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林业科学 ›› 2016, Vol. 52 ›› Issue (5): 150-159.doi: 10.11707/j.1001-7488.20160518

• 论文与研究报告 • 上一篇    下一篇

面向零件的人造板材矩形件锯切排样数学建模及遗传算法求解

张国梁1,2,3, 蔡小娜1,4, 侯晓鹏2,3, 赵旦5, 周玉成2,3, 葛浙东2,3   

  1. 1. 河北农业大学木材科学与工程研究所 保定 071000;
    2. 中国林业科学研究院林业新技术研究所 北京 100091;
    3. 中国林业科学研究院木材工业研究所 北京 100091;
    4. 河北农业大学基础课部 沧州 061100;
    5. 中国科学院遥感与数字地球研究所 北京 100094
  • 收稿日期:2015-10-21 修回日期:2015-12-09 出版日期:2016-05-25 发布日期:2016-06-01
  • 通讯作者: 侯晓鹏
  • 基金资助:

    中国林业科学研究院林业新技术所基本科研业务费专项(CAFINT2012K01);河北省自然科学基金资助项目(E2015204039);河北省科技计划项目(15217218)。

Part-Oriented Cutting Layout Mathematical Modeling and Solving by Genetic Algorithm for Rectangular Wood Based Panel Parts

Zhang Guoliang1,2,3, Cai Xiaona1,4, Hou Xiaopeng2,3, Zhao Dan5, Zhou Yucheng2,3, Ge Zhedong2,3   

  1. 1. Institute of Wood Science and Engineering, Agricultural University of Hebei Baoding 071000;
    2. Research Institute of Forestry New Technology, CAF Beijing 100091;
    3. Research Institute of Wood Industry, CAF Beijing 100091;
    4. Department of Basic Courses, Agricultural University of Hebei Cangzhou 061100;
    5. Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences Beijing 100094
  • Received:2015-10-21 Revised:2015-12-09 Online:2016-05-25 Published:2016-06-01

摘要:

[目的] 探讨人造板材矩形零件锯切排样的启发式规则,建立锯切排样的数学模型并研究求解方法,为解决由于整体套排导致国产排样系统使开料锯在工作过程中锯路变化繁琐、降低切割效率的问题提供科学依据。[方法] 基于一套板式家具下料清单中往往有2种或2种以上零件存在相互配合尺寸的情况,提出基于配合尺寸的分组降维启发式规则,按配合尺寸由大到小排序并将所有矩形零件分组,使每组零件种类不大于4种; 以余料面积最小为评价指标,建立面向零件的锯切排样数学模型,通过设定冗余系数估算基材板需求量,以矩形零件数量及在基材板上的排样长度、宽度和面积不超限为约束条件,设立排样宽度系数并通过为矩形零件和基材板的长、宽尺寸增加一个单位的锯路宽度以抵消在基材板最下端和最右端的"虚拟锯路损失"; 采用遗传算法进行模型求解并利用惩罚函数法处理约束条件,经染色体整数编码、初始种群建立、具有一定自适应性的惩罚因子建立、基于外点惩罚函数的适应度函数建立和遗传操作,利用结合MATLAB遗传算法工具箱而建立的排样算法计算出描述排样方案的向量; 通过实例验证模型和算法的可行性。[结果] 所有矩形零件的排样方案通过4个参数来描述,即某个排样零件的排放目标板材号、在基材板上的排放行号及横向或竖向的排放方式; 排样矩阵的行数为4,列数为矩形零件总数,每列表示1个零件的排样结果。应用实例表明,基于配合尺寸的启发式规则使多种矩形零件分组排样,每组排样方案的最优控制向量可明显划分为高低不同的4段,分别表示4个参数; 遗传运算在限定的迭代次数内都趋于收敛,体现出较好的全局寻优能力,排样方案的可视化图形满足"一刀切"的锯切工艺要求,且锯路规整,有利于提高锯切效率。[结论] 基于配合尺寸的启发式规则和面向零件的锯切排样模型对于人造板材优化排样具有一定可行性,可为板式家具锯切排样提供新的解决方法,但要提高开料锯的锯切效率,还需将走刀次数、惩罚因子的优化选择等加以综合考虑。

关键词: 锯切排样, 分组降维, 配合尺寸, 面向零件, 遗传算法, 惩罚函数

Abstract:

[Objective] In order to find gap of non-availability in most domestic literatures, which sawing velocity was dropped down due to the frequent change of saw line, this research investigated a heuristic rule for rectangular parts cutting layout of wood-based panel, built mathematical model and studied solving method. [Method] Based on the situation that in a suit of material list, coupled dimension existed among two or more kinds of parts, therefore, a grouping and dimension reducing heuristic rule was put forward. All rectangle parts were sorting by coupled dimension in descending order, each group consisting no more than four kinds parts. Taking the minimum remaining area as evaluation index, a part-oriented mathematical model was set up. In this model, the quantity demanded for base panel was estimated by setting redundancy factor, and four aspects including quantity, length, width and area of placed parts on base panel should be all wlthin the limitation value. Moreover, layout width ratio was set and single unit saw line width was added on length and width of both rectangular parts and base panel so as to offset fictitious saw line loss located at undermost and rightmost side of base panel. Genetic algorithm (GA) was adopted to find global optimal solution for layout and punishment function was used to deal with constrains. By integer coding of chromosome, establishing of initial population, punishment factors with certain adaptability and fitness function based on exterior point punishment function and genetic manipulation, vector on behalf of layout solution was calculated through the layout algorithm which was built in cooperation with GA toolbox of MATLAB. Instances were applied to test feasibility of the model and algorithm. [Result] Layout solution of all rectangular parts was described by four parameters, consisting of code, row and direction (vertical and transverse). Layout matrix has 4 rows, and the column was the total quantity of all parts. Each column represented layout solution of each part. The instances showed that multiple parts could be grouped based on coupled dimension-based heuristic rule, optimal controlled vector standing for layout solution for each group was divided into four sections with varied height, and these four sections meant the four parameters. It was also demonstrated that GA tended to convergence within limited iterations and gave relatively good capability of global optimization. In addition, visualization of layout solution displayed meet the demand of "guillotine cutting" and the regular saw line was good for increasing sawing efficiency. [Conclusion] The coupled dimension-based heuristic rule and part-oriented mathematical model were suitable for cutting layout of wood-based panel and therefore a new method was presented for cutting layout of panel-type furniture. However, in order to enhance cutting productivity, the elements such as feeding times of cutting saw, optimized selection of punishment factor should also be taken into account comprehensively.

Key words: cutting layout, grouping and dimension-reducing, coupled dimension, part-oriented, genetic algorithm (GA), punishment function

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