可变尺寸板材二维下料优化算法  

Optimization algorithm for 2D cutting stock problem of variable-sized sheets

作　　者：潘卫平 PAN Weiping(College of Information Engineering,Hainan Vocational University of Science and Technology,Haikou 571126,China)

机构地区：[1]海南科技职业大学信息工程学院,海南海口571126

出　　处：《自动化与仪器仪表》2025年第3期11-14,共4页Automation & Instrumentation

基　　金：国家重点研发计划资助项目(2019YFB1705002);海南省自然科学基金项目(622RC726);海南科技职业大学校级科研资助项目(HKKY2024-BS-07);海南省第五轮特色重点学科“计算机科学与技术”资助项目。

摘　　要：针对可变尺寸板材二维下料问题,提出一种基于条带四块排样方式的优化算法。首先构造可变尺寸板材二维下料问题的线性规划数学模型,将下料问题转化为线性规划问题和排样问题。然后构造排样方式生成算法,第一步计算由一行或一列矩形件组成的各种尺寸的条带的价值,生成最优条带;第二步计算由相同方向相同长度条带组成的块的价值,生成最优块;第三步隐式枚举板材的四块划分,选择排样价值最大的一个四块划分形成四块排样方式。最后,采用文献例题和实际生产实例验证所提算法,结果表明所提算法在提高板材利用率和计算效率两方面均有效。This paper proposes an optimization algorithm based on a four-block strip cutting pattern for the two-dimensional cutting stock problem of variable-sized sheets.Firstly,a linear programming mathematical model for the two-dimensional cutting stock problem of variable-sized sheets is constructed,transforming the cutting problem into a linear programming problem and a cutting problem.Then,an algorithm for generating cutting patterns is constructed.The first step calculates the value of strips of various sizes composed of one row or one column of rectangular pieces to generate optimal strips.The second step calculates the value of blocks composed of strips of the same direction and length to generate optimal blocks.The third step implicitly enumerates the four-block partitions of the sheet and selects the one with the maximum pattern value to form the four-block cutting pattern.Finally,the proposed algorithm is validated using examples from literature and practical production instances.The results demonstrate the effectiveness of the proposed algorithm in improving both sheet utilization and computational efficiency.

关 键 词：二维下料问题 排样问题 可变尺寸板材 条带 线性规划 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]