Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint k. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter d or budget k allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

进化算法（EA）已发现许多成功的实际应用，其中的优化问题通常受到各种不确定性的影响。为了从理论上理解EA的实际行为，需要进行一系列的工作来分析EA的运行时间以在不确定性下进行优化。现有的研究主要集中在噪声和动态优化上，而不确定性优化的另一种常见类型，即鲁棒优化，则鲜有涉及。在本文中，我们分析了具有基数约束k的（1 + 1）-EA求解健壮线性优化问题（即健壮场景下的线性问题）的预期运行时间。考虑了两种常见的健壮方案，即健壮删除和最坏情况。特别是，我们导出了健壮参数d或预算k的狭窄范围，从而允许（1 + 1）-EA在多项式运行时间中找到最佳解决方案，这揭示了EA进行健壮优化的潜力。