<p>Foamed concrete exhibits notable properties and is widely used in civil engineering. However, the incorporation of multiple material components brings complexity into the prediction of compressive strength and optimization of mixture design, particularly when economic considerations are involved. To address this challenge, this study integrates three machine learning (ML) models with the genetic algorithm (GA) to: (1) develop a data-driven model to accurately predict the compressive strength of silt-based foamed concrete, and (2) propose an optimization strategy for mixture design from the perspectives of strength and cost-effectiveness. A real-world case study is investigated, where an experimental dataset of compressive strength involving various factors is used to train and test three ML models. In the first step, GA is employed to automatically tune the hyperparameters for three ML models. Comparative analysis reveals that the artificial neural network (ANN) outperforms other models in terms of prediction accuracy, with an <i>R</i>² value of 99.03% and MAE of 0.14 on the dataset. In the second step, the proposed mixture-design optimization successfully identifies the optimal material proportions that enable the compressive strength close to the target value and agree greatly with the measured data. The mixture-design optimization can save about 15% of the construction budget. Further multi-objective optimization indicates that the cement content could be reduced by 12% on average while satisfying the required strength.</p>