Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist algorithms (1+1)EA and ($\mu$+1)EA are analyzed, and it is unknown whether the non-elitism mechanism could help to escape the local optima existed in OneMax$_{(0,1^n)}$. In general, there are few theoretical results on the benefits of the non-elitism in evolutionary algorithms. In this work, we analyze on the influence of the non-elitism via comparing the performance of the elitist (1+$\lambda$)EA and its non-elitist counterpart (1,$\lambda$)EA. We prove that with probability $1-o(1)$ (1+$\lambda$)EA will get stuck in the local optima and cannot find the global optimum, but with probability $1$, (1,$\lambda$)EA can reach the global optimum and its expected runtime is $O(n^{3+c}\log n)$ with $\lambda=c \log_{\frac{e}{e-1}} n$ for the constant $c\ge 1$. Noting that a smaller offspring size is helpful for escaping from the local optima, we further resort to the compact genetic algorithm where only two individuals are sampled to update the probabilistic model, and prove its expected runtime of $O(n^3\log n)$. Our computational experiments also verify the efficiency of the two non-elitist algorithms.

翻译：许多真实世界应用程序都具有时间链接属性, 最近Zheng等人(TEVC 2021)对其拟议的时间链接 OneMax 问题、 OneMax$ {( 0, 1 ⁇ n) $ 进行了唯一理论分析。 然而, 仅分析了两种精英算法(1+1) EA 和 $( mu$+1) EA 。 目前还不清楚非精英机制是否能帮助摆脱 Onemax 的本地 Optima 存在 Onemax $ ( 0, 1 ⁇ n) 。 总体而言, 在演化算法中, 有关非精英化的效益的理论结果很少。 在这项工作中, 我们通过比较 Elistitat ( 1+$\ lumbda$) 及其非精英对等( 1, $\ lambda$) 的功能分析非精英算法( 1+(1) 美元 ( 1+\ lambda美元) 。 我们证明, 本地选法中只有1 美元 (+\\ $ labda $ ( $) 美元) 的概率, comisalalalalalalal ration ral $ (1, $ (1, ladeal) ac) a.