Since 2009, Moving Target Defense (MTD) has become a new paradigm of defensive mechanism that frequently changes the state of the target system to confuse the attacker. This frequent change is costly and leads to a tradeoff between misleading the attacker and disrupting the quality of service. Optimizing the MTD activation frequency is necessary to develop this defense mechanism when facing realistic, multi-step attack scenarios. Attack modeling formalisms based on DAG are prominently used to specify these scenarios. It represents the attack goal in the root of a tree that is recursively refined into subgoals to show the different ways the attacker can compromise the system. According to some specific models, the tree is augmented with countermeasures, time, costs, or probabilities.Our contribution is a new DAG-based formalism for MTDs and its translation into a Price Timed Markov Decision Process to find the best activation frequencies against the attacker's time/cost-optimal strategies. For the first time, MTD activation frequencies are analyzed in a state-of-the-art DAG-based representation. Moreover, this is the first paper that considers the specificity of MTDs in the automatic analysis of attack modeling formalisms. Finally, we present some experimental results using UPPAAL STRATEGO to demonstrate its applicability and relevance.