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。     

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。     

求解三维装载约束下车辆路径问题的混合禁忌搜索算法

三维装载约束下车辆路径问题是车辆路径问题集合中极为复杂的问题。针对这一问题,提出了三种混合禁忌搜索算法。该算法首先设计了空间处理方式,通过在初始解构造阶段采用不同的装载规则来实现客户货物的装载,然后引入禁忌搜索算法对解空间进行搜索。最后,扩展了Solomon的标准用例对三种算法进行了实验,实现结果显示提出的算法是求解该问题的有效算法,同时其中一种算法相对而言具有一定的优势。     

遗传算法求解复杂集装箱装载问题方法研究

现场集装箱装载问题多为多目标、多约束优化的复杂问题.遗传算法本身的鲁棒性、并行搜索性以及在NP完全问题求解中的广泛应用,表明遗传算法是解决复杂集装箱装载问题的有效途径.探讨了遗传算法在求解这一复杂问题过程中的应用,给出了有效的编码形式和解码运算.算例求解结果显示出很好的效果.     

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。     

求解强异类集装箱装载问题的混合蚁群算法

针对强异类集装箱装载问题,设计了一种混合蚁群算法。算法中搜索空间分为货物摆放的优先序列和货物摆放的状态两部分;引入体积大的货物优先放入的启发式规则;将蚂蚁搜索得到的序列与历史最优序列进行交叉,取三者最优序列作为该蚂蚁的搜索路径;在更新信息素时,采取两种挥发系数更新信息素以避免信息素过快饱和,同时分析了算法的复杂度。通过三个强异类实例的测试,表明算法得到的装载方案有较高的空间利用率。     

求解最大割问题的多启动禁忌搜索算法

为了增强局部搜索算法在求解最大割问题上的寻优能力,提高解质量,提出了一种多启动禁忌搜索（MSTS）算法。算法主要包括两个重要组件:一是用于搜索高质量局部优化解的禁忌搜索算法;二是具有全局搜索能力的重启策略。算法首先通过禁忌搜索组件获取局部优化解;然后应用设计的重启策略重新生成初始解并重启禁忌搜索过程。重启策略基于随机贪心的思想,综合利用了“构造”和“扰动”这两种方法生成新的起始解,来逃离局部最优的陷阱从而找到更高优度的解。采用了国际文献中公认的21个算例作为本算法的测试实验集并进行实算, 并与多个先进算法进行比较,MSTS算法在18个算例上得到最好解值,高于其他对比算法。实验结果表明,MSTS算法具有更强的寻优能力和更高的解质量。     

基于混合遗传算法的多约束集装箱装载问题研究

在考虑集装箱装载货物底置等级、侧放方式、堆码层数等一些实际应用的约束条件下,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,并以此为基础构造了一种混合遗传算法。     

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。     

分布估计算法求解集装箱装载问题

集装箱装载是一个空间优化分解的布局问题,其约束条件多,属于典型的NP完全问题,求解难度大。在考虑实际应用中的约束条件下,使用三空间分割的布局方法对剩余空间进行分解,并采用空间合并原则将闲置空间与可用空间进行合并达到充分利用,并结合分布估计算法（ EDA）求解多约束装箱问题。分布估计算法采用统计学习的方法建立一个描述解分布的概率模型,再对概率模型进行随机采样产生新的种群,如此反复进行,实现种群的进化,最终获取最优解。实验仿真结果表明该算法应用于实际空间规划设计中具有重要的实际意义。     

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.     

A parallel hybrid local search algorithm for the container loading problem

In this contribution, a parallel hybrid local search algorithm for the three‐dimensional container loading problem (CLP) is proposed. First a simulated annealing method for the CLP is developed, which is then combined with an existing tabu search algorithm to form a hybrid metaheuristic. Finally, parallel versions are introduced for these algorithms. The emphasis is on CLP instances with a weakly heterogeneous load. Numerical tests based on the well‐known 700 test instances from Bischoff and Ratcliff are performed, and the outcome is compared with methods from other authors. The results show a high solution quality obtained with reasonable computing time.     

Container loading with multi-drop constraints

In this paper, an algorithm for the container-loading problem (CLP) with multi-drop constraints is presented. When adding multi-drop constraints, we demand that the relevant boxes must be available, without rearranging others, when each drop-off point is reached. To make the solutions feasible in the real world, it is further demanded that all boxes are placed in a feasible manner with respect to load-bearing strength and with proper support from below. This makes it possible to load consignments originating from builder merchants. A heuristic based on a tree search framework is proposed. It uses greedy solutions to evaluate each choice taken. To make the framework more generic, a dynamic breadth is proposed. Based on problem characteristics and the time limit imposed, it will choose the breadth of the tree, making sure that the time is utilised most profitably. The algorithm is tested on new real-world data from a Danish company distributing construction products. For the solutions to these problems to be feasible in a real-world setting, both multi-drop and load-bearing strength constraints are essential. The obtained results show that the proposed model and algorithm are able to solve the new real-world problems in fractions of a second. Furthermore, results obtained on benchmark problems indicate that the algorithm performs comparably with other more specialised methods.     

Intelligent scheduling with tabu search: An application to jobs with linear delay penalties and sequence-dependent setup costs and times

In this article we study thetabu search (TS) method in an application for solving an important class of scheduling problems. Tabu search is characterized by integrating artificial intelligence and optimization principles, with particular emphasis on exploiting flexible memory structures, to yield a highly effective solution procedure. We first discuss the problem of minimizing the sum of the setup costs and linear delay penalties when N jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. A prototype TS method is developed for this problem using the common approach of exchanging the position of two jobs to transform one schedule into another. A more powerful method is then developed that employs insert moves in combination with swap moves to search the solution space. This method and the best parameters found for it during the preliminary experimentation with the prototype procedure are used to obtain solutions to a more complex problem that considers setup times in addition to setup costs. In this case, our procedure succeeded in finding optimal solutions to all problems for which these solutions are known and a better solution to a larger problem for which optimizing procedures exceeded a specified time limit (branch and bound) or reached a memory overflow (branch and bound/dynamic programming) before normal termination. These experiments confirm not only the effectiveness but also the robustness of the TS method, in terms of the solution quality obtained with a common set of parameter choices for two related but different problems.     

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.     

最小赋权支配集的迭代禁忌搜索算法

最小赋权支配集是一个NP困难的组合优化问题,有着广泛的应用背景。提出了一个高效的求解最小赋权支配集的迭代禁忌搜索算法。该算法采用随机贪心构造算法构造初始解,并利用快速的局部禁忌搜索算法寻找局部最优解,通过随机扰动和修复策略来搜索新的区域,以期跳出当前的局部最优解。用顶点数为800到1 000的大规模标准测试例子测试提出的算法。数值实验结果和与现存的启发式算法比较结果表明了算法是有效的。     

Approximate algorithms for the container loading problem

In this paper we develop several algorithms for solving three–dimensional cutting/packing problems. We begin by proposing an adaptation of the approach proposed in Hifi and Ouafi (1997) for solving two–staged unconstrained two–dimensional cutting problems. We show how the algorithm can be polynomially solved for producing a constant approximation ratio. We then extend this algorithm for developing better approximate algorithms. By using hill–climbing strategies, we construct some heuristics which produce a good trade–off between the computational time and the solution quality. The performance of the proposed algorithms is evaluated on different problem instances of the literature, with different sizes and densities (a total of 144 problem instances).     

基于双禁忌对象的并行禁忌搜索算法

禁忌搜索算法是解决组合优化问题的一种主要方法,是克服NP完全问题的一个有效途径。随着计算网格的发展,将禁忌搜索算法引入到这种分布式并行计算环境中,具有广泛的应用价值。提出了一个基于双禁忌对象的禁忌搜索算法,在此算法的基础上,利用并行化分散搜索策略来提高算法的求解精度。实验结果表明该并行禁忌搜索算法性能较高。     

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.