Formal verification techniques need to deal with the complexity of the systems rified. Most often, this problem is solved by taking an abstract model of the system and aiming at a complete verification of an approximation of the system. This paper proposes a complementary verification approach, in which the approximation is introduced into the verification algorithm, instead of the system model: we achieve an approximate verification of a fairly complete and detailed system model. The proposed technique relies on coupling a Genetic Algorithm with a simulator of the system under verification, and is especially suited for verifying performance-related aspects. To prove the effectiveness of our approach, we applied it to the quantitative verification of a network protocol: the TCP protocol operating on a given network. A Genetic Algorithm is able to find a configuration of the traffic over the network that sensitizes a critical problem in the TCP protocol that would be difficult to find ...