一种卷板填充分层递归排样的优化算法

研究了卷板填充排样问题,提出了一种分层递归排样的优化算法。算法使用水平剪切线将卷板分层,每层的宽度和卷板宽度相同,高度和层最左端的主毛坯高度相同;通过调用递归过程确定卷板中层的排列,为各层选定主毛坯,并确定毛坯的排列方式;采用分支定界技术缩小搜索空间。实验结果说明该算法比文献中最近报道的几种算法都有效。     

矩形毛坯最优层排样方式的动态规划算法*

讨论矩形毛坯无约束二维剪切排样问题,提出层排样方式的动态规划算法,使板材所含毛坯总价值最大。排样时使用一组平行的剪切线将板材分割为多个层,层的长度等于板材的长度或宽度,宽度等于最左边主毛坯的高度。通过动态规划算法确定所有可能尺寸层的最大价值和板材中层的最优组合。实验结果表明,该算法在满足实际应用要求的同时,板材利用率和计算时间两方面都较有效。     

生成匀质块排样方式的递推算法

讨论矩形毛坯有约束二维剪切排样问题:将一张板材剪切成已知尺寸的一组毛坯,使排样方式的价值(板材中所含毛坯的总价值)最大;排样方式中每种毛坯的数量不能超过需求量.采用匀质块排样方式,每刀都从当前板材上切下一根水平或竖直的同质条带,其中仅含相同尺寸的毛坯.采用动态递推算法生成匀质块排样方式,在保证解的质量的前提下,有效地缩短计算时间,达到节约材料的目的.     

二维多阶段矩形剪切排样算法

讨论有需求约束的二维剪切矩形排样问题:将一张板材剪切成一组已知尺寸的毛坯,使排样价值(板材中包含的毛坯总价值)最大,约束条件是排样方式中包含每种毛坯数量都不能超过其需求量。采用普通条带多阶段排样方式,每次剪切都从板材上产生一根水平或者竖直的普通条带,条带中可以包含不同尺寸毛坯。引入分支限界与贪婪策略,以提高算法效率。实验结果表明,该算法可以有效提高排样价值。     

矩形毛坯最优三块排样的新算法

针对矩形毛坯二维下料问题,提出采用三块排样的下料算法,以达到最小化板材消耗量和简化切割工艺的目标。该算法将列生成法和排样方式生成算法相结合,生成一个含多个排样方式(排样图)的集合,然后通过解整数规划问题获得各个排样方式的使用次数。排样方式生成算法通过构造并求解整数规划模型,求出最优三块排样。采用的三块排样,切割工艺简单,能有效提高切割效率。实验结果表明,该算法可以明显减少板材消耗。     

改进的矩形毛坯三块排样方式及其算法

致力于改进矩形毛坯三块排样方式的生成算法,采用三种策略缩小解的搜索范围,并将该算法与线性规划相结合形成排样方案生成算法,用于求解大规模矩形毛坯排样问题.通过实验证明,与二阶段、T形、两段、三阶段排样算法相比,排样方案生成算法生成的排样方案虽然板材利用率稍低,但排样方案简单,能够简化切割工艺.     

长板单一尺寸矩形毛坯定长分割优化排样

讨论剪刃长度小于金属板材长度，单一尺寸矩形毛坯的优化排样问题。将长板分割成多块子板，除最后一块外，所有子板具有相同的长度与相同的毛坯排列。通过对Agrawal提出的单一尺寸矩形毛坯最优化排样方法进行扩展，使之适用于确定最优的子板长度，实验计算结果表明所述算法非常有效，给出例题数据的排样结果，并和企业的通常作法相比较，说明采用该方法的节材潜力。     

应用精确两阶段排样图的板材下料算法

求解基于精确两阶段排样图的二维下料问题,用最小的板材成本,生产出所需要的全部毛坯。将顺序启发式算法和排样图生成算法相结合,顺序生成排样方案中的各个排样图;采用顺序价值修正策略,在生成每个排样图后修正其中所含各种毛坯的价值。经过多次迭代生成多个排样方案,从中选择最好者。实验计算时与商业软件和文献算法相比较,结果表明所述算法可以更为有效地减少板材消耗。     

二维剪切排样的束搜索启发式算法

针对约束二维矩形剪切排样问题,提出了一种基于束搜索的三阶段剪切排样算法。其切割过程包括三个阶段：板材剪切成段,段剪切成条带,条带切割成准确尺寸毛坯。采用动态规划确定段的价值,复杂度低的拼接递推不同长度子板的初始价值和板材的初始可行解,束搜索优化板材的排样方式。束搜索的节点用矩形对表示,分别是段组合而成的局部方式和未填充的剩余子板。以局部方式价值与剩余子板的初始价值之和作为节点的估计值。按估计值选择精英节点继续分支,其他节点直接删除不再回溯。实验结果表明该算法可缩短三阶段同质排样的计算时间,且所获得的余料大,利于余料的回收管理和再利用。     

基于多阶排样方式的矩形件二维板材下料算法

针对二维剪切下料的特点,提出一种基于多阶排样方式的优化算法。递归构造多阶排样方式,称若干行若干列同种矩形件按照相同方向排列在一起形成的排样方式为0阶排样方式,n(n为正整数)阶排样方式由两个n-1阶排样方式沿着水平方向或竖直方向拼合而成。设计多阶排样方式的递归生成算法,按照阶数从小到大顺序生成多阶排样方式。将列生成算法与多阶排样方式生成算法相结合得到下料方案,按照板材使用张数最少原则确定下料方案中每个排样方式的使用次数。将这里排样方式分别与文献中的匀质条带三块排样方式、双排多段排样方式、简单块占角排样方式和递归四块排样方式进行对比,实验计算结果表明,多阶排样方式的排样价值高于以上4种排样方式。进一步地,将该下料算法与文献下料算法进行对比,实验结果表明该下料算法可提高板材利用率。     

基于两段排样方式的矩形件优化下料算法

针对矩形件下料问题,提出一种基于两段排样方式的优化下料算法。首先构造一 种约束排样算法,生成矩形件在板材上的两段排样方式。然后采用列生成算法依据矩形件剩余 需求量迭代调用上述约束排样算法生成一个虚拟下料方案,按照不产生多余矩形件原则选取虚 拟下料方案中的部分排样方式加入到实际下料方案中,更新矩形件剩余需求量;重复上述步骤 直到矩形件剩余需求量为零。采用文献中基准例题将该算法与2 种文献算法进行比较,数值实 验结果表明该算法下料利用率比2 种文献算法分别高1.61%和0.78%。     

A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

A heuristic recursive algorithm for the two-dimensional rectangular strip packing problem is presented. It is based on a recursive structure combined with branch-and-bound techniques. Several lengths are tried to determine the minimal plate length to hold all the items. Initially the plate is taken as a block. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. The dividing cut is vertical if the block width is equal to the plate width; otherwise it is horizontal. Both lower and upper bounds are used to prune unpromising branches. The computational results on a class of benchmark problems indicate that the algorithm performs better than several recently published algorithms.     

Hybrid heuristic algorithm for two-dimensional steel coil cutting problem

This paper is concerned with the problem of two-dimensional cutting of small rectangular items, each of which has its own deadline and size, from a large rectangular plate, whose length are more than one thousand times its width, so as to minimize the trim loss and the reduction of the times of clamping and changing speed are also concerned. This problem is different with the classical two-dimensional cutting problem. In view of the distinguishing features of the problem proposed, we put forward the definition of non-classical cutting, that is to say, put a series of items on the rectangular plates in their best layout, so as to enhance utility and efficiency at the same time. These objectives may be conflicting and a balance should be necessary, so we present a Hybrid Heuristic Algorithm (HHA), consisting of clustering, ordering, striping and integer programming etc. We demonstrate the efficiency of the proposed algorithm through the comparison with the algorithm we studied before.     

Heuristic for the two-dimensional arbitrary stock-size cutting stock problem

A heuristic is presented for the two-dimensional arbitrary stock-size cutting stock problem, where a set of rectangular items with specified demand are cut from plates of arbitrary sizes that confirm to the supplier’s provisions, such that the plate cost is minimized. The supplier’s provisions include: the lengths and widths of the plates must be in the specified ranges; the total area of the plates with the same size must reach the area threshold. The proposed algorithm uses a pattern-generation procedure with all-capacity property to obtain the patterns, and combines it with a sequential heuristic procedure to obtain the cutting plan, from which the purchasing decision can be made. Practical and random instances are used to compare the algorithm with a published approach. The results indicate that the trim loss can be reduced by more than half if the algorithm is used in the purchasing decision of the plates.     

Heuristic algorithm for a cutting stock problem in the steel bridge construction

A rectangular two-dimensional cutting stock problem in the steel bridge construction is discussed. It is the problem of cutting a set of rectangular items from plates with arbitrary sizes that lie in the supplier specified ranges, such that the necessary plate area is minimized. Several types of cutting patterns are used to compose the cutting plan. All of them are easy to generate and cut except the last one. The algorithm uses both recursive and dynamic programming techniques to generate patterns of the last type. The computational results of 22 practical instances indicate that the algorithm can produce solutions close to optimal, and the computation time is reasonable for practical use.     

Heuristic for constrained T-shape cutting patterns of rectangular pieces

T-shape patterns are often used in dividing stock plates into rectangular pieces, because they make good balance between plate cost and cutting complexity. A dividing cut separates the plate into two segments, each of which contains parallel strips, and the strip orientations of the two segments are perpendicular to each other. This paper presents a heuristic algorithm for constrained T-shape patterns, where the optimization objective is to maximize the pattern value, and the frequency of each piece type does not exceed the demand. The algorithm considers many dividing-cut positions, determines the pattern value associated to each position using a layout-generation procedure, and selects the one with the maximum pattern value as the solution. Pseudo upper bounds are used to skip some non-promising positions. The computational results show that the algorithm is fast and able to get solutions better than those of the optimal two-staged patterns in terms of material utilization.     

双排多段排样方式及其生成算法

为解决大规模矩形毛坯无约束的二维剪切排样问题,提出双排多段排样方式及其 生成算法。排样时采用一条剪切线将板材切分为两段,用一组剪切线将每段切分成一系列的块, 每个块由一组水平方向的同质条带构成。采用枚举法确定两段分界线的最优位置,通过求解背 包模型确定所有可能尺寸的块的最大价值和块在段中的最优布局。利用文献中的2 组基准测题 对所述算法进行测试,实验结果表明,该算法能在合理的计算时间内取得较好的优化结果。     

Reactive GRASP for the strip-packing problem

This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite height so as to minimize the required height. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances which have been previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures. The results show that the GRASP algorithm outperforms recently reported metaheuristics.