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.     

混合遗传算法在圆形件优化排样中的应用研究

本文研究的是圆形件优化排样问题,是将卷材切成若干种圆形毛坯,使所产生的废料最少以达到节约材料的目的。本文在我们提出的放置算法(ASA)的基础上,采用混合遗传算法作为搜索策略;实验测试结果表明,本文算法可以和排样领域著名的法国学者Hifi在国外检索刊物上提出的算法相媲美,该算法的计算时间可以满足一般实践应用的要求,所得排样方案的材料利用率较高。     

简化同尺寸矩形毛坯排样方式的动态规划算法

同尺寸矩形毛坯排样方式的最优性包括毛坯数量最优性和切割工艺最优性。前者是指排样方式中所含毛坯数最大;后者是指在所有实现毛坯数量最优性的排样方式中,切割工艺最为简单。采用条带数衡量排样方式的复杂性,用动态规划算法生成条带数最少的最优排样方式。实验计算结果表明,所述算法能够明显简化下料工艺,对指导生产实践具有较重要的意义。     

Generating optimal T-shape cutting patterns for circular blanks

Circular blanks are often used in the manufacturing of the stators and rotors of electric motors. Some factories in China use T-shape cutting patterns to improve material usage. The author presents an algorithm to generate optimal T-shape cutting patterns for circular blanks. In the patterns more than one row of identical blanks can appear in a strip. A strip is in one of the two perpendicular directions, namely X direction or Y direction. The algorithm uses the knapsack algorithm and an implicit enumeration method to determine the optimal combination of blank rows in the strips, the strip numbers and directions in the pattern. The principles and steps of the algorithm are described in detail. The computational results indicate that the algorithm is efficient both in computation time and in material usage. Finally, the solution to an example is given.     

New approaches to nesting rectangular patterns

In this study, two approaches are explored for the solution of the rectangular stock cutting problem: neuro-optimization, which integrates artificial neural networks and optimization methods; and genetic neuro-nesting, which combines artificial neural networks and genetic algorithms. In the first approach, an artificial neural network architecture is used to generate rectangular pattern configurations, to be used by the optimization model, with an acceptable scrap. Rectangular patterns of different sizes are selected as input to the network to generate the location and rotation of each pattern after they are combined. A mathematical programming model is used to determine the nesting of different sizes of rectangular patterns to meet the demand for rectangular blanks for a given planning horizon. The test data used in this study is generated randomly from a specific normal distribution. The average scrap percentage obtained is within acceptable limits. In the second approach, a genetic algorithm is used to generate sequences of the input patterns to be allocated on a finite width with infinite-length material. Each gene represents the sequence in which the patterns are to be allocated using the allocation algorithm developed. The scrap percentage of each allocation is used as an evaluation criterion for each gene for determining the best allocation while considering successive generations. The allocation algorithm uses the sliding method integrated with an artificial neural network based on the adaptive resonance theory (ART1) paradigm to allocate the patterns according to the sequence generated by the genetic algorithm. It slides an incoming pattern next to the allocated ones and keeps all scrap areas produced, which can be utilized in allocating a new pattern through the ART1 network. If there is a possible match with an incoming pattern and one of the scrap areas, the neural network selects the best match area and assigns the pattern. Both approaches gave satisfactory results. The second approach generated nests having packing densities in the range 95–97%. Improvement in packing densities was possible at the expense of excessive computational time. Parallel implementation of this unconventional approach could well bring a quick and satisfactory solution to this classical problem.     

解决二维下料问题的顺序启发式算法

求解二维下料问题即求解如何用最少的板材排入所需的全部毛坯的问题。一种基于价值修正策略的顺序启发式算法被用来生成排样方案,方案中的排样方式按单位面积价值最大生成,在各排样方式顺序生成的过程中不断修正方式中使用到的毛坯的价值。迭代调用该过程多次生成多个排样方案,从中选择最优的排样方案。通过实验证明算法的有效性。     

Synthesis of mutual exclusion solutions based on binary semaphores

A graphical form of the mutual exclusion problem is considered in which each vertex represents a process and each edge represents a mutual exclusion constraint between the critical sections of the processes associated with its endpoints. An edge semaphore solution for mutual exclusion problems is defined, and those graphs which are edge solvable are characterized in terms of both a forbidden subgraph and a graph grammar. Finally, an efficient algorithm is given which generates the entry and exit sections for all processes in an edge-solvable problem     

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.     

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。     

Utilization Bounds for EDF Scheduling on Real-Time Multiprocessor Systems

The utilization bound for earliest deadline first (EDF) scheduling is extended from uniprocessors to homogeneous multiprocessor systems with partitioning strategies. First results are provided for a basic task model, which includes periodic and independent tasks with deadlines equal to periods. Since the multiprocessor utilization bounds depend on the allocation algorithm, different allocation algorithms have been considered, ranging from simple heuristics to optimal allocation algorithms. As multiprocessor utilization bounds for EDF scheduling depend strongly on task sizes, all these bounds have been obtained as a function of a parameter which takes task sizes into account. Theoretically, the utilization bounds for multiprocessor EDF scheduling can be considered a partial solution to the bin-packing problem, which is known to be NP-complete. The basic task model is extended to include resource sharing, release jitter, deadlines less than periods, aperiodic tasks, non-preemptive sections, context switches, and mode changes.     

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.     

A cutting stock problem and its solution in the manufacturing industry of large electric generators

T-shape cutting patterns are applied in the manufacturing of circular and sectorial blanks for stators and rotors of large electric generators. The author presents an algorithm to generate them. In the patterns more than one row of identical blanks can appear in a strip. A strip is in one of the two perpendicular directions, namely X- or Y-direction. The algorithm uses the knapsack algorithm and an implicit enumeration method to determine the optimal combination of blank rows in the strips, the strip numbers and directions in the pattern. The algorithm is applied to the real cutting stock data of a factory that makes large electric generators. The results indicate that the algorithm is efficient both in computation time and in material usage.     

Two-machine group scheduling problems in discrete parts manufacturing with sequence-dependent setups

This paper focuses on minimizing the total completion time in two-machine group scheduling problems with sequence-dependent setups that are typically found in discrete parts manufacturing. As the problem is characterized as strongly NP-hard, three search algorithms based on tabu search are developed for solving industry-size scheduling problems. Four different lower bounding mechanisms are developed to identify a lower bound for all problems attempted, and the largest of the four is aptly used in the evaluation of the percentage deviation of the search algorithms to assess their efficacy. The problem sizes are classified as small, medium and large, and to accommodate the variability that might exist in the sequence-dependent setup times on both machines, three different scenarios are considered. Such finer levels of classification have resulted in the generation of nine different categories of problem instances, thus facilitating the performance of a very detailed statistical experimental design to assess the efficacy and efficiency of the three search algorithms. The search algorithm based on long-term memory with maximal frequencies either recorded a statistically better makespan or one that is indifferent when compared with the other two with all three scenarios and problem sizes. Hence, it is recommended for solving the research problem. Under the three scenarios, the average percentage deviation for all sizes of problem instances solved has been remarkably low. In particular, a mathematical programming based lower bounding mechanism, which focuses on converting (reducing) the original sequence-dependent group scheduling problem with several jobs in each group to a sequence-dependent job scheduling problem, has served well in identifying a high quality lower bound for the original problem, making it possible to evaluate a lower average percentage deviation for the search algorithm. Also, a 16–17-fold reduction in average computation time for solving a large problem instance with the recommended search algorithm compared with identifying just the lower bound of (not solving) the same instance by the mathematical programming based mechanism speaks strongly in favor of the search algorithm for solving industry-size group scheduling problems.     

Synchronization transformations for parallel computing

This article describes a framework for synchronization optimizations and a set of transformations for programs that implement critical sections using mutual exclusion locks. The basic synchronization transformations take constructs that acquire and release locks and move these constructs both within and between procedures. They also eliminate, acquire and release constructs that use the same lock and are adjacent in the program. The article also presents a synchronization optimization algorithm, lock elimination, that uses these transformations to reduce the synchronization overhead. This algorithm locates computations that repeatedly acquire and release the same lock, then transforms the computations so that they acquire and release the lock only once. The goal of this algorithm is to reduce the lock overhead by reducing the number of times that computations acquire and release locks. But because the algorithm also increases the sizes of the critical sections, it may decrease the amount of available concurrency. The algorithm addresses this trade-off by providing several different optimization policies. The policies differ in the amount by which they increase the sizes of the critical sections. Experimental results from a parallelizing compiler for object-based programs illustrate the practical utility of the lock elimination algorithm. For three benchmark applications, the algorithm can dramatically reduce the number of times the applications acquire and release locks, which significantly reduces the amount of time processors spend acquiring and releasing locks. The resulting overall performance improvements for these benchmarks range from no observable improvement to up to 30% performance improvement. Copyright © 1999 John Wiley & Sons, Ltd.     

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。     

Mechanizing ω-order type theory through unification

This paper deals with the problems of applying a unification procedure in a mechanization of the full type theory. The early sections describe the unification problem and an algorithm which produces a complete set of unifiers. The special case of the 2nd order problem is differentiated. Then there is presented an extensive proof of completeness of the algorithm. The later sections are devoted to application of the unification in mechanical theorem proving. A generalization of the resolution principle as well as some specialized strategies are presented.     

遗传算法中初始群体技术的改进与实现

初始群体产生技术对遗传程序设计的进化结果有直接影响.为了改进进化结果和提高搜索效率,提出了一种递减检验的随机算法(DCRA),使其与领域经验知识相结合产生初始群体的遗传算法(EDGA).将EDGA算法应用于生产中的圆形件排样问题,实验结果表明,该算法产生了良好的效果.DCRA和EDGA对于遗传算法的其它应用领域将有一定的指导意义.     

Planning horizons for the deterministic capacity problem

We consider the problem of determining the optimal timing and sizing of new facility construction under a continuous technology model of possible sizes. The rate of convergence of short to long run optimal policies is established and planning horizon implications are explored. We also present an efficient algorithm for solving such problems for all horizon times by solving a single horizon time problem     

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。     

Using extended feature objects for partial similarity retrieval

In this paper, we introduce the concept of extended feature objects for similarity retrieval. Conventional approaches for similarity search in databases map each object in the database to a point in some high-dimensional feature space and define similarity as some distance measure in this space. For many similarity search problems, this feature-based approach is not sufficient. When retrieving partially similar polygons, for example, the search cannot be restricted to edge sequences, since similar polygon sections may start and end anywhere on the edges of the polygons. In general, inherently continuous problems such as the partial similarity search cannot be solved by using point objects in feature space. In our solution, we therefore introduce extended feature objects consisting of an infinite set of feature points. For an efficient storage and retrieval of the extended feature objects, we determine the minimal bounding boxes of the feature objects in multidimensional space and store these boxes using a spatial access structure. In our concrete polygon problem, sets of polygon sections are mapped to 2D feature objects in high-dimensional space which are then approximated by minimal bounding boxes and stored in an R-tree. The selectivity of the index is improved by using an adaptive decomposition of very large feature objects and a dynamic joining of small feature objects. For the polygon problem, translation, rotation, and scaling invariance is achieved by using the Fourier-transformed curvature of the normalized polygon sections. In contrast to vertex-based algorithms, our algorithm guarantees that no false dismissals may occur and additionally provides fast search times for realistic database sizes. We evaluate our method using real polygon data of a supplier for the car manufacturing industry. Edited by R. Güting. Received October 7, 1996 / Accepted March 28, 1997