中文摘要：

针对多线材变截面一维下料问题,提出顺序价值修正和动态规划算法求解。由于材料具有变截面的特征,同样重量的毛坯在线材不同位置切割时所需的长度是不同的,所以要进行重量与长度的转换,求出任意位置处对应的毛坯长度。然后根据上述方法顺序生成下料方案中的各个布局图,直到全部毛坯的需求得到满足。通过对毛坯的价值修正生成多个不同的下料方案,从中选择最好者作为解。通过与随机测试题比较,实验结果表明,所得解值非常接近最优,当用材料利用率度量时,最优解的材料利用率和所得解的平均利用率之差为0.51%;计算速度很快,通常在7 s以内,该算法更能快速生成布局图,提高材料利用率。

英文摘要：

For the problem of one-dimensional cutting stock for multiple stock lengths with variable cross-section,the sequential value correction and dynamic programming algorithm were proposed. Because the material was of variable cross-section characteristics,the stock length of cutting was varied at different positions under the same weight. Therefore,the conversion of weight and length must be carried out,and the stock length in the corresponding position was obtained. Then,according to the above method,the cutting patterns were generated sequentially,until all demands were met. Furthermore,multiple cutting plans were generated by adjusting the item values,and the best was selected among them. Comparing with random test,the experimental results indicate that the obtained solution is very close to the optimal solution. When the material utilization is measured,the difference between the material utilization rate of the optimal solution and the average utilization rate of the obtained solution is 0. 51%,and computing speed is usually quick within seven seconds. Thus,the proposed approach can generate cutting patterns quickly and improve material utilization.