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

MOAK: 一种面向相控阵天线机电耦合设计的多目标代理模型优化算法

School of Electrical Engineering and Automation, Anhui University, Hefei 230000, China

Received: 5 July 2025

Abstract

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.

摘要

为减小相控阵天线质量、降低制造成本, 并保障恶劣工况下辐射性能稳定性, 提出了一种基于Kriging模型的多目标代理优化算法——MOAK。该算法融合可行域探索准则和TCF-SMOTE准则形成组合加点准则, 通过可行域探索准则实现全域可行空间的有效辨识, 进而利用创新设计的TCF-SMOTE准则构建完整Pareto前沿, 实现高精度Pareto最优解集求解。其中, TCF-SMOTE准则通过截断约束函数(TCF)抑制Kriging模型构建中的极端违约值, 规避可行域边界模型失真; 同时, 应用SMOTE算法生成合成样本点, 增加Pareto解集(PS)数量, 提升Pareto前沿(PF)完整性。在3个标准测试函数的对比试验中, MOAK算法展现出了显著优势, 改善了常规代理模型优化算法中PS稀疏、PF刻画不完整的问题。将文中所提算法应用于相控阵天线前骨架优化设计, MOAK在结构轻量化、成本和辐射性能平衡方面提供了多样性解决方案, 满足不同设计偏好需求。其中, 典型优化方案在保持辐射性能稳定的前提下, 实现了质量减小35.4%, 成本降低80.2%, 计算时长缩减84.91%的综合效益。