Engineered metabolic pathways often suffer from flux imbalances that can overburden the cell and accumulate intermediate metabolites, resulting in reduced product titers. One way to alleviate such imbalances is to adjust the expression levels of the constituent enzymes using a combinatorial expression library. Typically, this approach requires high-throughput assays, which are unfortunately unavailable for the vast majority of desirable target compounds. To address this, we applied regression modeling to enable expression optimization using only a small number of measurements. We characterized a set of constitutive promoters in Saccharomyces cerevisiae that spanned a wide range of expression and maintained their relative strengths irrespective of the coding sequence. We used a standardized assembly strategy to construct a combinatorial library and express for the first time in yeast the five-enzyme violacein biosynthetic pathway. We trained a regression model on a random sample comprising 3% of the total library, and then used that model to predict genotypes that would preferentially produce each of the products in this highly branched pathway. This generalizable method should prove useful in engineering new pathways for the sustainable production of small molecules.