三轴激光切割方形件组批排样优化建模研究

Research on the Optimization Modeling of the Three-Axis Laser Cutting of Square Parts

摘要: 激光切割在处理大件原材料方面具有巨大优势，在激光切割方形件的生产中，排样优化与订单组批问题一直是企业节约原材料和能源使用的关键。在充分考虑其约束并建立其混合整数规划模型后，本文首先按产品的规格即长或宽的尺寸进行分类，将长度或者宽度相同的产品项归为一类，给予它们同一个型号，并排列成一个更大的产品项(item)组成一个栈(stack)。然后将栈(stack)按照从大到小的顺序依次组成条带(stripe)，直到达到条带(stripe)长度限制下的条带长度最大值。最后对得到的条带(stripe)进行预处理并利用遗传算法求出可行的排样方式。通过与传统按照每个产品项的ID进行全排列并对其使用遗传算法求解方法对比，本文提出方法使得板材有效利用率提高了近15%，同时也大大提高三轴激光切割的工作效率。

Abstract: Laser cutting has great advantages in processing large pieces of raw materials. In the production of laser cutting square pieces, layout optimization and order batching have always been the key to saving raw materials and energy use for enterprises. After fully considering its constraints and establishing its mixed-integer programming model, this paper first classifies products according to their specifications, that is, length or width, classifies products with the same length or width into one category, gives them the same model, and arranges them into a larger product item to form a stack. Then, the stack is formed into strips in order from the largest to the smallest, until the maximum strip length under the strip length limit is reached. Finally, the strip is preprocessed and a feasible layout method is found by genetic algorithm. Compared with the traditional method of arranging the ID of each product item and using genetic algorithm to solve it, the method proposed in this paper improves the effective utilization rate of the plate by nearly 20%. At the same time, it also greatly improves the working efficiency of three-axis laser cutting.