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This paper tackles the problem of analyzing the correctness and performance of a computer network protocol. Given the complexity of the problem, no currently used technique is able to achieve good results: formal techniques can discover some bugs but can be applied to over-simplified models, only; on the other hand, statistical techniques relying on simulation often fail to find some critical cases for the protocol. Our proposed approach relies on coupling a genetic algorithm with a simulator of the system under verification. Genetic algorithms recently proved themselves excellent tools for giving good, yet approximate, solution to hard-to-solve problems. To prove the effectiveness of our approach, we applied it to the quantitative verification of a network protocol: the complexity of this problem prevents the application of exact techniques, while experimental results show that the verification results we obtained are better than one can achieve with traditional statistical methods. As an example, the approach is applied to the verification of 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.