## 1 Introduction  
Injection molding is the process of producing parts composed of thermoplastic or thermosetting plastics. Plastics have the advantages of low density, stable chemical properties, high specific strength, good formability, easy coloring, low processing costs and a wide range of material sources, and they have been increasingly used in daily life and industrial production. In the automobile, aerospace, and other fields, replacing steel with plastic has become one of the main development directions of lightweight technology. There are many plastic-forming methods, among which injection molding has become the most effective and widely used due to its advantages of high forming efficiency and a high degree of automation. Plastic injection molding (PIM) has the following advantages: (1) High pressure is applied during the molding process, which enables the molding of products with detailed features and complex geometries. (2) The actual molding speed is fast, the cycle time is short, the product consistency is good, and the cost is reduced. (3) It has strong scalability, and fillers can be added to enhance the mechanical properties of the product for application in special fields, and a variety of different types of plastics can be used at the same time to achieve multi-material injection molding. (4) The product requires only a small amount of trimming or no trimming at all. (5) With a high degree of automation, PIM is usually completed by an operator to control and manage injection molding machines and robots. The injection molding process consists of five stages, as shown in Figure 1: mold opening (ejection), mold closing, filling, packing, and cooling [1]. Among the above stages, the cooling stage is the most important because it significantly affects the productivity and quality of the formed parts [2; 3]. The cooling stage generally accounts for a majority of the injection molding cycle. In injection molding, short cycle times are important for high productivity. Proper cooling channel design can significantly reduce cooling time and increase the productivity of the injection molding process. PIM also requires high-quality products. From the perspective of dimensional accuracy and appearance, the main defects of PIM should be avoided as much as possible, including warpage, volume shrinkage, and weld lines [4; 5]. An efficient cooling system that achieves uniform temperature distribution can minimize undesirable defects that affect the quality of the molded parts, such as hot spots, sink marks, differential shrinkage, thermal residual stress, and warpage. The cooling system is an important part of the injection mold and has the function of adjusting the temperature of the mold. Mold temperature has an important impact on the quality and forming efficiency of injection-molded products [6; 7]. As plastic melts flow, a mold temperature that is too low increases the shear force and internal stress, resulting in defects such as short shots and flow marks; on the contrary, a mold temperature that is too high results in defects such as short shots and flow marks. The plastic melt is prone to decomposition, leading to reduced precision and color changes in the final product. Additionally, uneven temperatures in the mold can cause cooling discrepancies between different parts of the product, resulting in temperature-induced stress, and secondary shrinkage of the product after demolding can have a large gap, resulting in warping and deformation. Products with an uneven wall thickness and complex shapes have a greater impact. Therefore, facing the development requirements of high-efficiency and high-quality injection molding, the optimization design technology of injection mold cooling systems has become the research mainstream of current injection mold design technology. The importance of the cooling process in injection molding has attracted a great deal of attention from plastics engineers and researchers.