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The two-dimensional knapsack problem requires to pack a maximum profit subset of “small” rectangular items into a unique “large” rectangular sheet. Packing must be orthogonal without rotation, i.e., all the rectangle heights must be parallel in the packing, and parallel to the height of the sheet. In addition, we require that each item can be unloaded from the sheet in stages, i.e., by unloading simultaneously all items packed at the same either y or x coordinate. This corresponds to use guillotine cuts in the associated cutting problem.In this paper we present a recursive exact procedure that, given a set of items and a unique sheet, constructs the set of associated guillotine packings. Such a procedure is then embedded into two exact algorithms for solving the guillotine two-dimensional knapsack problem. The algorithms are computationally evaluated on well-known benchmark instances from the literature.The C++ source code of the recursive procedure is available upon request from the authors.  相似文献   
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矩形件排样是典型的组合优化问题,在很大程度上影响着企业生产效率。将遗传算法与启发式规则相结合,同时在排样过程中考虑待排样式的公差,求解"一刀切"矩形件排样问题。首先,采用实数基因编码方式,由实数基因值与启发式信息结合确定待排样式的优先权。其次,基于待排样式的最小极限尺寸,采用两步解码方法。第一步为初始填充,将待排样式组合成满足"一刀切"的可行条料,并求解板材利用率最高的条料填充方式;第二步为对第一步剩余空白区的填充,求解不同启发式信息下,空白区利用率最高的待排样式填充方式。再者,基于待排样式的最大极限尺寸和板材尺寸,对最优排样方案进行调整。最后,以VB6.0为开发工具将算法实现,并通过实例对比分析证明了算法的有效性。  相似文献   
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