# An Intelligent Approach to the Unit Nesting Problem of Coil Material
## 1 Introduction  
It is urgent to develop resource-saving intelligent manufacturing under the constraints of the resources and environment. There are many advantages to sheet metal parts such as their light weight, high strength, good conductivity, and low cost. They are used in many industries, e.g., automotive, electronic appliances, and medical devices. The primary cutting method for sheet metal parts is punching. Due to the specification of the process, punching has several disadvantages: (1) the partial layout scheme is so simple that the utilization rate is low; (2) the molds have to be replaced regularly because of its short lift, which leads to high costs; and (3) the section of punched parts is rough that needs to be finished. With the advancement of laser technology, it is preferrable to use laser cutting instead of punching for its following advantages: (1) the workpiece of arbitrary shape can be cut; (2) it does not require mold; and (3) the cutting surface is smooth. Most of the existing research has been applied to the punching process; therefore, this is an innovative study on coil material. As a research hotspot, cutting stock problems are extensively addressed in automobile, glass, paper, clothing, and other industries. According to the dimensions of parts, the cutting problem can be classified as a one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) cutting problem. According to the shape of the parts, it can also be divided into rectangular and irregular part nesting problems. This study is applied to thesheet metal of the coil cutting process, and the optimized nesting map of 2D irregular parts is required. Currently, how to use the minimum quantities of resources to solve the cutting problem is one of the main research directions. Many researchers are drawn to the study of 2D cutting stock problems. For sheet cutting problems, [PERSON] et al. [1] proposed a mathematical model of local fitness to measure the fitting degree of polygons. [PERSON] et al. [2] preprocessed a combinatorial operation of parts to improve the performance of a 2D irregularly shaped part layout. [PERSON] et al. [3] proposed the concept of a collision-free region (CFR) to solve the problem of the beyond boundary constraint. [PERSON] et al. [4] proposed a new algorithm of two-staged cutting patterns. [PERSON] et al. [5] proposed a manufacturability-oriented rectangular part cutting stock method to consider the optimization objective of obtaining high material utilization and a short cutting path. [PERSON] [6] introduced a hybrid algorithm that combines the fruit fly optimization algorithm (FOA) with the bottom-left fill approach to solve the 2D strip packing problem. [PERSON] et al. [7] presented a non-linear mathematical model and its linearization to represent the 2D cutting stock problem with usable leftovers (2D-CSPUL). [PERSON] and [PERSON] [8] introduced a novel approach that used heuristic and genetic algorithms for two-dimensional nesting. [PERSON] et al. [9] proposed a heuristic method based on the Jostie algorithm. [PERSON] et al. [10] presented an innovative genetic algorithm (GA) for the multi-objective optimization of 2D nesting. [PERSON] et al. [11] proposed an uncertain optimization method that improves computational efficiency under the premise of considering the stiffness of the material. [PERSON] et al. [12] presented a novel computational strategy for collision detection to reduce the enormous computational time. [PERSON] et al. [13] proposed a meta-heuristic algorithm, and it has an effective utilization ratio, nested height, and computational effort. For the cutting problem of coils, [PERSON] et al. [14] divided the coil into segments with different lengths, and the segments were cut into rectangular pieces. [PERSON] et al. [15] divided the coil into different strips, and then each strip was cut into desirable rectangles. The above method is suitable for rectangular parts, which will cause great waste for irregular parts.