## 1 Introduction  
The demand for plastic optical lenses has been increasing in the industry. The precision requirements for high-tech optical products have become stringent, which has led to the growth of global markets for high-precision optical articles [1; 2]. Although the optical properties of glass, such as the refractive index and dispersion, are quite stable, the glass fabrication process is very complicated and difficult. Moreover, plastic products are lightweight, colorable, robust, and low cost. They can be manufactured using a one-step process regardless of their geometric complexity. Thus, plastic products have become crucial in contemporary industrial development. Despite the aforementioned advantages, plastic optical lenses may encounter volumetric shrinkage, which leads to the formation of thermally induced residual stress during the cooling process of injection molding. This residual stress slightly results in local variations in the birefringence, which affects the image quality [3]. Achieving a uniform temperature distribution for removing the residual stress is difficult in conventional cooling channels. Uneven shrinkage occurs if conventional cooling channels are used during the cooling process [4]. For designing conformal cooling channels, the geometric shape of conventional cooling channels can be appropriately adjusted through injection molding simulation. This helps to improve the defects caused by conventional cooling channels. The use of conformal cooling channels facilitates an even distribution of the surface temperature of the mold cavities, thereby reducing the thermally induced residual stress formed during the cooling process [5], effectively shortening the cooling time, and improving the cooling efficiency [6]. Researchers have devoted considerable attention to hybrid manufacturing processes, which combine metallic powder-based laser additive processes and subtractive machining processes. These hybrid manufacturing processes are considered the most promising technology for fabricating conformal cooling channels [7]. With metal additive manufacturing technology, complex conformal cooling channels can be fabricated to closely fit the shape of the mold cavity and core. Thus, uniform cooling can be achieved for products even in narrow regions or areas that may easily accumulate heat. Consequently, the quality of the products improves, and the cycle time decreases. This technology can be applied to products that vary in thickness. It allows the products to achieve uniform heat dissipation with a high cooling efficiency [8]. In recent years, optimization algorithms have been used to design cooling channels for plastic injection molds. [PERSON] [9] combined the advantages of the Davidon-Fletcher-Powell (DFP) method and the simulated annealing (SA) algorithm to optimize a cooling system layout. First, the DFP method was used to find the local optimum layout of the cooling channel. Then, the SA algorithm was adopted to determine the global optimum layout of the cooling channel, which allowed the surfaces of the mold cavities to possess a uniform temperature distribution. [PERSON] and [PERSON] [10] used design of experiments (DOE) and response surface methodology for designing an array of baffles in cooling channels. They established a mathematical model for obtaining the optimal configuration of cooling channels with an array of baffles. This technique can effectively improve the heat removal performance and is applicable to large-sized molds and molds with complex cavity shapes. [PERSON] and [PERSON] [11] also proposed an optimization method for the design of U-shaped milled groove cooling channels. This method aimed to achieve temperature uniformity for the mold and utilized computer-aided engineering (CAE) for design modification. The mold of a car fender was selected to analyze its cooling channel design and verify the theoretical calculation. The quality levels of the products were compared before and after the optimization.