Analysis of Evolutionary Algorithms on Fitness Function With Time-Linkage Property

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