We compare the $(1,\lambda)$-EA and the $(1 + \lambda)$-EA on the recently introduced benchmark DisOM, which is the OneMax function with randomly planted local optima. Previous work showed that if all local optima have the same relative height, then the plus strategy never loses more than a factor $O(n\log n)$ compared to the comma strategy. Here we show that even small random fluctuations in the heights of the local optima have a devastating effect for the plus strategy and lead to super-polynomial runtimes. On the other hand, due to their ability to escape local optima, comma strategies are unaffected by the height of the local optima and remain efficient. Our results hold for a broad class of possible distortions and show that the plus strategy, but not the comma strategy, is generally deceived by sparse unstructured fluctuations of a smooth landscape.

翻译：本文比较了$(1,\lambda)$-EA和$(1 + \lambda)$-EA在最近引入的基准函数DisOM上的性能，该函数是具有随机植入局部最优点的OneMax函数。先前研究表明，若所有局部最优点的相对高度相同，则plus策略相比逗号策略的损失不超过因子$O(n\log n)$。本文证明，即使局部最优点的高度存在微小随机波动，也会对plus策略产生毁灭性影响，导致超多项式运行时间。相反，由于逗号策略具有逃离局部最优点的能力，故不受局部最优点高度的影响，仍保持高效性。我们的结果适用于一大类可能的扭曲情形，并表明plus策略（而非逗号策略）通常会被光滑景观中稀疏的无结构波动所误导。