New technologies for constructing and editing genomes are facilitating the creation of organisms with novel properties, but these organisms often suffer from phenotypic defects due to suboptimal design or mutations that arise during construction. While laboratory evolution has traditionally been used to optimize complex phenotypes, multiplex genome editing can complement and direct evolutionary approaches by creating combinatorial variants of specific allelic changes. Here, we present a method for identifying genomic modifications that optimize complex phenotypes by combining 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. We find that our model-guided approach is less susceptible to bias from population dynamics and recombination efficiency, can be effectively used on sets of over 100 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 approach for high-throughput quantification of allelic effects that could be used with any method for generating targeted genotypic diversity.