无关的标量指标。
英文摘要
Resilience is a system's capability to prepare for, resist, absorb, and recover from adverse events. By definition, resilience therefore encompasses multiple criteria that can conflict and may prescribe different decisions. Importantly, a system must also maintain its effectiveness during routine operations and appropriately scale its preparedness for adverse events. Although resilience is inherently multicriteria, existing models often focus on a single criterion and do not explicitly analyze potential conflicts, the associated trade-offs, and their implications for decision-making. We formulate rebound, resistance, loss, and maximum performance degradation as separate resilience criteria in a general two-stage multicriteria model of network flows over time that integrates preparedness, effectiveness, and response. We show that, in general, such multicriteria optimization models are intractable and develop an enclosure-based heuristic for approximating the nondominated set. Our computational results show that different preparedness instruments and activation timings are associated with different resilience criteria and that the corresponding trade-offs are strongly instance-specific. Thus, resilience should be approached from an explicit multicriteria perspective rather than through a universal, preference-independent scalar index.
