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There is a growing number of network attacks and the data on the network is more exposed than ever with the increased activity on the Internet. Applying Machine Learning (ML) techniques for cyber-security is a popular and effective approach to address this problem. However, the data which is used by ML algorithms have to be protected. In this paper, we present a framework that combines autoencoder, multi-objective optimization algorithms, and different ML algorithms to encode the network data, reduce its size, and detect and classify the network attacks. The novel element used in this framework, with respect to earlier research, is the application of multi-objective optimization algorithms, such as Multi-Objective Differential Evolution or Non-dominated Sorting Genetic Algorithm-II, to handle the different objectives in the fitness function of the autoencoder (autoencoder decoding error and accuracy of ML algorithm). We evaluated six different ML algorithms for attack detection and classification on network dataset UNSWNB15. The performance of the proposed framework is compared with single-objective Differential Evolution. The results showed that Multi-Objective Differential Evolution outperforms the counterparts for attack detection, while all the evaluated algorithms showed similar performance for attack classification.