Linear functions have gained great attention in the run time analysis of evolutionary computation methods. The corresponding investigations have provided many effective tools for analyzing more complex problems. So far, the runtime analysis of evolutionary algorithms has mainly focused on unconstrained problems, but problems occurring in applications frequently involve constraints. Therefore, there is a strong need to extend the current analyses and used methods for analyzing unconstrained problems to a setting involving constraints.

In this paper, we consider the behavior of the classical $(1+1)$ Evolutionary Algorithm on linear functions under linear constraint. We show tight bounds in the case where the constraint is given by the OneMax function and the objective function is given by either the OneMax or the BinVal function. For the general case we present upper and lower bounds.

线性函数在进化计算方法的运行时分析中得到了极大的关注。相应的调查提供了许多有效的工具来分析更复杂的问题。到目前为止，进化算法的运行时分析主要集中在不受约束的问题上，但是在应用程序中发生的问题经常涉及约束。因此，迫切需要将当前用于分析无约束问题的分析和使用的方法扩展到涉及约束的设置。

在本文中，我们考虑了经典的行为 $（\mathrm{1个}+\mathrm{1个}）$线性约束下线性函数的进化算法。在约束由OneMax函数给定而目标函数由OneMax或BinVal函数给定的情况下，我们显示出严格的界限。对于一般情况，我们给出上限和下限。