Increasing the final titer of a multi-gene metabolic pathway can be viewed as a multivariate optimization problem. While numerous multivariate optimization algorithms exist, few are specifically designed to accommodate the constraints posed by genetic engineering workflows. We present a strategy for optimizing expression levels across an arbitrary number of genes that requires few design-build-test iterations. We compare the performance of several optimization algorithms on a series of simulated expression landscapes. We show that optimal experimental design parameters depend on the degree of landscape ruggedness. This work provides a theoretical framework for designing and executing numerical optimization on multi-gene systems.