矩形件套裁排样的一种优化解法  

An Optimal Method of Solving Rectangle Nesting Problem

作　　者：扈少华[1] 张淋江[1] 潘立武[1] 管卫利[2] HU Shao-hua;ZHANG Lin-jiang;PAN Li-wu;GUAN Wei-li(Department of Automation and Control, He＇nan University of Animal Husbandry ＆ Economy, He＇nan Zhengzhou 450011, China;Information Engineering College, Nanning University, Guangxi Nanning 530200, China)

机构地区：[1]河南牧业经济学院自动化与控制系,河南郑州450011 [2]南宁学院信息工程学院,广西南宁530200

出　　处：《机械设计与制造》2018年第6期219-221,225,共4页Machinery Design & Manufacture

基　　金：河南省重大科技专项(121100111000);河南省科技厅科技攻关项目(152102210320);河南省高等学校重点科研项目(15B52000)

摘　　要：求解矩形件套裁排样问题,即用指定规格的板材切割出若干种矩形件,目标是极大化板材利用率。构造一种基于五块结构的矩形件套裁排样方式,该排样方式首先将板材划分为五个块,然后在每块中按照简单方式排样一种矩形件。建立五块排样方式的整数规划数学模型,并在Visual Studio和CPLEX中进行编程求解。用文献中的基准测题,检验五块排样方式的性能,数值实验结果表明,排样方式在提高板材利用率和简化板材切割工艺两方面均有效,且模型求解时间在实际应用中合理。The solves the nesting problem of rectangular pieces,that is several types of rectangular pieces are to be cut from a sheet with specified size,the objective of the problem is to maximize the sheet utilization. A nesting pattern of rectangular pieces that based on Five-block structure is constructed. With this pattern,sheet is divided into five blocks,single type rectangular pieces are arranged on each block in a simple way. Integer programming model of the Five-block pattern was built and programmed in Visual Studio and CPLEX. The performance of the Five-block pattern was tested through benchmark instances in literature,numerical experimental results show that the proposed Five-block pattern is effective in improving sheet utilization and simplifying cutting process,also the computation time of the model is reasonable in practical application.

关 键 词：矩形件 套裁排样问题 五块排样方式 简单块 整数规划 

分 类 号：TH16[机械工程—机械制造及自动化] TP394[自动化与计算机技术—计算机应用技术]