Laboratory evolution has traditionally been used to optimize complex phenotypes of engineered microbial strains. However, only a subset of the resulting mutations may affect the phenotype of interest and many others may have unintended effects. Targeted methods like multiplex genome editing can complement evolutionary approaches by creating combinatorial variants of specific changes, but it remains challenging to identify which alleles influence the desired phenotype. Here, 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. We show 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, we find that our model-guided approach is less susceptible to bias from population dynamics and recombination efficiency, can be effectively used on large numbers of target alleles, and can additionally identify beneficial de novo mutations arising in the background of a targeted approach. Beyond improving engineered genomes, our work provides a proof-of-principle for high-throughput quantification of allelic effects which can be combined with any method for generating targeted genotypic diversity.