## 1 Introduction  
Thermoacoustic refrigerators are devices that use sound waves to generate cooling without moving parts, as discussed by [PERSON]'s classic book [1] and by recent review articles [2, 3] that introduced the basic principles and current applications of thermoacoustic devices. Due to the complex relationship between the multiple variables that determine thermoacoustic refrigerator performance, optimization studies are required from a practical point of view. Many proposals are currently being explored to optimize thermoacoustic refrigerators, not only in terms of the performance response to environmental concerns related to many refrigerants but also to obtain fast and simple engineering estimates. The performance response depends primarily on the system's design parameters, including the operating conditions, the structural geometry of the stack/regenerator, the thermo-physical properties of the stack, the working fluid, and the acoustic driver. These design parameters can be studied and optimized from different perspectives and study groups/areas, such as the following:  
Energy efficiency and thermodynamics: Improving the energy efficiency of the thermoacoustic cycle involves studying heat transfers, energy losses, and conversion efficiencies in the cooling process. For example, [PERSON] et al. [4] developed a new iterative numerical scheme to optimize and solve acoustic field and heat flow in thermoacoustics stacks, applying genetic algorithms. [PERSON] et al. [5] maximized the COP efficiency to optimize thermoacoustic devices. [PERSON] et al. [6] developed a comprehensive design and optimization algorithm for designing thermoacoustic devices that can serve as sustainable refrigeration systems. [PERSON] et al. [7] proposed an algorithm as an easy-to-follow guideline for the design of thermoacoustic refrigerators that predicted values of 40-50% of Carnot's efficiency for the thermoacoustic core. [PERSON] et al. [8] aimed to present a new kind of thermoacoustic standing wave-like device that would allow for easy and independent control of the pressure field and the particle velocity field after investigating the optimal acoustic field in the stack region for the main parameters of interest, i.e., the temperature gradient, the thermoacoustic heat flow, and the coefficient of performance. [PERSON] et al. [9] optimized the geometric variables, namely, the stack position, the stack length, the blockage ratio, and the plate spacing involved in designing thermoacoustic refrigerators formulated as a three-criterion non-linear programming problem with discontinuous derivatives (DNLP) in the software GAMS. [PERSON] et al. [10] aimed to achieve the highest coefficient of performance (COP = 4.89) by applying a genetic algorithm (the multi-objective genetic algorithm) to optimize the design parameters of the standing wave thermoacoustic refrigerator system. [PERSON] et al. [11] presented a generalized heat transfer model using a complex heat transfer exponent where both the real and the imaginary part of the heat transfer exponent change the power-versus-efficiency relationship quantitatively. [PERSON] [12] described the design methodology of thermoacoustic electricity generators using a standard loudspeaker as a linear alternator for low-cost, low-power thermoacoustic electricity generators. Materials and structural design: Optimizing the materials of the acoustic resonator and internal components can enhance the durability and efficiency of the thermoacoustic coooler. This involves studies on composite materials, aerogels, thermal conductivity, mechanical resistance, and durability under operating conditions. For example, [PERSON] et al. [13] investigated as stack material cotton wool, glass wool, ceramics, silica aerogel, carbon fibers, and carbon powder by measuring flow resistance at high acoustic frequencies, 4-20 kHz, and thermal transport properties as the engines were miniaturized. [PERSON] et al.