The fitness level method is a widely used technique for estimating the mean hitting time of elitist evolutionary algorithms on level-based fitness functions. However, this paper identifies its main limitation: the linear lower bound derived from traditional fitness level partitioning is not tight when applied to many non-level-based fitness functions. A new subset level method is introduced to address this limitation. It selects a subset of non-optimal solutions, partitions them into levels, and then estimates linear bound coefficients based on drift analysis. Explicit expressions are proposed to compute the lower bound on the mean hitting time of elitist evolutionary algorithms. The proposed method is validated using six instances of the knapsack problem. Results show that the new method can be used to quickly estimate the lower bound on the mean hitting time of elitist evolutionary algorithms. This expands the application scope of the fitness level method to non-level-based functions.

翻译：适应度等级方法是估计精英进化算法在基于等级的适应度函数上平均命中时间的常用技术。然而，本文指出了其主要局限：当应用于许多非基于等级的适应度函数时，传统适应度等级划分导出的线性下界并不紧致。为克服此局限，本文引入了一种新的子集等级方法。该方法选取非最优解的一个子集，将其划分为若干等级，然后基于漂移分析估计线性界系数。本文提出了计算精英进化算法平均命中时间下界的显式表达式。所提方法通过背包问题的六个实例进行了验证。结果表明，新方法可用于快速估计精英进化算法的平均命中时间下界，从而将适应度等级方法的应用范围扩展至非基于等级的函数。