Optimal Design of the Microwave Oven Magnetic Shunt Transformer Using Physics-Based Equivalent Circuit Model and GNN-Guided NSGA-III Method

Magnetic shunt transformers (MSTs) used in microwave ovens are designed with deliberately high leakage inductance for current limiting and voltage regulation. This requirement couples the core dimensions, winding parameters, shunt geometry, material cost, and power losses. This paper presents an optimal design strategy in which every candidate is evaluated by a physics-based equivalent circuit model and a graph neural network (GNN)-guided non-dominated sorting genetic algorithm III (NSGA-III) optimizer. In the proposed framework, all candidate designs are evaluated for their electromagnetic performance, while the GNN is used only to adapt the crossover probability, mutation probability, and diversity score in NSGA-III. A symmetry-reduced magnetic circuit formulation is derived for the EI-core, and winding resistance, material cost, regional core loss, and engineering constraints are calculated from explicitly defined variables. Benchmark functions and EI-type MSTs are used to examine the computational performance of the hybrid optimizer and the resulting cost–loss trade-off design. In the reported case, the selected compromise design reduces the material cost from 25.170 to 24.898 Renminbi (RMB) and changes the predicted loss from 171.538 to 172.337 W. Transient three-dimensional finite-element analysis and the experimental prototype validate the designed MST, and the corresponding difference from the circuit-model prediction is 1.72%.