Machine-learning technologies have exhibited robust competences in solving many petroleum engineering problems. The accurate predictivity and fast computational speed enable a large volume of time-consuming engineering processes such as history-matching and field development optimization. The Southwest Regional Partnership on Carbon Sequestration (SWP) project desires rigorous history-matching and multi-objective optimization processes, which fits the superiorities of the machine-learning approaches. Although the machine-learning proxy models are trained and validated before imposing to solve practical problems, the error margin would essentially introduce uncertainties to the results. In this paper, a hybrid numerical machine-learning workflow solving various optimization problems is presented. By coupling the expert machine-learning proxies with a global optimizer, the workflow successfully solves the history-matching and CO2 water alternative gas (WAG) design problem with low computational overheads. The history-matching work considers the heterogeneities of multiphase relative characteristics, and the CO2-WAG injection design takes multiple techno-economic objective functions into accounts. This work trained an expert response surface, a support vector machine, and a multi-layer neural network as proxy models to effectively learn the high-dimensional nonlinear data structure. The proposed workflow suggests revisiting the high-fidelity numerical simulator for validation purposes. The experience gained from this work would provide valuable guiding insights to similar CO2 enhanced oil recovery (EOR) projects.