As technology evolves, software systems become more and more voluminous and complex. Being currently unable to produce programs free of errors, and in order to ensure that program behaviors comply with their specifications, formal verification of their essential properties is paramount. To this end, model-checking verification approach has been widely used and continues to be. However, if these properties have been verified on a system model, would they still true during any real system execution? So, modeled behavior of a system would be exactly the same in real executions when interacting with its environment? That is why verification during current system execution is essential stage even as a complementary way to other verification approaches. In this paper, we are concerned by runtime verification optimization of component-based systems in Behavior Interactions Priority (BIP) framework in order to significantly reduce time overhead. Our contribution in this paper is to consider only component states involved in the property being verified. The required states imply their associated components to be activated and those useless are disabled. Also, when a steady state is reached during monitoring process, the monitor is stopped which reduces system consumption resources. Our experiment results showed that a non negligible amount of space-time overhead was avoided.