Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+$+$$+$1) EA introduced by Rajabi and Witt (2022) adds stagnation detection to the classical (1+$+$$+$1) EA with standard bit mutation. This algorithm flips each bit independently with some mutation rate, and stagnation detection raises the rate when the algorithm is likely to have encountered a local optimum. In this article, we investigate stagnation detection in the context of the k$k$$k$-bit flip operator of randomized local search that flips k$k$$k$ bits chosen uniformly at random and let stagnation detection adjust the parameter k$k$$k$⁠. We obtain improved runtime results compared with the SD-(1+$+$$+$1) EA amounting to a speedup of at least (1−o(1))2πm−−−−√$(1-o(1))2πm$$(1-o(1))2πm$⁠, where m$m$$m$ is the so-called gap size, that is, the distance to the next improvement. Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k$k$$k$ due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the k$k$$k$-bit flip operator with stagnation detection.

最近提出了一种称为停滞检测的机制，该机制在遇到局部最优时自动调整进化算法的变异率。所谓的SD-(1+$+$$+$1) Rajabi 和 Witt (2022) 引入的 EA 在经典 (1+$+$$+$1) 带有标准位突变的 EA。该算法以一定的变异率独立翻转每个位，当算法可能遇到局部最优时，停滞检测会提高速率。在这篇文章中，我们研究了在k$k$$k$- 翻转的随机局部搜索的位翻转运算符k$k$$k$随机均匀选择位，让停滞检测调整参数k$k$$k$⁠。与 SD-(1+$+$$+$1) EA 相当于至少加速( 1 − o ( 1 ) )2 π米−−−−√$(1个-o(1个))2个π米$$(1-o(1))2πm$⁠ , 其中米$米$$m$就是所谓的gap size，也就是下一次改进的距离。此外，我们提出了额外的方案，即使算法错过了一个可行的选择，也可以防止无限优化时间k$k$$k$由于不幸的事件。最后，我们给出了一个示例，其中标准位变异仍然优于k$k$$k$- 具有停滞检测的位翻转运算符。