Drift analysis is a powerful tool for analyzing the time complexity of evolutionary algorithms. However, it requires manual construction of drift functions to bound hitting time for each specific algorithm and problem. To address this limitation, general linear drift functions were introduced for elitist evolutionary algorithms. But calculating linear bound coefficients effectively remains a problem. This paper proposes a new method called drift analysis of hitting probability to compute these coefficients. Each coefficient is interpreted as a bound on the hitting probability of a fitness level, transforming the task of estimating hitting time into estimating hitting probability. A novel drift analysis method is then developed to estimate hitting probability, where paths are introduced to handle multimodal fitness landscapes. Explicit expressions are constructed to compute hitting probability, significantly simplifying the estimation process. One advantage of the proposed method is its ability to estimate both the lower and upper bounds of hitting time and to compare the performance of two algorithms in terms of hitting time. To demonstrate this application, two algorithms for the knapsack problem, each incorporating feasibility rules and greedy repair respectively, are compared. The analysis indicates that neither constraint handling technique consistently outperforms the other.

翻译：漂移分析是分析进化算法时间复杂度的有力工具。然而，它需要为每个特定算法和问题手动构造漂移函数以界定命中时间。为解决这一局限性，研究者为精英进化算法引入了通用的线性漂移函数。但如何有效计算线性界系数仍是一个难题。本文提出了一种称为命中概率漂移分析的新方法来计算这些系数。每个系数被解释为适应度层级命中概率的一个界，从而将估计命中时间的任务转化为估计命中概率。随后，我们开发了一种新颖的漂移分析方法来估计命中概率，其中引入路径来处理多峰适应度地形。我们构建了显式表达式来计算命中概率，显著简化了估计过程。所提方法的一个优势是能够同时估计命中时间的下界和上界，并比较两种算法在命中时间方面的性能。为展示此应用，我们比较了求解背包问题的两种算法，它们分别采用了可行性规则和贪婪修复策略。分析表明，这两种约束处理技术均未始终优于对方。