In this article, the design of a S-band klystron lamp with a central frequency of 3 GHz and a five-cavity structure is modeled as a many-objective optimization problem. The optimization objectives include maximizing gain, bandwidth, and efficiency, while minimizing the structural length. To solve this problem, a new evolutionary algorithm based on genetic algorithms has been developed, which utilizes an Adaptive Elitist Relation (AER) to establish a proper balance between convergence and diversity in the objective space. The algorithm’s performance was validated against the well-known NSGA-III algorithm using four benchmark functions (DTLZ1–4), and the results demonstrated competitive or superior performance of the proposed method. Klystron simulation was carried out by executing the one-dimensional AJDISK computational code within MATLAB. After extracting the final Pareto front, designs with efficiency greater than 35% were selected, and their robustness index was calculated based on the one-sided Euclidean norm of the average deviation of objectives from the nominal state across 20 random scenarios with ±1 MHz uncertainty in cavity frequencies. The results indicate that it is possible to identify designs with high gain, suitable bandwidth, short length, and desirable stability against frequency errors. The proposed method can serve as a framework for robust design in microwave systems with multiple objectives and practical uncertainties.