Constraints in multi-objective optimization (equation (11), equations ( )-( ) in the Supplemental Information) ensure that the optimized feed ingredient mixture ratios meet the nutritional constraint of the target feed. Predicting accurate nutritional compositions from NIRS fingerprints entails having diverse compositions due to nutritional variation. In our dataset, the number of samples for each feed ingredient class was too small to reproduce all the nutritional variability that might be observed in industrial production. Hence, we employed Monte Carlo sampling to obtain 1000 simulations with varying nutritional compositions among and within feed ingredients groups. Monte Carlo is a sampling-based methodology that allows us to generate random scenarios based on the probability distributions of the predicted nutrients to observe the effect of nutritional variability on the final optimization. This methodology is extensively used in stochastic optimization in quantitative applications such as in science, engineering and economics, to optimize the process performances explicitly accounting for uncertainty . We utilized the predicted nutritional compositions for each feed ingredient to build multivariate t-distributions to sample from. We considered multivariate tdistributions to account for the correlation among nutrients, ensuring that the simulated formulations respect nutritional constraints. A random error, derived from univariate normal distributions of 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 values, was finally added to the sampled nutritional values to account for the model error in prediction. The optimization model was run independently for each simulation in a stochastic optimization framework.