求解三维装箱问题的多层启发式搜索算法

文中提出了一个高效求解三维装箱问题的多层启发式搜索算法.该算法基于块装载的思想,按照块选择算法确定每个阶段采用的块,然后以一种固定的装载方式装载块,直到无法继续装载.文中的主要贡献在于发展了一个有效的复合块生成算法,特别的,提出了基于多层搜索的块选择算法,该算法用多层搜索来评价可行块,然后选择最合适的块进行装载.对1500个三维装箱问题测试数据的计算结果表明,提出的算法几乎在所有测试数据上的填充率都超过了目前已知的优秀算法.     

基于多元优化算法的三维装箱问题的研究

用多元优化算法（Multi-variant optimization algorithm,MOA）实现三维装箱问题的求解.算法通过随机放置和局部调整从而逐步逼近最优解.随机放置是将随机选择的几个箱子装入容器中;局部调整是根据目标函数值对随机放置容器的箱子序列作局部调整优化;通过递推的随机放置和局部调整优化,目标函数值逐步逼近最优值,从而获得一个较为理想的三维装箱方案.算法通过对BR1~BR10共1000组三维装箱问题测试实例的测试仿真,得到理想的装箱效果,说明用多元优化算法实现三维装箱问题的有效性和可行性.     

面向梯形箱子的三维装箱问题算法研究

针对梯形箱子的三维装箱问题,提出了一种基于空间分割的构造性启发式算法,根据梯形箱子三维装箱问题的特点,设计了相应的空间分割策略、空间合并策略与空间重组策略,在此基础上加入遗传算法,提高算法局部与全局搜索能力。实验结果表明,该算法能有效处理梯形箱子三维装箱问题。     

求解三维装箱问题的多层树搜索算法

提出了一种求解三维装箱问题的多层树搜索算法, 该算法采用箱子–片–条–层–实体的顺序生成装载方案, 装载方案由实体表示. 该算法由3层搜索树构成. 第1层为三叉树, 每个树节点的3个分叉分别对应向实体中填入XY面平行层、XZ面平行层、YZ面平行层; 第2层为二叉树, 每个树节点的两个分叉分别对应向层内装载两个相互垂直的最优条; 第3层为四叉树, 用于将同种的多个箱子生成片. 在同时满足摆放方向约束和完全支撑约束的前提下, 该算法求解BR12~BR15得到的填充率高于现有装箱算法.     

三维装箱问题的组合启发式算法

通过组合拟人启发式和模拟退火算法,提出了三维装箱问题的组合启发式算法.拟人启发式算法的主要思想来源于日常砌墙中的策略.利用找点法以及水平和垂直参考线规则来控制装填过程.用模拟退火算法改进拟人启发式.经过一些数据的测试,实验结果表明,该算法能够同文献中的优秀算法竞争.     

基于装箱树算法求解集装箱装载问题的研究

研究了把同种货物装入一个集装箱内，使箱子内的空间利用率为最大的集装箱装载问题．首先，运用启发式算法,充分考虑了箱子和货物的方位、剩余空间等问题．然后，通过主空间装填、空间分层、剩余空间优化等建立一个装箱树．最后，用Java程序完成装箱树算法，并实现集装箱装载问题的求解．用实例验证了算法的可行性，能够投入实际应用．     

多约束三维装箱问题的研究综述

至今三维装箱已经诞生出了很多优秀的研究结果,这其中包含有启发式算法,遗传算法,蚁群算法,以及模拟退火算法等解决方法。近几年来随着物流行业的飞速发展,成本控制在物流行业中显得尤为重要,因此,针对三维装箱这一类典型NP-complete问题有了更高的要求。在此,对三位装箱近几年来几种典型的研究算法进行了相应的详细介绍,并通过对各种算法进行比对分析,总结了多约束三维装箱过程现阶段所存在的一些问题,最后展望了该问题的发展方向。     

有卸货顺序约束的集装箱装载问题及算法研究

对有卸货顺序约束的三维集装箱问题进行了描述.基于禁忌规则,采用了求解该问题的模拟退火算法,设计了货物的摆放规则和序列生成方式.采用3种邻域,根据邻域的不同,构造了2种禁忌表.根据问题的特点,在模拟退火算法抽样过程中加入了禁忌规则.介绍了算法的原理,给出了具有代表性算例试验结果并且进行了分析.试验结果表明,提出的混合算法对有卸货顺序约束的集装箱三维装载问题的有效性.     

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.     

一种带脆度的尺寸可变装箱问题

作为经典装箱问题的扩展,尺寸可变装箱问题在现实生活中有着极高的应用背景。分析了尺寸可变装箱问题在解决货物装载运输问题上的不足,由此提出了一种带脆度的尺寸可变装箱问题。除了经典装箱问题中物品体积和箱子容量这两个参数,还引入了物品类型和箱子脆度等参数,给出了相关的数学模型。在经典的FFD（First Fit Decreasing）算法的基础上进行了推广,提出了新的启发式算法NFFD,它对箱子的特性进行了预处理,再进行装箱。分析了该算法的复杂性。对NFD、FFD和NFFD算法进行了数值模拟实验,实验结果表明,在相关参数符合均匀分布的条件下,NFFD算法的效果是最好的。     

A tree search algorithm for the container loading problem

This paper presents a binary tree search algorithm for the three dimensional container loading problem (3D-CLP). The 3D-CLP is about how to load a subset of a given set of rectangular boxes into a rectangular container, such that the packing volume is maximized. In this algorithm, all the boxes are grouped into strips and layers while three constraints, i.e., full support constraint, orientation constraint and guillotine cutting constraint are satisfied. A binary tree is created where each tree node denotes a container loading plan. For a non-root each node, the layer set of its left (or right) child is obtained by inserting a directed layer into its layer set. A directed layer is parallel (or perpendicular) to the left side of the container. Each leaf node denotes a complete container loading plan. The solution is the layer set whose total volume of the boxes is the greatest among all tree nodes. The proposed algorithm achieves good results for the well-known 3D-CLP instances suggested by Bischoff and Ratcliff with reasonable computing time.     

一种求解集装箱装载问题的启发式算法

所谓集装箱装载问题,就是将若干大小不同的长方体盒子装进一个大小已知的长方体容器,其目标是最大化容器的积裁率.对这一问题,国内外学者利用不同的哲学思想,提出了诸如遗传算法、模拟退火算法等求解算法.本文提出一种求解此问题的基于最大穴度优先原则的启发式算法.算法中使用了两个重要的策略:最大穴度原则和最小边度原则.用一些公开的算例对算法性能进行了实算测试,测试结果表明:算法所得结果的容器积载率高,是求解集装箱装载问题的有效算法.     

A heuristic block-loading algorithm based on multi-layer search for the container loading problem

This paper presents an efficient heuristic block-loading algorithm based on multi-layer search for the three-dimensional container loading problem. First, a basic heuristic block-loading algorithm is introduced. This algorithm loads one block, determined by a block selecting algorithm, in one packing phase, according to a fixed strategy, until no blocks are available. Second, the concept of composite block is introduced, the difference between traditional block and composite block being that composite block can contain multiple types of boxes in one block under some restrictions. Third, based on the depth-first search algorithm, a multi-layer search algorithm is developed for determining the selected block in each packing phase, and making this result closer to the optimal solution. Computational results on a classic data set show that the proposed algorithm outperforms the best known algorithm in almost all the test data.     

A parallel multi-population biased random-key genetic algorithm for a container loading problem

This paper presents a multi-population biased random-key genetic algorithm (BRKGA) for the single container loading problem (3D-CLP) where several rectangular boxes of different sizes are loaded into a single rectangular container. The approach uses a maximal-space representation to manage the free spaces in the container. The proposed algorithm hybridizes a novel placement procedure with a multi-population genetic algorithm based on random keys. The BRKGA is used to evolve the order in which the box types are loaded into the container and the corresponding type of layer used in the placement procedure. A heuristic is used to determine the maximal space where each box is placed. A novel procedure is developed for joining free spaces in the case where full support from below is required. The approach is extensively tested on the complete set of test problem instances of Bischoff and Ratcliff [1] and Davies and Bischoff [2] and is compared with 13 other approaches. The test set consists of 1500 instances from weakly to strongly heterogeneous cargo. The computational experiments demonstrate that not only the approach performs very well in all types of instance classes but also it obtains the best overall results when compared with other approaches published in the literature.     

A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem

The rectangle knapsack packing problem is to pack a number of rectangles into a larger stock sheet such that the total value of packed rectangles is maximized. The paper first presents a fitness strategy, which is used to determine which rectangle is to be first packed into a given position. Based on this fitness strategy, a constructive heuristic algorithm is developed to generate a solution, i.e. a given sequence of rectangles for packing. Then, a greedy strategy is used to search a better solution. At last, a simulated annealing algorithm is introduced to jump out of the local optimal trap of the greedy strategy, to find a further improved solution. Computational results on 221 rectangular packing instances show that the presented algorithm outperforms some previous algorithms on average.     

一种基于蜜蜂进化选择算子的布局遗传算法

三维矩形布局问题属于NP 难问题,对于三维矩形布局问题的求解大多依赖于各 种启发式算法。该文以布局物体体积递减为定序规则,结合布局物体在布局空间中的几何可行 域,以吸引子法为定位规则,利用蜜蜂进化型遗传算法优化吸引子函数中的参数来求解三维矩 形布局问题(BEGA),得到新型布局遗传算法。最后对不同的算例进行了计算,并与以标准比 例选择作为选择算子的传统布局遗传算法(SPGA)等对比证明了该算法的有效性。     

A novel hybrid tabu search approach to container loading

The container loading problem, which is significant for a number of industrial sectors, aims to obtain a high space utilisation in the container while satisfying practical constraints. This paper presents a novel hybrid tabu search approach to the container loading problem. A loading heuristic is devised to incorporate heuristic strategies with a handling method for remaining spaces to generate optimal loading arrangements of boxes with stability considered. The tabu search technique, which covers the encoding, evaluation criteria and configuration of neighbourhood and candidate solutions, is used to improve the performance of the loading heuristic. Experimental results with benchmark data show that the hybrid approach provides a better space utilisation than the published approaches under the condition of all loaded boxes with one hundred percent support from below. Moreover, it is shown that the hybrid tabu search can solve problems with the constraints of weight limit and weight distribution with real world data.     

An AND/OR-graph Approach to the Container Loading Problem

The container loading problem consists of packing boxes of various sizes into available containers in such a way as to optimize an objective function. In this paper we deal with the special case where there is just one available container and the objective is to maximize the total volume (or the total utility value, supposing that each box has a utility value) of the loaded boxes. We firstly present three heuristic solution methods for the unconstrained problem. Two of them solve the original three-dimensional problem by layers and by stacks reducing it into several problems with lower dimensions. The third one consists of representing possible loading patterns as complete paths in an AND/OR-graph. Bounds and heuristics are proposed in order to reduce the solution space. A proper heuristic is also given to treat the constrained problem by using the AND/OR-graph approach. Moreover, computational results are presented by solving a number of examples.     

正三角形容器内等圆Packing问题的启发式算法

等圆Packing问题研究如何将n个单位半径的圆形物体互不嵌入地置入一个边长尽量小的正三角形容器内,作为一类经典的NP难度问题,其有着重要的理论价值和广泛的应用背景.模拟退火算法是一种随机的全局寻优算法,通过将启发式格局更新策略与基于梯度法的局部搜索策略融入模拟退火算法,并与二分搜索相结合,提出一种求解正三角形容器内等圆Packing问题的启发式算法.该算法将启发式格局更新策略用来产生新格局和跳坑,用梯度法搜索新产生格局附近能量更低的格局,并用二分搜索得到正三角形容器的最小边长.对41个算例进行测试的实验结果表明,文中算法改进了其中38个实例的目前最优结果,是求解正三角形容器内等圆Packing问题的一种有效算法.     

An efficient heuristic algorithm for arbitrary shaped rectilinear block packing problem

Arbitrary shaped rectilinear block packing problem is a problem of packing a series of rectilinear blocks into a larger rectangular container, where arbitrary shaped rectilinear block is a polygonal block whose interior angle is either 90° or 270°. This problem involves many industrial applications, such as VLSI design, timber cutting, textile industry and layout of newspaper. Many algorithms based on different strategies have been presented to solve it. In this paper, we proposed an efficient heuristic algorithm which is based on principles of corner-occupying action and caving degree describing the quality of packing action. The proposed algorithm is tested on six instances from literatures and the results are rather satisfying. The computational results demonstrate that the proposed algorithm is rather efficient for solving the arbitrary shaped rectilinear block packing problem.