摘要
针对工程实际中一维下料优化问题,这里采用以原材料使用量最少为目标,以每根原材料的余料长度小于最短零件长度等为约束,建立数学优化模型,提出使用一种基于递推矩阵的列生成算法进行求解该模型。此算法主要通过求解列生成优化模型中的递推矩阵,生成添加列,最终得出下料方案。最后针对单一订单的情况,并根据实例优化计算所得结果进行对比,分析可知该算法能够减少下料方式,验证了该算法的有效性,在工程实际中可以有效借鉴此方法。
Aiming at the problem of one-dimensional cutting stock optimization in Engineering practice,the mathematical optimization model was established though using the minimum amount of raw materials used as the target it,the constraint was that the length of the residual material of each raw material was less than the shortest part length.The column generation algorithm based on recursive matrix was proposed to solve the model.This algorithm mainly generated the additional columns by solving the recursive matrix in the column generation optimization model,and obtained the cutting stock scheme in the end.Finally,according to the case of a single order,and the results of the optimization calculation were compared.The analysis showed that the algorithm could reduce the ways of cutting stock and verified the effectiveness of the algorithm.This method can be effectively used for reference in engineering practice.
作者
马俊燕
韩志会
骆德铖
肖海华
MA Jun-yan;HAN Zhi-hui;LUO De-cheng;XIAO Hai-hua(Guangxi Key Laboratory of Manufacting Systems and Manufacting Technology,College of Mechanical Engineering,Guangxi University,Guangxi Nanning 530004,China)
出处
《机械设计与制造》
北大核心
2022年第1期117-119,共3页
Machinery Design & Manufacture
基金
国家自然科学基金(51265002)
广西教育厅(2017KY0023)
广西科技厅(2018GXNSFAA138158)。
关键词
一维下料问题
数学模型
矩阵变化
列生成算法
整数规划
One-Dimensional Cutting Stock Problem
Mathematical Model
Matrix Variation
Column Generation Algorithm
Integer Programming
