基于混合整数数学规划的方形件产品排样优化研究

Research on Square Piece Products Layout Optimization Based on Mixed Integer Mathematical Programming

摘要: 本文针对方形件产品的排样优化问题，提出了一种基于混合整数数学规划的解决方案。首先，通过建立混合整数数学规划模型，考虑了产品项的高精度和高自由度，以及需要满足的三阶段切割需求，制定了相应的约束条件。在算法实现过程中，通过对数据集的预处理，使得宽度相似的产品项能够按顺序输入，以满足齐头切的要求。针对二维三阶段切割下料问题，使用混合遗传算法和BL算法等进行编码建立混合数学整数规划模型以及相应的约束条件，并通过多次试验得到了较好的排样方案，实现了高效的板材利用率，分别达到81.903%，81.249%，84.575%以及85.246%。实验结果表明，所提出的方法均取得了显著的优化效果，为方形件产品的生产提供了有效的排样方案。

Abstract: This paper proposes a solution based on mixed integer mathematical programming for the layout optimization problem of square piece products. First, by establishing a mixed integer mathematical programming model, taking into account the high precision and high degree of freedom of the product items, as well as the three-stage cutting requirements that need to be met, the corresponding constraints are formulated. During the implementation of the algorithm, through preprocessing of the data set, product items with similar widths can be input in order to meet the requirements of simultaneous cutting. Aiming at the problem of two-dimensional and three-stage cutting and blanking, a hybrid mathematical integer programming model and corresponding constraints were established using hybrid genetic algorithms and BL algorithms for coding. A better layout plan was obtained through multiple experiments and an efficient layout was achieved. The plate utilization rates reached 81.903%, 81.249%, 84.575% and 85.246% respectively. Experimental results show that the proposed methods have achieved significant optimization effects and provide an effective layout scheme for the production of square piece.