Abstract- Significant benefits would follow from improving the signal growth rates of certain high-power microwave (HPM) sources, including the relativistic klystron oscillator (RKO). Optimization of the growth rate via analytical and standard numerical techniques is intractable because of the high dimensionality of the design space and the existence of many local optima. Instead, the growth rate is optimized using a real-valued evolutionary algorithm (EA), which performs mutation, selection, and recombination on a population of candidate design parameters. Practical application of EAs requires the availability of a computationally efficient model of design quality. Two models of the RKO are developed relating the growth rate of the microwave output power to the design parameters. Both models have computationally efficient implementations, and one of them generalizes easily to a novel multi-cavity class of RKO devices, which has significantly better growth rates than standard two-cavity RKOs. Many design optimization problems of interest involve physical constraints. The GENOCOP evolutionary algorithm includes features which support the incorporation of physical constraints in the problem specification through the maintenance of separate search and reference populations, where the latter consists entirely of feasible individuals. It provides “blind ” operators to recombine individuals from the two populations to produce new reference population individuals. However, the use of these blind operators can result in unnecessary modification of the search individual, and domain specific recombination operators can result in improved effectiveness. As with any optimization technique, GENO-COP also allows the use of either the penalty function or repair method for evaluation of infeasible individuals. Computational experiments are performed comparing the effectiveness of each possible combination of these constraint handling techniques.