Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation.