中文摘要：

为了有效解决企业实际生产中的长板矩形优化排样问题,对矩形优化排样算法进行了研究,给出了一个基于两阶分块式长板矩形优化排样算法,该算法在第一阶段完成长板的最佳分段,第二阶段完成矩形在子段上的最优排样。对于两个阶段分别通过问题转化,将二维矩形优化排样问题转化为背包问题,并建立相应的数学模型。根据所建立的数学模型并基于分支定界的动态规划算法开发的应用系统,解决了企业实际生产中的长板矩形优化排样问题。企业实际应用表明,该算法为求解长板矩形优化排样问题的有效方法。

英文摘要：

To solve the problem of rectangles optimal nesting of the long board in the actual production for enterprises, it was studied the rectangular optimal nesting algorithms, and the optimal nesting algorithm of rectangle based on two stage sub-block long board was put for- ward. In the first stage, the optimal segmentation of the long board was achieved. In the second stage, the optimal nesting of the rectangle was achieved in the above section. Through the conversion about two stages, the two-dimensional rectangular optimal nesting issues were transformed to the knapsack issues, and the mathematical models were established. The rectangles optimum nesting issues of the long board in the actual production were solved by the application system developed by the dynamic programming algorithm based on branch and bound technique. The application shows that the algorithm is an effective way to solve the rectangular optimal nesting of the long board.