  In real-world applications, many optimization problems have the time-linkage
property, that is, the objective function value relies on the current solution
as well as the historical solutions. Although the rigorous theoretical analysis
on evolutionary algorithms has rapidly developed in recent two decades, it
remains an open problem to theoretically understand the behaviors of
evolutionary algorithms on time-linkage problems. This paper takes the first
step to rigorously analyze evolutionary algorithms for time-linkage functions.
Based on the basic OneMax function, we propose a time-linkage function where
the first bit value of the last time step is integrated but has a different
preference from the current first bit. We prove that with probability $1-o(1)$,
randomized local search and $(1+1)$ EA cannot find the optimum, and with
probability $1-o(1)$, $(\mu+1)$ EA is able to reach the optimum.
