基于两阶段的分段单一矩形优化排样

为有效解决分段单一矩形优化排样问题,给出一个求解分段单一矩形优化排样问题的两阶段方法。第一阶段完成标准子段最佳排样方式求解,并将二维排样问题转化为一维下料问题,第二阶段使用适合于一维下料问题求解的算法完成板材最佳排样方式求解。使用该方法开发了一个单一矩形优化排样系统,该系统既可以解决分段单一矩形排样问题也可以解决其他类型的单一矩形优化排样问题。企业应用实例表明该方法是求解分段单一矩形优化排样问题的一个较为有效的方法。     

单一尺寸矩形毛坯排样时长板的最优分割

讨论了存在剪刃长度约束时单一尺寸矩形毛坯的优化排样问题,将板材分割成多张子板,通过优化确定子板张数、各子板长度和毛坯在各子板上的排列,使事 板材中所含毛坯数达到最大;并对Agrawal提出的单一尺寸矩形毛了优化排样方法进行扩展,构造出一种分支定界方法,用于解决长板最优分割问题,实验计算结果表明,所述算法非常有效;最后给出了例题数据的排样结果,与企业的通常做法相比较,说明了采用本方法的节材潜力。     

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。     

基于蚁群优化算法求解矩形件排样问题

布局问题来源于生产实际,优秀的布局可以提高原料利用率,降低成本,提高经济效益,对许多行业有重要意义。矩形件优化排样是一类具有NP完全难度的组合优化问题。人工蚁群算法是对蚂蚁群体行为的模拟抽象,该算法具有分布计算、信息正反馈和启发式搜索等特点。本文将蚁群算法和剩余矩形法结合用于解决矩形排样问题,首先用蚁群算法将矩形件排样问题转化为一个排列问题;然后通过剩余矩形排样算法排出每一个排列所对应的排样图;最后用算法对文献[9]中的两个算例进行了验证,表明了其有效性。     

一种快速的有约束矩形件优化排样模型

为了有效地解决有约束的矩形件优化排样问题,提出一种快速的求解算法;通过比较待排样矩形件的不同排样模式,选择最优排样方案。算法完全基于解析计算,虽不能寻找理论最优解,但相比于各种启发式算法大大提高了排样速度。实验结果表明,算法能够在较短的计算时间内获得满意的排样效果,是一种效率较高的有约束矩形件排样算法。     

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。     

基于排样矩形的直角边零件下料算法

针对实际操作中直角边零件下料利用率不高的问题,导入排样矩形的概念,将直角边零件下料问题分解为若干优化子问题,在此基础上,基于动态规划思想通过求解子问题构建全局最优解.实验表明,与传统的直角边零件板材切割相比,使用本文算法能够使板材的利用率提高30％-50％;与其他几种典型算法相比,本算法板材利用率提高显著,并且排样方案...     

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.     

基于遗传算法的大规模矩形件优化排样

大规模矩形件优化排样是一个典型的组合优化问题，属于NP-hard问题．实际工程中对一个排样方案一般有满足“一刀切”的工艺要求，“一刀切”要求增加了对排样的约束．提出的优化算法，将矩形匹配分割算法作为遗传算法染色体的解码器实现一个排样方案，用遗传算法进行排样方案的全局搜索．算例比较表明，该算法可以求得满足“一刀切”约束的最优解．     

矩形件无约束二维板材剪切的4块排样算法

针对矩形件无约束二维板材剪切排样问题,提出一种新的4块排样方式及其生成算法.该排样方式将板材划分成4个块,对每个块,按照递归方式进行排样.选择一行同种矩形件放置在块的左下角,沿着这行矩形件的上边界和右边界将该块剩余部分划分成两个更小的子块以待进一步递归考察.首先,构造动态规划算法一次性生成所有可能尺寸的块中矩形件的递归...     

矩形件简单块占角排样方式的动态规划

目的 针对矩形件无约束2维剪切排样问题,提出一种可简化板材切割工艺的简单块占角排样方式,并构造这种排样方式的动态规划生成算法。方法 该排样方式在板材左下角按照简单块方式排样若干行若干列同种矩形件,将板材剩余部分划分为两个子板;将子板按照上述方法继续递归排样和划分,直至子板排满矩形件为止。采用动态规划确定所有可能尺寸的板材左下角排样的最优矩形件、矩形件的最优行列数和板材剩余部分的最优子板划分。运用规范尺寸排除不必要的计算。结果 将本文算法与目前常见的算法进行比较,实验结果表明本文算法计算时间合理,排样价值较高。在第1组41道基准例题中,本文算法所有例题均求出了精确解,同质块T型算法、同质块两段算法和复合条带两段算法分别有7道、5道和4道例题未求出精确解。在第2组20道基准例题中,本文算法只有1道例题未求出精确解,普通三阶段算法、同质块T型算法、同质块两段算法和匀质条带三块算法分别有18道、15道、15道和20道例题未求出精确解。在第3组50道随机例题中,本文算法、普通两段算法和同质块两段算法板材利用率分别为99.913 7%、99.862 3%和99.796 1%。在第4组31道基准例题中,本文算法所有例题均求出了精确解,普通占角排样算法有2道例题未求出精确解。结论 本文算法计算时间远小于精确算法,优化效果接近精确算法;本文算法计算时间与多种启发式算法接近,但优化效果好于多种启发式算法。     

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。     

An improved genetic algorithm for facility layout problems having inner structure walls and passages

This study proposes an improved genetic algorithm (GA) to derive solutions for facility layouts that are to have inner walls and passages. The proposed algorithm models the layout of facilities on gene structures. These gene structures consist of a four-segmented chromosome. Improved solutions are produced by employing genetic operations known as selection, crossover, inversion, mutation, and refinement of these genes for successive generations. All relationships between the facilities and passages are represented as an adjacency graph. The shortest path and distance between two facilities is calculated using Dijkstra's algorithm of graph theory. Comparative testing shows that the proposed algorithm performs better than other existing algorithms for the optimal facility layout design. Finally, the proposed algorithm is applied to ship compartment layout problems with the computational results compared with an actual ship compartment layout.Scope and purposeFacility layout problems (FLPs) concerning space layout optimization have been investigated in depth by researchers in many fields, such as industrial engineering, management science, and architecture, and various algorithms have been proposed to solve FLPs. However, these algorithms for the FLP cannot consider inner structure walls and passages within the block plan (or available area). They are also limited to a rectangular boundary shape of the block plan. Therefore, these algorithms could not be directly applied to problems having the curved boundary shape such as ship compartment layout, and an innovative algorithm which can treat such problems is needed. In this study, an improved genetic algorithm (GA) is proposed for solving problems having the inner structure walls and passages within an available area of a curved boundary. A comparative test of the proposed algorithm was performed to evaluate its efficiency. Finally, the proposed algorithm is applied to ship compartment layout problems with the computational results compared with an actual ship compartment layout. From the comparative test and the preliminary applications made to the ship's compartment layout, we demonstrate that the proposed algorithm has the ability to solve the FLPs having the inner structure walls and passages within the available area of the curved boundary.     

二维板材组包排样问题的离散差分进化算法求解

为了提高包装箱的空间利用率,提出一种基于离散差分进化算法的方法,以求解二维板材组包排样问题.采用带符号的序列代表一个排样方案,提出了基于最低水平线的空隙可再利用启发式算法,对单个包的子序列进行解码,获得对单包的排样子问题的自动排样方案,使板材充分填充产生的空隙;为了改进排样结果,提出邻近策略以进一步提高空间利用率.实验结果表明,对仿真实验数据,该算法获得了比遗传算法更好的结果;对实际生产数据,该算法所得结果比原有排样方案的空间利用率更高.     

矩形布局优化问题的局部搜索蜂群算法

带平衡约束的矩形布局问题属于组合优化问题,当问题规模增大时求解困难。为提高求解效率,设计了一个蜂群算法,通过分析解的分布,提供了基于贪心策略的群体初始化方案,选择了有效的变异算子,将蜂群算法的搜索空间聚焦于最优解可能的区域。另外设计了一个二次局部搜索算法,对解的质量进行进一步提升。在10个公开的案例上与目前性能最好的算法进行了对照,提出的蜂群算法在其中9个较大规模的案例上超过了现有算法。理论分析和实验结果表明,相对于现有算法,所提蜂群算法能明显提高求解效率。     

A new approach to differential dynamic programming for discrete time systems

This paper proposes a new differential dynamic programming algorithm for solving discrete time optimal control problems with equality and inequality constraints on both control and state variables and proves its convergence. The present algorithm is different from differential dynamic programming algorithms developed in [10]-[15], which can hardly solve optimal control problems with inequality constraints on state variables and whose convergence has not been proved. Composed of iterative methods for solving systems of nonlinear equations, it is based upon Kuhn-Tucker conditions for recurrence relations of dynamic programming. Numerical examples show file efficiency of the present algorithm.     

Scheduling of Virtual Cellular Manufacturing Systems: A Biogeography-Based Optimization Algorithm

Virtual cellular manufacturing system (VCMS) is one of the modern strategies in the production facilities layout, which has attracted considerable attention in recent years. In this system, machines are located in different positions on the shop floor and virtual cells are a logical grouping of machines, jobs, and workers from the viewpoint of the production control system. These features not only enhance the system’s agility but also allow a dynamic reassignment of cells as demand changes. This paper addresses the VCMS scheduling problems where the jobs have different orders on machines and the objective is to simultaneously minimize the weighted sum of the makespan and total traveling distance in order to create a balance between criteria. The research methodology firstly consists of a mathematical programming model with regard to the production constraints in order to describe the characteristics of the VCMS. Secondly, a basic genetic algorithm (GA), a biogeography-based optimization (BBO) algorithm, an algorithm based on hybridization of BBO and GA, and the BBO algorithm accompanied by restart phase are developed to solve the VCMS scheduling problems. The developed algorithms have been compared to each other and their performance are evaluated in terms of their best solution and computational time as effectiveness and efficiency criteria, respectively. Consequently, the performance of the best algorithm has been evaluated by the state-of-the-art algorithm, GA, in the literature. The results show that the best algorithm based on BBO could find solutions at least as good as the last famous algorithm, GA, in the literature.     

动态主用户流量模型的跨层优化设计

为适应主用户流量变化较快的场景,在不完美频谱感知的情况下最大化认知用户的吞吐量,提出了一种基于集中式Overlay认知无线网络中感知时间与资源分配跨层优化算法。将优化目标分解为信道分配和检测时间同功率分配联合优化两个子问题,通过子算法迭代,最终得到感知时间与资源分配的联合最优解。仿真结果表明,相对于仅考虑频谱感知或资源分配的单层优化算法,该算法可在兼顾公平的前提下使次用户吞吐量得到有效提升。