Evolutionary computation has shown its superiority in dynamic optimization, but for the (dynamic) time-linkage problems, some theoretical studies have revealed the possible weakness of evolutionary computation. Since the theoretically analyzed time-linkage problem only considers the influence of an extremely strong negative time-linkage effect, it remains unclear whether the weakness also appears in problems with more general time-linkage effects. Besides, understanding in depth the relationship between time-linkage effect and algorithmic features is important to build up our knowledge of what algorithmic features are good at what kinds of problems. In this paper, we analyze the general time-linkage effect and consider the time-linkage OneMax with general weights whose absolute values reflect the strength and whose sign reflects the positive or negative influence. We prove that except for some small and positive time-linkage effects (that is, for weights $0$ and $1$), randomized local search (RLS) and (1+1)EA cannot converge to the global optimum with a positive probability. More precisely, for the negative time-linkage effect (for negative weights), both algorithms cannot efficiently reach the global optimum and the probability of failing to converge to the global optimum is at least $1-o(1)$. For the not so small positive time-linkage effect (positive weights greater than $1$), such a probability is at most $c+o(1)$ where $c$ is a constant strictly less than $1$.

翻译：进化计算在动态优化中已展现出其优越性，但对于（动态）时序关联问题，一些理论研究揭示了进化计算可能存在的弱点。由于理论分析的时序关联问题仅考虑了极强的负时序关联效应的影响，尚不清楚该弱点是否也出现在具有更一般时序关联效应的问题中。此外，深入理解时序关联效应与算法特征之间的关系，对于建立"何种算法特征适用于何种问题"的知识体系至关重要。本文分析了一般时序关联效应，并考虑了具有一般权重的时序关联OneMax问题，其中权重的绝对值反映影响强度，符号反映正负影响方向。我们证明：除了一些较小且为正的时序关联效应（即权重为$0$和$1$的情况）外，随机局部搜索(RLS)和(1+1)EA无法以正概率收敛到全局最优解。更精确地说，对于负时序关联效应（负权重情况），两种算法均无法高效达到全局最优解，且未能收敛到全局最优解的概率至少为$1-o(1)$。对于非极小的正时序关联效应（大于$1$的正权重），该概率至多为$c+o(1)$，其中$c$为严格小于$1$的常数。