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在工业定制化生产中，板材常采用三阶段齐切割排样方式，经过三个阶段必须切出完整的产品。针对这一问题，提出以板材利用率最大为目标，建立了板材二维齐切割的混合整数规划模型。将三阶段切割问题抽象为具有尺寸限制的排序问题，在第一阶段采用横切和竖切两种切割方式，所切割的产品项可以0°或90°放置，后续两个阶段的切割要满足任意两个产品项无重叠。为提高求解效率，把模型分解为主问题和若干子问题，并提出遗传算法和列生成的迭代重优化框架及其算法求解该问题。在每次迭代中，遗传算法均能提供多个满足条件的列，并作为新列添加到主问题中。此外，算法能够对板材利用率较低的解进行重优化，提高劣解变换到最优解的可能性。实验结果表明，所提算法在小规模算例中，能够求得精确解；在大规模算例中，求解所得的板材利用率在85%以上，求解时间较短，能够适应工业化生产的要求。
Abstract：In industrial customized production, the three-stage guillotine cutting layout method is often used, and a complete product must be cut after three stages. To address this issue, a mixed integer programming model for two-dimensional guillotine cutting of sheet metal was established with the goal of maximizing sheet metal utilization. The three-stage cutting problem was abstracted as a sorting problem with size constraints. In the first stage, two cutting methods were used: horizontal and vertical cutting. The cut product items could be placed at 0° or 90°, and the subsequent two stages of cutting must meet the requirement of no overlap between any two product items. To improve solution efficiency, the model was decomposed into a main problem and several sub problems, and an iterative re-optimization framework and algorithm for genetic algorithm and column generation were proposed to solve the problem. In each iteration, the genetic algorithm could provide multiple columns that met the conditions and added them as new columns to the main problem. In addition, the algorithm could re-optimize solutions with low utilization of sheet metal, improving the possibility of transforming the inferior solution to the optimal solution. The experimental results showed that in small-scale examples, the model could obtain accurate solutions. The proposed algorithm achieved a plate utilization rate of over 85% in large-scale examples, with a short solving time and could meet the requirements of industrial production.
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基本信息:
DOI：10.13705/j.issn.1671-6841.2023226
中图分类号:TH16;TP18
引用信息:
[1]冀荣根,胡志华,田曦丹,等.基于列生成和遗传算法的三阶段齐切割问题[J].郑州大学学报(理学版),2025,57(04):63-70.DOI:10.13705/j.issn.1671-6841.2023226.
基金信息:
国家自然科学基金面上项目(71871136); 上海市自然科学基金面上项目(23ZR1426500)
2023-09-23
2023
2024-09-06
2025-10-24
2025
3
2024-10-21
2024-10-21
2024-10-21