The main focus of this work is the optimization of a thermoacoustic plate stack in a standingwave thermoacoustic refrigerator using genetic algorithm. A numerical model of the thermoacoustic stack and its iterative solving process are firstly presented. A comparison to DeltaEC modelling shows that the presented method is effective in predicting the acoustic field and the energy flow. Based on the numerical model, the stack is optimized in terms of four and five variables for both single objective and multiple objectives. In the four-variable models, the length and position of the stack, the plate spacing and the stack porosity are investigated. In the five-variable model, the acoustic frequency is considered additionally. In the single-objective optimization, the objective function is either the cooling power or the coefficient of performance of the stack, and the multi-objective model has two objective Corresponding author: Yehui Peng,