In this paper the problem of cyclic instability in dynamic environments is presented. This cyclic instability is generated when binary rule-based nomadic agents (agents entering or leaving the environment) interact in complex ways, generating undesirable outputs for the final user. Our strategy is focused on minimizing this cyclic behaviour, using optimization algorithms, in particular Genetic and Differential Evolution Algorithms. These algorithms are applied to the Average Change Function. Different test instances were used to evaluate the performance of these algorithms. Additionally, statistical tests were applied to measure their performance.