基于空间分解的集装箱布局启发式算法及布局空间利用率规律

针对集装箱布局提出了一种利用三叉树结构表达三维矩形物体布局状态空间的方法。通过将布避空间依据分割,每次放入相对于当前布局空间来说是满足特定折最优布局块,将该布局块定位于当前布局空间后部的左下角,来完成不同大小的三维矩形全的布局方案的确定,并给出试验结果。     

一种基于四叉树结构的排料算法

提出了一种利用四叉树结构来描述矩形物体排料过程的算法。为了确保排料布局的合理性，满足工业上的一刀切要求，需采用组合规则和邻接规则来合成矩形块，这样做还可减少废料碎片、降低算法复杂度、提高板材利用率。     

基于动作空间的三维装箱问题的确定性高效率求解算法

三维装箱问题要求将有限个三维矩形物体尽可能多地装入到一个三维矩形箱子中,使得箱子的填充率即体积利用率最大.在求解三维装箱问题的穴度算法的基础之上,进一步做了以下改进:(1)将当前剩余空间中可能放入的每个体积最大的三维矩形虚拟物体所对应的空间定义为动作空间,在动作空间内放入物体并使穴度的定义体现放入物体与动作空间的吻合程度;(2)在物体放入位置的选择上直接体现"金角银边草肚皮"的思想,每一步只选择最靠近箱子边缘的一个动作空间来装载物体;(3)结合捆绑策略,将形状大小相同的物体捆绑为一个较大的矩形块进行放入,对捆绑块形状大小的选择为在不超出动作空间的前提下尽量用物体填满该空间的两至三个维度.实验结果表明,改进后的穴度算法在付出很少的开销代价的情况下显著地提高了箱子的填充率.     

求解VLSI布局问题的启发式算法

在人们现实布局实践经验的启发下。对 VLSI 布局问题提出了一个启发式算法。该算法由定序规则和定位规则组成,定序规则用来确定布局物体放入布局空间的先后顺序,定位规则规定每一布局物体都被当前最优的占角动作放入布局空间。对5个 MCNC 算例的测试结果表明,本文算法与基于 O-tree 表示的算法相比,速度提高15～56倍;对于其中4个算例,面积利用率提高0.95%～5.31%。     

蚁群算法求解复杂集装箱装载问题

针对复杂集装箱装载问题(CLP),应用启发式信息与蚁群算法求解了最优装载方案。首先,建立了复杂集装箱装载问题的数学模型,利用蚁群算法对解空间的强搜索能力、潜在并行性及可扩充性,结合三空间分解策略将布局空间依次分割;然后,装入满足约束条件的最优货物块,完成不同大小三维矩形货物的装载布局。在此基础上,设计了基于空间划分策略的蚁群算法。最后以700件货物装入40尺(12.025m)高柜箱进行计算,结果表明该方法能提高集装箱的空间利用率,同时兼顾了多个装载约束条件,可应用性好。     

三维矩形块布局的序列三元组编码方法

解空间的序列对编码方法是解二维矩形体聚块布局问题的完整且有限(P-admissible)的编码方法.它产生于直观的分划过程(gridding procedure).受二维序列对编码方法的启示,对三维矩形聚块布局问题,也应该存在序列三元组编码方法.然而将直观分划过程直接推广到三维空间是困难的.通过对序列和部分序列的运算和分析,得到了三维矩形块聚块布局的序列三元组编码方法,此编码方法是完整且有限的.     

基于蒙特卡罗方法的矩形布局问题研究

根据蒙特卡罗方法产生的随机步长,控制矩形在布局空间中移动.矩形移动时,自动满足边界约束条件,简化了矩形可行域边界的计算过程.结合定位函数,得到的可行域可用于完成矩形的布局.测试结果表明,使用该方法求解矩形布局问题,布局空间90％以上被矩形占据.     

平面布局的一个拓扑模型：方图

本文提出了平面布局的方图模型。方图表达了矩形物体平面布局中的许多空间关系。一个方图定义了一类具有不同布置物位置坐标值,但却具有相同空间关系的布局方案集。但方图的构连却并不依赖于物体的位置坐标值的确定,这使我们可能把平面布局设计分成两步:①生成方图;②根据方图的结构限制,求布局的具体尺寸。这一策略大大改善了平面布局设计的计算复杂性。本文详尽阐述了方图的许多概念与定义,介绍了计算机自动构造方图的算法,并将方图与已存的空间布局模型作了对比分析。     

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．     

基于遗传算法的不同形状物体布局求解研究

通过对不同形状物体布局特点的分析,依据遗传算法的基本思想,选择通过对不同形状物体布局特点的分析,根据遗传算法的基本思想,选择合适的编码方法、遗传算子和适应性度函数,提出一种基于遗传算法的不同形状物体布局求解算法.该算法可实现对不同形状物体进行布局求解.计算机仿真实验表明,该算法具有收敛速度快,能够在较短时间内获得较佳的布局方案.     

动态吸引子在布局求解中的应用

在研究分析现有布局启发算法的基础上，提出了动态吸引子的概念，并据此建立了动态的定位函数和布局求解算法,分析了定位函数中各参数和坐标点的含义．通过调整定位函数中参数的取值，可得到满足不同条件和要求的优化布局方案．最后通过实例验证了该算法的合理性．     

基于动作空间求解二维矩形Packing 问题的高效算法

对于二维矩形Packing这一典型的NP难度问题,在黄文奇等人提出的拟人型穴度算法的基础上,通过定义动作空间来简化对不同放入动作的评价,使穴度的计算时间明显缩短,从而使算法能够快速地得到空间利用率较高的布局图案.实验测试了Hopper和Turton提出的21个著名的二维矩形Packing问题的实例.改进的算法对其中的每一个实例都得到了空间利用率为100％的最优布局,且在普通PC机上的平均计算时间未超过7分钟.实验结果表明,基于动作空间对拟人型穴度算法所进行的改进是明显而有效的.     

Design of efficient packing system using genetic algorithm based on hyper heuristic approach

In practice the maximum usage of container space arises in many applications which is one of the crucial economical requirements that have a wide impact on good transportation. A huge amount of monetary infrastructure is spent by companies on packing and transportation. This study recommends that there exists a scope for further optimization which if implemented can lead to huge saving. In this paper, we propose a new hyper heuristic approach which automates the design process for packing of two dimensional rectangular blocks. The paper contributes to the literature by introducing a new search technique where genetic algorithm is coupled with the hyper heuristic to get the optimal or sub optimal solution at an acceptable rate. The results obtained show the benefits of hyper-heuristic over traditional one when compared statistically on large benchmark dataset at the 5% level of significance. Improvements on the solution quality with high filling rate up to 99% are observed on benchmark instances.     

求解三维装箱问题的混合模拟退火算法

提出了一个高效求解三维装箱问题(Three Dimensional Container Loading Problem 3D-CLP)的混合模拟退火算法.三维装箱问题要求装载给定箱子集合的一个子集到容器中,使得被装载的箱子总体积最大.文中介绍的混合模拟退火算法基于三个重要算法:(1)复合块生成算法,与传统算法不同的是文中提出的复合块不只包含单一种类的箱子,而是可以在一定的限制条件下包含任意种类的箱子.(2)基础启发式算法,该算法基于块装载,可以按照指定装载序列生成放置方案.(3)模拟退火算法,以复合块生成和基础启发式算法为基础,将装载序列作为可行放置方案的编码,在编码空间中采用模拟退火算法进行搜索以寻找问题的近似最优解.文中采用1500个弱异构和强异构的装箱问题数据对算法进行测试.实验结果表明,混合模拟退火算法的填充率超过了目前已知的优秀算法.     

An efficient deterministic heuristic for two-dimensional rectangular packing

This paper proposes a deterministic heuristic, a best fit algorithm (BFA), for solving the NP-hard two-dimensional rectangular packing problem to maximize the filling rate of a rectangular sheet. There are two stages in this new approach: the constructive stage and the tree search stage. The former aims to rapidly generate an initial solution by employing the concepts of action space and fit degree in evaluating different placements. The latter seeks to further improve the solution and searches for promising placements by a partial tree search procedure. We then compare BFA with other approaches in terms of solution quality and computing time. We carry out computational experiments on two sets of well-known benchmark instances, C21 proposed by Hopper and Turton, and N13 proposed by Burke et al. BFA gained an average filling rate of 100% for the C21 instances within short times, indicating that all the layouts obtained are optimal. To the best of our knowledge, this is the first time that optimal layouts on all the 21 instances were obtained by a deterministic algorithm. As for the N13 instances, to date, researchers have found optimal solutions to the first three instances, whereas BFA solved seven, including the first three, within a reasonable period. An additional work is to adapt BFA to solve a relevant problem, the constrained two-dimensional cutting (or packing) problem (CTDC). Though BFA is not for the CTDC in the original design such that some specific characteristics of CTDC are not considered, the adapted algorithm still performed well on 21 public CTDC instances.     

Exhaustive approaches to 2D rectangular perfect packings

In this paper, we consider the two-dimensional rectangular strip packing problem, in the case where there is a perfect packing; that is, there is no wasted space. One can think of the problem as a jigsaw puzzle with oriented rectangular pieces. Although this comprises a quite special case for strip packing, we have found it useful as a subroutine in related work. We demonstrate a simple pruning approach that makes a branch-and-bound-based exhaustive search extremely effective for problems with less than 30 rectangles.     

A least wasted first heuristic algorithm for the rectangular packing problem

The rectangular packing problem is to pack a number of rectangles into a single large rectangular sheet so as to maximize the total area covered by the rectangles packed. The paper first presents a least wasted first strategy which evaluates the positions used by the rectangles. Then a random local search is introduced to improve the results and a least wasted first heuristic algorithm (LWF) is further developed to find a desirable solution. Twenty-one rectangular-packing instances are tested by the algorithm developed, the experimental results show that the presented algorithm can achieve an optimal solution within reasonable time and is fairly efficient for dealing the rectangular packing problem. LWF still performs well when it is extended to solve zero-waste and non-zero-waste strip packing instances.