满足货物承载能力约束的集装箱装载问题研究

本文采用基于矩阵的货物空间约束表达形式和货物承载能力约束表达形式以及简单块生成策略,对基于Beam Search算法的集装箱装载算法进行了改进,以使其能够有效进行满足货物承载能力约束的集装箱装载问题的优化计算,实验结果表明了该算法的有效性。     

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.     

集装箱装入问题的研究

集装箱装载问题是一种有广泛应用背景的组合优化问题,它属于NP-hard问题。禁忌搜索算法(TS)是求解组合问题的一种主要方法,有很强的全局搜索能力。集装箱装入属于有多种约束的空间资源优化问题。约束条件多,求解困难。根据同类型货物一次性装载的思想,提出了一种新的基于空间划分的启发式算法。     

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。     

多箱型三维装箱问题及其优化研究

对多箱型三维装箱问题进行了描述,提出了求解该问题的禁忌算法。算法基于自然数编码,设计了货物的摆放规则和序列生成方式,采用三种邻域,利用邻域操作控制集装箱数量限制,采用惩罚函数处理集装箱重量约束和重心约束。介绍了算法的原理,给出了具有代表性算例实验结果并且进行了分析。实验结果表明了提出的禁忌算法对优化多箱型三维装箱问题的有效性。     

混合二元蚁群算法求解集装箱装载问题

集装箱装载问题是一个具有复杂约束条件的组合优化问题,属于NP-hard问题。针对集装箱装载问题的特点,设计了空间三叉树,对可利用空间采用三叉树划分策略,利用二元蚁群算法结合启发式算法进行求解,即先利用二元蚁群算法确定预备装入货物集,再用启发式算法决定货物的装入优先级顺序,并给出了有效的装箱算法。实例结果表明该算法的有效性和实用性。     

求解三维装箱问题的混合遗传模拟退火算法

集装箱装载是货物运输过程中重要的一步,其属于NP-hard问题。为了提高效率,降低成本,提出了以集装箱体积利用率最大化为目标建立三维装载模型,同时考虑体积约束、重量约束、重心约束、方向约束。利用混合遗传、模拟退火与三空间分割启发式装载算法求解模型,算法中融入局部最优解保存策略来避免局部较好解在后续的算法过程中出现适应度降低的情况。通过强异类算例与弱异类算例对算法进行性能测试,并结合具体的货物装载数据,得出三维装载图与目标函数值。结果表明,该算法应用于集装箱装载有着较好的效果。     

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．     

集装箱轻重货物混合平衡装载模型与算法

负载平衡是集装箱装运过程中的基本约束,轻重货物混合装载时较难满足,如何精确量化负载平衡、实现轻重货物混合平衡装载亟待研究。以集装箱轻重货物混合平衡装载问题为研究对象,构造负载平衡函数,综合考虑负载平衡、位置、重量和旋转等约束,建立轻重货物混合平衡装载模型;根据对负载平衡的影响程度,将待装货物分类组成轻重货物单元,在采用评估函数和中心骨架等启发式方法分类处理的基础上,设计轻重货物混合平衡装载算法。3 000个算例表明：所提出的模型和算法能够在保证集装箱容积利用率不低于90%的同时使负载平衡约束满足率达96.07%以上。     

同类货物集装箱装载问题的启发式算法

提出了求解同类货物集装箱装载问题的一种启发式算法.算法中采用了层的思想,集装箱的每个面都可用来构建层.通过对二维布局、层高组合和用来构建层的集装箱面的选择等三个方面的优化求解,得到了具有较高装载率的集装箱装载方案.实例结果表明,该算法是求解同类货物集装箱装载问题的一种行之有效的方法.     

Three-dimensional container loading models with cargo stability and load bearing constraints

Mathematical models for the problem of loading rectangular boxes into containers, trucks or railway cars have been proposed in the literature, however, there is a lack of studies which consider realistic constraints that often arise in practice. In this paper, we present mixed integer linear programming models for the container loading problem that consider the vertical and horizontal stability of the cargo and the load bearing strength of the cargo (including fragility). The models can also be used for loading rectangular boxes on pallets where the boxes do not need to be arranged in horizontal layers on the pallet. A comprehensive performance analysis using optimization software with 100s of randomly generated instances is presented. The computational results validate the models and show that they are able to handle only problems of a moderate size. However, these models might be useful to motivate future research exploring other solution approaches to solve this problem, such as decomposition methods, relaxation methods, heuristics, among others.     

基于应用约束的三维空间的处理和比较

在三维装箱问题中,集装箱问题是一个复杂的组合优化问题,是属于NP-hard问题。提出了六种空间划分和不同规则的空间合并,并将稳定性约束和承载力约束加入其中,通过测试标准数据集去比较应用约束对空间利用率的影响。测试结果显示了承载力约束对不同的空间划分的影响,以及对哪一种空间划分的影响最大,以及在基于稳定性约束和承载力约束的共同作用下,哪一种空间划分的空间利用率最好。同时,与国内外相同研究方向的算法进行了对比,测试结果显示了该算法的性能要高于目前国内外的算法。     

Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier

In this paper, we present heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem arising in a real-world situation. In this problem, customers make requests of goods, which are packed in a sortment of boxes. The objective is to find minimum cost delivery routes for a set of identical vehicles that, departing from a depot, visit all customers only once and return to the depot. Apart of the usual 3D container loading constraints which ensure that the boxes are packed completely inside the vehicles and that the boxes do not overlap each other in each vehicle, the problem also takes into account constraints related to the vertical stability of the cargo and multi-drop situations. The algorithms are based on the combination of classical heuristics from both vehicle routing and container loading literatures, as well as two metaheuristic strategies, and their use in more elaborate procedures. Although these approaches cannot assure optimal solutions for the respective problems, they are relatively simple, fast enough to solve real instances, flexible enough to include other practical considerations, and normally assure relatively good solutions in acceptable computational times in practice. The approaches are also sufficiently generic to be embedded with algorithms other than those considered in this study, as well as they can be easily adapted to consider other practical constraints, such as the load bearing strength of the boxes, time windows and pickups and deliveries. Computational tests were performed with these methods considering instances based on the vehicle routing literature and actual customers’ orders, as well as instances based on a real-world situation of a Brazilian carrier. The results show that the heuristics are able to produce relatively good solutions for real instances with hundreds of customers and thousands of boxes.     

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.     

面向纸板三维装箱问题的剩余空间最优算法

针对瓦楞纸板在装箱过程中遇到的多种实际约束,提出一种基于剩余空间最优和多种实际约束的快速求解算法。该算法先根据纸板的先进后出和组合装载约束,确定纸板的装箱序列,接着将三维装箱问题转换成带高度约束的二维装箱问题,再基于剩余空间最优策略,选择空间的分割方式和纸板的放置方式,并对剩下的空间进行合并和重新分割,从而求解得到纸板装载放置的结果,实现容器空间利用率最高和使用数目最小的目标。通过计算随机算例和实际算例,以及对结果的三维可视化显示,验证该算法能实现多种约束,空间利用率高,运算效率高并具有有效性和实用性。     

A NLP approach for evaluating storey-buckling strengths of steel frames under variable loading

The problem of determining elastic buckling strengths for unbraced steel frames under variable loading is investigated in this paper. Whereas the pattern of applied loads is specified prior to stability analysis of a frame under proportional loading, load patterns are not predefined in variable loading. The conventional methods for evaluating the stability strength of unbraced frames under proportional loading are not applicable for variable loading, since the load pattern is unknown. Taking into account the concept of storey-based buckling, the problem of frame stability under variable loading is presented as a pair of minimization and maximization problems subject to stability constraints, which are solved by a nonlinear programming (NLP) method. The proposed variable loading approach takes into account the variability of applied loads during the life span of the structure, and as such, provides accurate evaluation of elastic frame-buckling strengths.     

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.     

电推卫星方圆过渡结构轻量化设计

讨论在考虑强度约束和动力学约束的情况下,全电推进卫星的方圆主承力过渡结构的轻量化设计.利用三维拓扑优化技术对方圆过渡结构进行优化设计,确定方圆过渡结构的传力路径,并据此进行创新构型设计.对创新构型进行强度及动力学分析,验证其在强度性能、动力学性能上的优越性.