生成矩形毛坯最优两段排样方式的确定型算法

排样价值、切割工艺和计算时间是排样问题主要考虑的3个因素.文中提出一个新的基于排样模式的确定型排样算法——同质块两段排样算法,此算法适合剪冲下料工艺,在实现工艺简化的同时提高了排样价值时间比.首先通过动态规划算法生成最优同质块,然后求解一维背包问题生成块在级中的最优排样方式和级在段中的最优排样方式,最后选择两个段生成最优的两段排样方式.通过3组经典测题对该文算法进行了测试,将算法与4种著名算法进行了比较.实验结果表明,该文算法的优化结果好于以上4种著名算法,有效地提高了板材利用率,并且计算时间合理.     

生成冲裁条带四块排样方式的最优算法

提出一个生成冲裁条带四块布局方式的最优算法,用于解决冲裁件无约束排样问题。该算法用三条剪切线把板材划分成四个块,每个块里面只包含方向和长度都相同的冲裁条带。首先生成所有可能长度的冲裁条带,然后求解背包问题生成冲裁条带在块里面的最优布局,最后通过枚举三条剪切线位置得到不同的四块组合,选择使排样价值最大的四块组合生成最优的四块排样方式。实验结果表明,该算法不仅可以提高材料利用率,而且计算时间合理。     

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。     

生成矩形毛坯最优T形排样方式的递归算法

讨论矩形毛坯无约束两维剪切排样问题．采用由条带组成的T形排样方式，切割工艺简单．排样时用一条分界线将板材分成2段，同一段中所有条带的方向和长度都相同．一段含水平条带．另一段含竖直条带．采用递归算法确定分界线的最优位置以及每段中条带的最优组合．以便使下料利用率达到最高．采用大量随机生成的例题进行实验，结果表明该算法在计算时间和提高材料利用率2方面都较有效．     

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.     

同尺寸矩形毛坯排样的连分数分支定界算法

在确定同尺寸矩形毛坯最优排样方式的算法中,连分数算法的时间效率最高,但所生成排样方式的切割工艺复杂．提出连分数分支定界算法,该算法应用连分数法确定毛坯数最优值,采用贴切的上界估计方法;在搜索过程中只保留上界不小于最优值的分支,遇到下界等于最优值的分支时结束搜索．实验结果表明,该算法的时间效率和连分数算法接近,并可以有效地简化切割工艺,生成切割工艺最简单的排样方式．最后,通过实例分析说明该算法的节约材料潜力。     

生成最优同形块两阶段布局方式的确定型算法

为解决大规模二维布局问题,提出一种生成同形块两阶段布局方式的确定型算法。首先通过动态规划确定最优同形块;然后求解背包问题确定同形块在同形级中的布局方式和同形级在同形段中的最优布局方式;最后选择两个同形段生成最优同形块布局方式。通过43道基准测题,将该算法与经典两阶段和三块算法进行比较。实验结果表明,该算法不仅能满足剪切工艺,在计算时间和板材利用率上优于以上算法,而且能在合理时间内取得好的优化结果。     

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。     

冲裁条带最优多段排样方式的动态规划算法

讨论冲裁件无约束剪冲排样问题,用动态规划算法生成冲裁条带多段排样方式。采用一组相互平行的分割线将板材分成多个段,每段含一组方向和长度都相同的条带。通过动态规划算法确定所有可能尺寸段的最优价值以及板材中段的最优组合,使整张板材价值达到最大。实验结果表明该算法能够提高材料利用率,计算时间能满足实际应用的需要。     

An exact algorithm for generating homogenous T-shape cutting patterns

Both the material usage and the complexity of the cutting process should be considered in generating cutting patterns. This paper presents an exact algorithm for constrained two-dimensional guillotine-cutting problems of rectangles. It uses homogenous T-shape patterns to simplify the cutting process. Only homogenous strips are allowed, each of which contains rectangular blanks of the same size and direction. The sheet is divided into two segments. Each segment consists of strips of the same length and direction. The strip directions of the two segments are perpendicular to each other. The algorithm is based on branch and bound procedure combined with dynamic programming techniques. It is a bottom-up tree-search approach that searches the solution tree from the branches to the root. Tighter bounds are established to shorten the searching space. The computational results indicate that the algorithm is efficient both in computation time and in material usage.     

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。     

一种高效的矩形套裁排样的带填充排样算法

提出一种带填充排样算法,实现矩形毛坯套裁排样。该算法首先用水平剪切线将板材分层,每层的宽度和板材宽度相同,高度和层最左端的主毛坯高度相同;通过调用两个递归过程确定最优排样方式,第一个过程确定每层左端的主毛坯,第二个过程确定层右端区域的毛坯排列方式。采用分支定界技术缩小搜索空间。实验计算结果说明所述算法比文献中最近报道的几种算法都有效。     

Sequential value correction heuristic for the two-dimensional cutting stock problem with three-staged homogenous patterns

A sequential value correction heuristic is presented for the two-dimensional cutting stock problem with three-staged homogenous patterns, considering both input-minimization and simplicity of the cutting process. The heuristic constructs many cutting plans iteratively and selects the best one as the solution. The patterns in each cutting plan are generated sequentially using simple recursive techniques. The values of the item types are corrected after the generation of each pattern to diversify the cutting plans. Computational results indicate that the proposed heuristic is more effective in input minimization than published algorithms and commercial stock cutting software packages that use three-staged general or exact patterns.     

Heuristic and exact algorithms for generating homogenous constrained three-staged cutting patterns

An approach is proposed for generating homogenous three-staged cutting patterns for the constrained two-dimensional guillotine-cutting problems of rectangles. It is based on branch-and-bound procedure combined with dynamic programming techniques. The stock plate is divided into segments. Each segment consists of strips with the same direction. Only homogenous strips are allowed, each of which contains rectangles of the same size. The approach uses a tree-search procedure. It starts from an initial lower bound, implicitly generates all possible segments through the builds of strips, and constructs all possible patterns through the builds of segments. Tighter bounds are established to discard non-promising segments and patterns. Both heuristic and exact algorithms are proposed. The computational results indicate that the algorithms are capable of dealing with problems of larger scale. Finally, the solution to a cutting problem taken from a factory that makes passenger cars is given.     

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。     

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.     

Using Wang's two-dimensional cutting stock algorithm to optimally solve difficult problems

P. Y. Wang's classic bottom-up two-dimensional cutting stock algorithm generates cutting patterns by building rectangles both horizontally and vertically. This algorithm uses a parameter β ₁ to tradeoff the number of rectangles generated by the algorithm and hence the quality of the cutting pattern solution obtained versus the amount of computer resources required. Several researchers have made relatively straightforward modifications to Wang's basic algorithm resulting in improved computational times. However, even with these modifications, Wang's approach tends to require large amounts of computer resources in order to optimally or near-optimally solve difficult two-dimensional guillotine cutting stock problems. In this paper, we present an iterative approach that judiciously uses Wang's basic algorithm (with some previously defined modifications) to obtain optimal cutting patterns to difficult two-dimensional cutting stock problems in reasonable computer run times.