矩形件套裁排样的一种优化解法

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.