动态BinVal函数上（mu+1）- EA的解析
Runtime analysis of the (mu+1)-EA on the Dynamic BinVal function
摘要：
我们研究进化算法在一个动态的设置，每一代不同的适应度函数被选择，并选择相对于当前的适应度函数。具体来说，我们考虑动态BinVal，其中每一代的适应度函数由线性函数BinVal给出，但在每一代中，位的顺序是随机排列的。对于（1+1）-EA，已知对于突变参数存在效率阈值$c_0$，在该效率阈值处，运行时间从准线性切换到指数。先前的经验证据表明，对于较大的群体大小$μ$，阈值可能会增加。我们证明，这是至少在最佳附近的$\varepsilon$ -邻域的情况下：（μ+1）-EA的阈值变得任意大，如果选择足够大的$μ$。然而，最令人惊讶的结果是通过对$μ=2$的二阶分析获得的：阈值随着接近最佳值而增加。特别是，最难优化的区域不在最优值附近。
英文摘要：
We study evolutionary algorithms in a dynamic setting, where for each generation a different fitness function is chosen, and selection is performed with respect to the current fitness function. Specifically, we consider Dynamic BinVal, in which the fitness functions for each generation is given by the linear function BinVal, but in each generation the order of bits is randomly permuted. For the (1+1)-EA it was known that there is an efficiency threshold $c_0$ for the mutation parameter, at which the runtime switches from quasilinear to exponential. A previous empirical evidence suggested that for larger population size $μ$, the threshold may increase. We prove that this is at least the case in an $\varepsilon$-neighborhood around the optimum: the threshold of the (μ+1)-EA becomes arbitrarily large if the $μ$ is chosen large enough. However, the most surprising result is obtained by a second order analysis for $μ=2$: the threshold INcreases with increasing proximity to the optimum. In particular, the hardest region for optimization is NOT around the optimum.
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