MOAK: a multi-objective surrogate model optimization algorithm for electromechanical coupling design of phased array antennas

To reduce the mass and manufacturing cost of phased array antennas while ensuring stable radiation performance under harsh operating conditions, this paper proposes a multi-objective surrogate optimization algorithm based on the Kriging model—MOAK. The algorithm integrates a feasible-region exploration criterion with a TCF-SMOTE criterion to form a hybrid infill strategy. The feasible-region exploration criterion enables effective identification of the global feasible space, after which the innovative TCF-SMOTE criterion is employed to construct a complete Pareto front, thereby achieving high-accuracy Pareto-optimal solution sets. Specifically, the TCF-SMOTE criterion suppresses extreme constraint violations in Kriging model construction through a truncated constraint function (TCF), mitigating model distortion near feasible-domain boundaries. In addition, the SMOTE algorithm is applied to generate synthetic sample points, increasing the number of Pareto solutions (PS) and improving the completeness of the Pareto front (PF). Comparative experiments on three standard benchmark functions demonstrate that the MOAK algorithm significantly outperforms conventional surrogate-model-based optimization algorithms, alleviating the problems of sparse PS distribution and incomplete PF characterization. When applied to the optimization design of the pre-skeleton of a phased array antenna, MOAK provides diverse solutions for balancing structural lightweighting, cost, and radiation performance, thereby meeting different design preference requirements. In a representative optimized design, MOAK achieved a 35.4% reduction in mass, an 80.2% reduction in cost, and an 84.91% reduction in computation time, while maintaining stable radiation performance.