Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model. As previous works show, this iteration-based perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based cGA (sig-cGA) optimizes the commonly regarded benchmark functions OneMax (OM), LeadingOnes, and BinVal all in quasilinear time, a result shown for no other EDA or evolutionary algorithm so far. For the recently proposed stable compact genetic algorithm—an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model—we prove that it optimizes OM only in a time exponential in its hypothetical population size. Similarly, we show that the convex search algorithm cannot optimize OM in polynomial time.

中文翻译：

---

基于显着性的分布估计算法

分布估计算法 (EDA) 是随机搜索试探法，可创建解空间的概率模型，该模型根据根据模型采样的解的质量进行迭代更新。正如之前的工作所示，这种基于迭代的观点可能导致模型的不稳定更新，特别是接近随机边界值的位频率。为了克服这个问题，我们提出了一种基于经典紧凑遗传算法 (cGA) 的新 EDA，该算法考虑了更长的样本历史，并仅根据其分类为具有统计显着性的信息更新其模型。我们证明了这种基于显着性的 cGA (sig-cGA) 在拟线性时间内优化了普遍认为的基准函数 OneMax (OM)、LeadingOnes 和 BinVal，迄今为止没有其他 EDA 或进化算法显示的结果。对于最近提出的稳定紧凑遗传算法——一种试图通过对均匀分布模型施加偏差来防止不稳定模型更新的 EDA——我们证明它仅在其假设种群大小的时间指数中优化 OM。同样，我们表明凸搜索算法不能在多项式时间内优化 OM。