Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect caused by noise. Sampling is a popular strategy, which evaluates the objective a couple of times, and employs the mean of these evaluation results as an estimate of the objective value. In this work, we introduce a novel sampling method, median sampling, into EAs, and illustrate its properties and usefulness theoretically by solving OneMax, the problem of maximizing the number of 1s in a bit string. Instead of the mean, median sampling employs the median of the evaluation results as an estimate. Through rigorous theoretical analysis on OneMax under the commonly used onebit noise, we show that median sampling reduces the expected runtime exponentially. Next, through two special noise models, we show that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be better than mean sampling; otherwise, it may fail and mean sampling can be better. The results may guide us to employ median sampling properly in practical applications.

进化算法（EA）是一种受自然启发的元启发式方法，在各种实际的优化问题中都有广泛的应用。在这些问题中，客观评估通常是不准确的，因为在现实世界中噪声几乎是不可避免的，而减弱噪声引起的负面影响是至关重要的问题。采样是一种流行的策略，它多次评估目标，并将这些评估结果的平均值用作目标值的估计。在这项工作中，我们将一种新颖的采样方法（中值采样）引入到EA中，并通过解决OneMax（最大化位串中1位数的问题）来从理论上说明其性质和有用性。中位数采样使用评估结果的中位数作为估计值，而不是平均值。通过在常用的onebit噪声下对OneMax进行严格的理论分析，我们表明中值采样会以指数方式减少预期的运行时间。接下来，通过两个特殊的噪声模型，我们表明，当噪声适应度的2分位数随着真实适应度的增加而增加时，中值采样会好于均值采样。否则，它可能会失败，意味着采样效果会更好。结果可能指导我们在实际应用中适当地使用中值采样。