Heuristic and genetic approach for nesting of two-dimensional rectangular shaped parts with common cutting edge concept for laser cutting and profile blanking processes

This paper presents a novel two-dimensional nesting strategy suitable for sheet metal industries employing laser cutting and profile blanking processes. The proposed nesting approach is developed by the combination of heuristic and genetic algorithms in order to generate an effective nested pattern, in such a way that, it minimizes the sheet material wastage and also the cutting tool path distance, while arranging a set of rectangular parts in a rectangular sheet. With the proposed bottom–left heuristic method, at first, the parts are considered in a specific sequence and orientation, and each part is translated to the feasible bottom left most position on the previously placed parts and then adjusted to form the common cutting edges with adjacent parts. Further, the heuristic algorithm ensures the formation of clusters, in which a group of parts share the cutting edges, for effective handling of parts while cutting. Finally the optimal and effective nested pattern is generated by the genetic evaluation process which reproduces several sets of nested patterns, before converging to the optimality. The effectiveness of the proposed work, in terms of utilization of sheet material, is demonstrated by comparing the results obtained from the literature. Furthermore the uniqueness of the present approach in enhancing the nested pattern efficiency and minimizing the tool path distance with common cutting edge concept is illustrated.     

基于下料特征的大规模零件分组优化方法

针对诸多算法在处理大规模零件下料问题时易陷入时间效率和材料利用率矛盾的问题,提出一种基于零件下料特征的分组优化方法.首先采用图论工具对零件下料特征关联进行分析,建立零件相似特征关联有权无向图与零件下料配合特征关联有权无向图;然后将样本零件所表现的下料特征作为分组约束,通过对无向图最小生成树(MST)的分割完成待下料零件的自适应分组.优化前根据材料利用率对零件分组进行排序,优化中对零件的组间分布进行动态补偿,最后合并各组优化结果得到原问题的下料方案.实验结果表明,该方法是可行的和有效的.     

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。     

基于梯形和平行四边形的圆片剪冲下料算法设计与实现

提出一种在矩形板材上引入梯形条带来进行排样的方法,首先用两条平行的分界 线将板材分为两个大小一致的直角梯形段和一个平行四边形段,分别采用递归算法和动态规划 算法确定梯形段和平行四边形段中条带的最优组合,从而确定最优排样方式;再结合线性规划 算法解决圆片下料问题,使得整个下料方案的材料利用率最大化。最后采用大量随机生成的例 题进行实验,实验结果表明该算法能有效提高材料利用率。     

A heuristic for nesting problems of irregular shapes

Layout has a close relationship with product cost in the vein of how to most efficiently cut product patterns from raw materials. This is the so-called “nesting problem”, which occurs frequently in sheet metal and furniture industries, wherein material utilization needs to be maximized. In this paper, a quick location and movement (QLM) algorithm is proposed to solve the situation of irregular shapes nested on multiple irregular sheets. This approach includes two major parts: it first approximates irregular shapes to a polygon with the use of a cluster of straight lines, and second, it arranges the approximated shapes one-by-one with the proposed step-by-step rule. Finally, this study investigates and compares examples presented by other authors. The results show that the QLM algorithm takes less time to calculate a layout and the material utilization efficiency is higher compared to other methods.     

圆片下料并行遗传算法的设计与实现

针对制造行业中的圆片下料问题,为了在合理的计算时间内使材料的利用率尽可能高,提出并行遗传下料算法（PGBA）,以下料方案的材料利用率作为优化目标函数,将下料方案作为个体,采用多线程的方式对多个子种群并行进行遗传操作。首先,在并行遗传算法的基础上设计特定的个体编码方式,采用启发式方法生成种群的个体,以提高算法的搜索能力和效率,避免早熟现象的发生;然后,采用性能较好的遗传算子进行自适应的遗传操作,搜索出一种近似最优的下料方案;最后,通过多种实验验证算法的有效性。结果表明,与启发式算法相比,PGBA的计算时间有所增加,但材料利用率得到了较大的提高,能有效提高企业的经济效益。     

An optimal layout methodology for cold forming rectangular parts using genetic algorithms

Cold forming is widely used in manufacturing processing, and the layout of rectangular parts in the strip is manually accomplished, which is a time-consuming task and may be a major bottleneck in effectively improving the utilization ratio of material and the productivity. The mathematical model for optimal layout of cold forming is first developed, and then the constrained optimal layout problem is transformed to an unconstrained optimal one with penalty function strategy. A simple genetic algorithms for this optimal layout is proposed, and an example is examined to show the validity of this proposed genetic methodology. Although the simple genetic algorithms is employed, a higher material utilization ratio and productivity is achieved.     

满足工艺品剪切要求的二维不规则排料算法

主要研究在矩形铁皮原材料上排放若干种二维不规则工艺品零件。对零件轮廓矢量图进行分类,采用形心重合定位填充算法对不规则图形进行组合,然后使用对排、单排、改进型的最低水平线排料策略,在满足“一刀切”的工艺品剪切要求和同种规格零件尽量放在一起的前提下,尽量提高原材料的利用率。实验结果表明排料算法的原材料利用率较高,同时满足剪切工艺要求。     

Efficient stock cutting for laminated manufacturing

When an object is made using Laminated Manufacturing (LM), the output is a rectangular block with the required object trapped inside. In order to enable extraction of the object, the remaining sheet in each layer is cut into square grids that grow into tiny tiles. Thus, the remaining stock inside and surrounding the object is in the form of tiled fragments. The operator ‘decubes’ or removes these tiles using sharp tools and extracts the object. Making use of the remaining stock as support structure and grid cutting to enable extraction of the object are very innovative ideas in the ‘paste-and-cut’ LM approach. However, this method is very inefficient for two reasons: firstly, cutting efficiency is poor since laser spends most of its time in grid cutting; secondly, decubing takes several hours. In this paper, an efficient method of cutting the remaining stock to extract the object is presented.Extraction of the object from the stock block has analogy with the extraction of casting from its mold—the present and proposed methods respectively being analogous to sand casting and permanent mold casting processes. In the proposed method, rather than fragmenting the remaining stock into tiny tiles, it is segmented into two stock halves that open about a parting surface of minimum area. This optimal parting surface is obtained for the convex hull of the object, rather than for the object itself, due to its complete visibility along any pair opposite directions. The convex hull is further segmented into the object and plugs. The plugs are so shaped that they do not get entangled inside the concave portions of the object. The plugs whose drawing directions coincide with the opening direction of the stock halves are merged with the corresponding stock halves. The object, all the plugs and both the stock halves form the stock block. All these pieces are made together in the LM machine. For disassembly, first the convex hull will be extracted by opening the stock halves. Subsequently the plugs that fill the concave portions of the object will be extracted from the convex hull. Thus, grid cutting and decubing are eliminated in the proposed method resulting in drastic reduction in prototyping time and improved quality of the prototype.     

An optimizing model to solve the nesting problem of rectangle pieces based on genetic algorithm

In the process of cement equipment manufacturing, the demand of rectangle pieces of steel structure is very large. The traditional manual nesting, which is simply cutting by hand-making according to the arrangement of the number and size, causes the low efficiency and material wasting. To solve the problem above, this paper proposes an optimizing model for nesting problem of rectangle pieces. Firstly, with the aim of the maximum utilization ratio of the sheet, the optimization mathematical model for nesting problem of rectangle pieces is established. The lowest horizontal line searching algorithm is described in detail. Secondly, the mathematical model is solved to get the optimal solution by the combination of genetic algorithm and the lowest horizontal line searching algorithm. In the solution process, this paper presents the methods of gene encoding and decoding, definition of fitness function, the design of genetic operators and the design of algorithm operating parameters. Finally, we use one sheet as an example to illustrate the proposed model and algorithm process. Experimental results have shown that the proposed approach is able to achieve rectangle pieces nesting with the maximum material utilization ratio.     

基于临界多边形的不规则件启发式排样算法

为提高不规则件启发式排样的材料利用率,提出一种基于重心临界多边形和边适应度的不规则件启发式排样算法GEFHNA。首先,定义了边适应度以衡量排样过程中原材料与不规则件间贴合程度,在此基础上给出了将边适应度与重心NFP（GNFP）相结合的排放策略以减少排样过程中可能产生的空隙面积;其次,给出了基于Weiler-Atherton多边形裁剪算法的剩余原材料求解方法,重用排样过程中产生的孔洞,减少孔洞面积;最后,给出了基于上述排样策略和材料重用策略的启发式排样算法GEFHNA,给出了与智能算法和同类软件的实验比较。对欧洲排样问题兴趣小组提供的基准测试用例的实验结果表明,GEFHNA的耗时约为基于智能算法的排样方法的千分之一,同时在与两款商业软件NestLib和SigmaNest的11个基准测试的对比中,GEFHNA获得了7/11个相对最优的排样面积利用率。     

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.     

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．     

Generating optimal two-section cutting patterns for rectangular blanks

This paper presents an algorithm for generating unconstrained guillotine-cutting patterns for rectangular blanks. A pattern includes at most two sections, each of which consists of strips of the same length and direction. The sizes and strip directions of the sections must be determined optimally to maximize the value of the blanks cut. The algorithm uses an implicit enumeration method to consider all possible section sizes, from which the optimal sizes are selected. It may solve all the benchmark problems listed in the OR-Library to optimality. The computational results indicate that the algorithm is efficient both in computation time and in material utilization. Finally, solutions to some problems are given.     

Waste minimization in irregular stock cutting

This paper addresses a category of two dimensional NP-hard knapsack problem in which a given convex/non-convex planner items (polygons) have to be cut out of a single convex/non-convex master surface (stock). This cutting process is found in many industrial applications such as sheet metal processes, home-textile, garment, wood, leather and paper industries. An approach is proposed to solve this problem, which depends on the concept of the difference between the area of a collection of polygons and the area of their convex hull. The polygon assignment inside the stock is subjected to feasibility tests to avoid overlapping, namely, angle test, bound test, point inclusion and polygon intersection test. An iterative scheme is used to generate different polygon placements while optimizing the objective function. Computer software is developed to solve and optimize the problem under consideration. Few examples are conducted for different combinations of convex, non-convex items and stocks. Well-known benchmark problems from the literature are tested and compared with our approach. The results of our algorithm have an interesting computational time and can compete with the results of previous work in some particular problems. The computational performance of the developed software indicates the efficiency of the algorithm for solving 2-D irregular cutting of non-convex polygons out of non-convex stock.     

基于粒子群与模拟退火算法的板材优化下料

提出一种用于处理板材下料问题的粒子群与模拟退火混合算法。同时,在把下料模式转化为实际设计时,提出了一种类似于Bottom Left（BL）算法的转换方法。模拟实验结果表明这种混合方法的性能明显优于粒子群算法。     

Prediction of workpiece elastic deflections under cutting forces in turning

One of the problems faced in turning processes is the elastic deformation of the workpiece due to the cutting forces resulting in the actual depth of cut being different than the desirable one. In this paper, a cutting mechanism is described suggesting that the above problem results in an over-dimensioned part. Consequently, the problem of determining the workpiece elastic deflection is addressed from two different points of view. The first approach is based on solving the analytical equations of the elastic line, in discretized segments of the workpiece, by considering a stored modal energy formulation due to the cutting forces. Given the mechanical properties of the workpiece material, the geometry of the final part and the cutting force values, this numerical method can predict the elastic deflection. The whole approach is implemented through a Microsoft Excel^© workbook. The second approach involves the use of artificial neural networks (ANNs) in order to develop a model that can predict the dimensional deviation of the final part by correlating the cutting parameters and certain workpiece geometrical characteristics with the deviations of the depth of cut. These deviations are calculated with reference to final diameter values measured with precision micrometers or on a CMM. The verification of the numerical method and the development of the ANN model were based on data gathered from turning experiments conducted on a CNC lathe. The results support the proposed cutting mechanism. The numerical method qualitatively agrees with the experimental data while the ANN model is accurate and consistent in its predictions.     

Xurography: rapid prototyping of microstructures using a cutting plotter

This paper introduces xurography, or "razor writing," as a novel rapid prototyping technique for creating microstructures in various films. This technique uses a cutting plotter traditionally used in the sign industry for cutting graphics in adhesive vinyl films. A cutting plotter with an addressable resolution of 10 /spl mu/m was used to cut microstructures in various films with thicknesses ranging from 25 to 1000 /spl mu/m. Positive features down to 35 /spl mu/m and negative features down to 18 /spl mu/m were cut in a 25 /spl mu/m thick material. Higher aspect ratios of 5.2 for positive features and 8 for negative features were possible in a 360 /spl mu/m thick material. A simple model correlating material properties to minimum feature size is introduced. Multilayered microstructures cut from pressure sensitive and thermal activated adhesive films were laminated in less than 30 min without photolithographic processes or chemicals. Potential applications of these microstructures are explored including: shadow masking, electroplating, micromolds for PDMS, and multilayered three-dimensional (3-D) channels. This inexpensive method can rapidly prototype microfluidic devices or tertiary fluid connections for higher resolution devices. [1488].     

An algorithm for the determination of optimal cutting patterns

This paper presents a new mathematical programming formulation for the problem of determining the optimal manner in which several product rolls of given sizes are to be cut out of raw rolls of one or more standard types. The objective is to perform this task so as to maximize the profit taking account of the revenue from the sales, the costs of the original rolls, the costs of changing the cutting pattern and the costs of disposal of the trim. A mixed integer linear programming (MILP) model is proposed which is solved to global optimality using standard techniques. A number of example problems, including an industrial case study, are presented to illustrate the efficiency and applicability of the proposed model.Scope and purposeOne-dimensional cutting stock (trim loss) problems arise when production items must be physically divided into pieces with a diversity of sizes in one dimension (e.g. when slitting master rolls of paper into narrower width rolls). Such problems occur when there are no economies of scale associated with the production of the larger raw (master) rolls. In general, the objectives in solving such problems are to [5]:

• •minimize trim loss;
• •avoid production over-runs and/or;
• •avoid unnecessary slitter setups.

The above problem is particularly important in the paper converting industry when a set of paper rolls need to be cut from raw paper rolls. Since the width of a product is fully independent of the width of the raw paper a highly combinatorial problem arises. In general, the cutting process always produces inevitable trim-loss which has to be burned or processed in some waste treatment plant. Trim-loss problems in the paper industry have, in recent years, mainly been solved using heuristic rules. The practical problem formulation has, therefore, in most cases been restricted by the fact that the solution methods ought to be able to handle the entire problem. Consequently, only a suboptimal solution to the original problem has been obtained and very often this rather significant economic problem has been left to a manual stage. This work presents a novel algorithm for efficiently determining optimal cutting patterns in the paper converting process. A mixed-integer linear programming model is proposed which is solved to global optimality using available computer tools. A number of example problems including an industrial case study are presented to illustrate the applicability of the proposed algorithm.