## 1 Introduction  
The processing function of traditional machine tools, such as lathes and milling machines, is relatively straightforward, especially when dealing with small workpieces. In contrast, modern processing equipment, including CNC engraving and milling machines, laser cutting machines, and electrical discharge machining machines, demonstrate significantly higher precision and efficiency in the processing of small workpieces [1, 2]. The CNC engraving and milling machine, being a new type of high-performance machine tool with excellent cost-effectiveness, effectively addresses the limitations of traditional machine tools, such as low precision, inefficiency, and inadequate flexibility, and gradually becomes an important branch in modern machine tool processing. It has found wide applications in furniture manufacturing, decoration, small precision mold manufacturing, and hardware production [3, 4]. As competition in the global market escalates, companies face a variety of challenges related to improving production efficiency, cutting costs, and enhancing product quality [5]. In this scenario, milling is recognized as a vital process in mechanical manufacturing, making it crucial to optimize its parameters. The careful selection of process parameters, such as spindle speed, feed rate, and milling depth, has a direct and significant impact on key milling performance metrics; these factors not only influence the rate at which the material is removed but also significantly affect tool wear and the surface finish of the final product [6, 7]. Therefore, optimizing these parameters systematically can lead to improved production efficiency while reducing resource waste and maximizing economic returns. Additionally, multi-objective optimization techniques facilitate the simultaneous assessment of conflicting goals [8], such as milling productivity, tool lifespan, and milling forces, allowing researchers to perform a thorough analysis of various solutions' effects and providing a solid foundation for informed decision making [9]. At the same time, in an era characterized by intelligent manufacturing practices, it is essential for businesses to continually adapt their technologies to align with rapidly changing market needs. Thus, accelerating research into both milling parameter optimization and multi-objective methodologies is critical not only for strengthening core competitiveness but also for guiding the entire industry toward enhanced efficiency and sustainable growth. Consequently, the importance and urgency associated with both milling parameter optimization and multi-objective strategies in modern manufacturing are becoming increasingly clear [10; 11]. During the milling process, the relationship between tool wear, milling force, and milling efficiency is particularly evident. These three elements are interconnected and together form a complex dynamic system [12]. More specifically, tool wear not only reduces performance but can also negatively impact the surface quality of the workpiece. The level of milling force is directly associated with both the stability and accuracy of machining operations on the machine tool. When excessive forces are present during milling, they can cause vibrations in the machine tool that diminish product surface finish and accelerate tool degradation, ultimately reducing its operational lifespan. Additionally, to improve milling efficiency, it is often necessary to increase feed rate; however, this approach may result in heightened tool wear and greater milling forces [13]. Therefore, while pursuing high-efficiency production presents a notable conflict among these three factors--on one hand, there exists an intention to enhance efficiency for cost savings; on the other hand, it remains crucial to manage both tool wear and milling force to maintain processing quality and ensure equipment safety [14]. The methods of multi-objective optimization have emerged as a significant research focus in the fields of engineering and technology in recent years.