Accelerated urbanization and digital transformation place increased demands on the sustainability and security of the critical information infrastructure of smart cities. Designing such an infrastructure is a complex multi-criteria task that requires the integration of heterogeneous requirements. A concept for designing the critical information infrastructure of a smart city has been developed, focusing on creating a single universal environment. This environment integrates the use of hybrid deep learning models based on backpropagation neural networks optimized by genetic algorithms and models with cyclic consistency to solve problems of data matching, anomaly detection and optimization of system parameters. The proposed models and methods were tested on the modeling data of the critical information infrastructure of the smart city of Moscow. The use of temporal logics made it possible to automatically verify the key properties of sustainability, identifying violations of the critical requirements of the original projects. The implementation of the parametric optimality criterion and its evaluation using the TOPSIS method and the GA-BPNN hybrid model demonstrated an increase in the accuracy of predicting indicators, a reduction in the convergence time of training and an improvement in the generalization ability. The obtained results prove that the proposed toolkit is a powerful tool for designing and managing sustainable, secure and efficient critical information infrastructure of a smart city.