基于二维平面装箱模型的产品切割问题研究

Research on Product Cutting Problem Based on Two-Dimensional Planar Packing Model

摘要: 下料问题，是指将给定产品合理地摆放在布局空间中，在满足必要的约束条件下，使利用率达到最高的方式。本文在分析木板利用率的基础上建立二维平面装箱模型，考虑到利润最大化建立二维平面多目标装箱模型解决以下问题：1) 结合“4块法”规划解决单产品切割问题；2) 利用贪心算法解决双产品切割问题；3) 利用最优占角策略解决满足任务数要求的双产品切割问题；4) 利用混合遗传算法(GA)和模拟退火算法(SA)的HGASA算法，解决多产品切个问题。

Abstract: Cutting stock problem refers to the way that a given product is reasonably placed in the layout space to achieve the highest utilization rate under the necessary constraints. This paper establishes a two-dimensional plane packing model based on the analysis of the utilization ratio of wood panels. Considering the profit maximization, a two-dimensional plane multi-objective packing model is established to solve the following problems: 1) solving the single product cutting problem by combining the “four-block” programming; 2) solving the double product cutting problem by using greedy algorithm; 3) using the optimal angle-occupying strategy to solve the problem of double product cutting which meets the requirement of task number; 4) solving the problem of multi-product cutting by using hybrid genetic algorithm (GA) and simulated annealing algorithm (SA).