We study first-hitting times in Differential Evolution (DE) through a conditional hazard frame work. Instead of analyzing convergence via Markov-chain transition kernels or drift arguments, we ex press the survival probability of a measurable target set $A$ as a product of conditional first-hit probabilities (hazards) $p_t=\Prob(E_t\mid\mathcal F_{t-1})$. This yields distribution-free identities for survival and explicit tail bounds whenever deterministic lower bounds on the hazard hold on the survival event. For the L-SHADE algorithm with current-to-$p$best/1 mutation, we construct a checkable algorithmic witness event $\mathcal L_t$ under which the conditional hazard admits an explicit lower bound depending only on sampling rules, population size, and crossover statistics. This separates theoretical constants from empirical event frequencies and explains why worst-case constant-hazard bounds are typically conservative. We complement the theory with a Kaplan--Meier survival analysis on the CEC2017 benchmark suite . Across functions and budgets, we identify three distinct empirical regimes: (i) strongly clustered success, where hitting times concentrate in short bursts; (ii) approximately geometric tails, where a constant-hazard model is accurate; and (iii) intractable cases with no observed hits within the evaluation horizon. The results show that while constant-hazard bounds provide valid tail envelopes, the practical behavior of L-SHADE is governed by burst-like transitions rather than homogeneous per-generati on success probabilities.

翻译：本研究通过条件风险框架探讨差分进化（DE）中的首次命中时间。不同于通过马尔可夫链转移核或漂移论证分析收敛性，我们将可测目标集$A$的存活概率表达为条件首次命中概率（风险）$p_t=\Prob(E_t\mid\mathcal F_{t-1})$的乘积。当存活事件上存在风险的确切下界时，该方法可导出与分布无关的存活恒等式及显式尾部边界。针对采用current-to-$p$best/1变异策略的L-SHADE算法，我们构建了可验证的算法见证事件$\mathcal L_t$，在该事件下条件风险存在仅取决于采样规则、种群规模和交叉统计量的显式下界。该方法将理论常数与经验事件频率分离，解释了为何最坏情况下的常数风险边界通常较为保守。我们通过在CEC2017基准测试集上进行Kaplan-Meier存活分析来补充理论。跨函数与计算预算的研究揭示了三种不同的经验机制：（i）强聚类成功模式，命中时间集中分布于短时爆发区间；（ii）近似几何尾部模式，常数风险模型具有较高准确性；（iii）在评估时限内未观测到命中的难解案例。结果表明，虽然常数风险边界提供了有效的尾部包络，但L-SHADE的实际行为受爆发式跃迁而非均匀的逐代成功概率所主导。