发表机构
Universidad de La Laguna（拉古纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对各向同性高斯环境动态下的ROOT问题，推导了固定部署解期望生存时间的严格下界与多步上界，经蒙特卡洛验证了理论预测，为部署决策提供分析支撑。
AI 中文摘要
鲁棒随时间优化（ROOT）是进化动态优化的一个新兴分支，旨在寻找能在多个连续环境中保持有效性的解。与传统的追踪移动最优（TMO）范式在每次环境变化后重新优化不同，ROOT明确重视解的持久性。尽管该领域已取得显著发展，但多数贡献仍停留在算法和实证层面，从理论角度理解的若干基本特性仍不清晰，其中之一就是生存时间，即部署解持续满足规定质量阈值的未来环境数量。虽然生存时间被广泛用作时间鲁棒性的度量，但人们对其期望值如何依赖环境动态、部署质量或问题特性知之甚少。本文研究固定部署解在各向同性高斯环境动态下的期望生存时间，将生存建模为离散首达问题，推导得到严格下界和可计算的多步上界。分析表明，在缓慢变化环境中，期望生存时间随Θ(σ⁻²)缩放，在高维场景下趋近于1次未来变化的最小值。全面的蒙特卡洛研究验证了理论预测，检验了对建模假设和参数不确定性的敏感性，并说明了这些界如何支持优化后的部署决策。所得框架为部署寿命提供了分析性表征，明确了所需部署时限何时可保证、排除或仍存在分析性未决问题。
英文摘要
Robust Optimization Over Time (ROOT) is a recent branch of evolutionary dynamic optimization that seeks solutions capable of remaining effective across multiple consecutive environments. Unlike the traditional track-the-moving-optimum (TMO) paradigm, which reoptimizes after every environmental change, ROOT explicitly values persistence. Although the field has grown considerably, most contributions remain algorithmic and empirical, leaving several fundamental properties poorly understood from a theoretical perspective. One such property is survival time, defined as the number of future environments in which a deployed solution continues to satisfy a prescribed quality threshold. While survival time is widely used as a measure of temporal robustness, little is known about how its expected value depends on environmental dynamics, deployment quality, or problem characteristics. This paper studies expected survival time for a fixed deployed solution under isotropic Gaussian environmental dynamics. Modeling survival as a discrete first-exit problem, we derive a rigorous lower bound and a computable multi-step upper bound. The analysis shows that expected survival scales as $Θ(σ^-{2})$ in slowly varying environments and approaches its minimum value of one future change in high dimensions. A comprehensive Monte Carlo study validates the theoretical predictions, examines sensitivity to modeling assumptions and parameter uncertainty, and illustrates how the bounds can support deployment decisions after optimization. The resulting framework provides an analytical characterization of deployment lifetime and identifies when a required deployment horizon can be guaranteed, ruled out, or remains analytically unresolved.
