Optimization of complex phenotypes in engineered microbial strains has traditionally been accomplished by laboratory evolution. However, only a subset of the resulting mutations may affect the phenotype of interest and many others may have unintended effects. Multiplexed genome editing can complement evolutionary approaches by creating diverse combinations of targeted changes, but in both cases it remains challenging to identify which alleles influence the desired phenotype. We present a method for identifying a minimal set of genomic modifications that optimizes a complex phenotype by combining iterative cycles of multiplex genome engineering and predictive modeling. We applied our method to the 63-codon E. coli strain C321.∆A, which has 676 mutations relative to its wild-type ancestor, and identified six single nucleotide mutations that together recover 59% of the fitness defect exhibited by the strain. The resulting optimized strain, C321.DA.opt, is an improved chassis for production of proteins containing non-standard amino acids. Our data reveal how multiple cycles of multiplex automated genome engineering (MAGE) and inexpensive sequencing can generate rich genotypic and phenotypic diversity that can be combined with linear regression techniques to quantify individual allelic effects. While laboratory evolution relies on enrichment as a proxy for allelic effect, our model-guided approach is less susceptible than enrichment to bias from population dynamics and recombination efficiency. We also show that the method can identify beneficial de novo mutations that arise adventitiously. Beyond improving the fitness of C321.∆A, our work provides a proof-of-principle for high-throughput quantification of individual allelic effects which can be used with any method for generating targeted genotypic diversity.