具有承载能力约束的集装箱装入问题的求解方法

对有承载能力约束的三维集装箱装入问题进行了描述,定义了货物承载约束的表示形式,并在全局寻优能力很强的集装箱装入的禁忌搜索算法中加入承载能力的计算和检查方法,设计了相关的处理策略.在优化空间利用率的同时减少或杜绝货物损坏现象的发生.实验结果表明,该算法对有承载能力约束的三维集装箱装入问题的有效性和实用性.     

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.     

集装箱装载问题的一种DNA遗传算法

三维集装箱装载是一个复杂的组合优化问题,约束条件多,属于NP完全问题,求解难度大.在考虑方向性约束和稳定性约束的情况下,提出了一种DNA遗传算法（DNA-GA）,给出了有效的编码和解码方法。实例计算结果表明,利用DNA-GA解决装箱问题是行之有效的一种方法,对推广DNA计算在求解NP难解问题中的应用具有一定的意义。     

Multi-objective multi-population biased random-key genetic algorithm for the 3-D container loading problem

The container loading problem (CLP) has important industrial and commercial application for global logistics and supply chain. Many algorithms have been proposed for solving the 2D/3D container loading problem, yet most of them consider single objective optimization. In practice, container loading involves optimizing a number of objectives. This study aims to develop a multi-objective multi-population biased random-key genetic algorithm for the three-dimensional single container loading problem. In particular, the proposed genetic algorithm applied multi-population strategy and fuzzy logic controller (FLC) to improve efficiency and effectiveness. Indeed, the proposed approach maximizes the container space utilization and the value of total loaded boxes by employing Pareto approach and adaptive weights approach. Numerical experiments are designed to compare the results between the proposed approach and existing approaches in hard and weak heterogeneous cases to estimate the validity of this approach. The results have shown practical viability of this approach. This study concludes with discussions of contributions and future research directions.     

A hybrid approach for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a recently practical combinatorial problem named Three-Dimensional Loading Capacitated Vehicle Routing Problem, which combines three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires a combinatorial optimization of a feasible loading and successive routing of vehicles to satisfy customer demands, where all vehicles must start and finish at a central depot. The goal of this combinatorial problem is to minimize the total transportation cost while serving customers. Despite its clearly practical significance in the real world distribution management, for its high combinatorial complexity, published papers on this problem in literature are very limited.     

A beam search approach to the container loading problem

The single container loading problem is a three-dimensional packing problem in which a container has to be filled with a set of boxes. The objective is to maximize the space utilization of the container. This problem has wide applications in the logistics industry. In this work, a new constructive approach to this problem is introduced. The approach uses a beam search strategy. This strategy can be viewed as a variant of the branch-and-bound search that only expands the most promising nodes at each level of the search tree. The approach is compared with state-of-the-art algorithms using 16 well-known sets of benchmark instances. Results show that the new approach outperforms all the others for each set of instances.     

A caving degree based flake arrangement approach for the container loading problem

A caving degree based flake arrangement (CDFA) approach for the NP-hard container loading problem is presented in this paper. Based on the caving degree approach, CDFA binds items in the same size into a larger flake whose binding number is 1 in one of its three dimensions, and then it tries to pack the flake into a corner nearest to the eight vertices of the container. Then, caving degree is redefined to evaluate different placements of flakes, such that an action is selected whose packing flake is as compact and close as possible with other flakes already in (the six surfaces of the container can be regarded as six special flakes). CDFA is extensively tested over two sets of famous benchmarks: 15 LN instances and 1500 BR instances. Experimental results show the high performance of this new approach. Especially for the LN set, CDFA improved current highest volume utilization by 1.3% and 0.5% for two difficult instances LN2 and LN6 respectively; at the same time it got optimal layouts for the other 13 instances, equalling current best records. This breaks current best record created and held by Bortfeldt and Gehring since 1998. Besides, CDFA achieved the second highest average volume utilization among several top efficient algorithms for the BR set.     

A hybrid differential evolution algorithm for multiple container loading problem with heterogeneous containers

We consider a multiple container loading problem, commonly known as the three-dimensional bin packing problem (3D-BPP), which deals with maximizing container space utilization while the containers available for packing are heterogeneous, i.e., varying in size. The problem has wide applications in cargo transportation, warehouse management, medical packaging, and so on. We develop a differential evolution (DE) algorithm hybridized with a novel packing heuristic strategy, best-match-first (BMF), which generates a compact packing solution based on a given box packing sequence and a container loading sequence. The effectiveness of the proposed algorithm is evaluated on a set of industrial instances and randomly generated instances. The results show that the proposed algorithm outperforms existing solution approaches in terms of solution quality.     

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).     

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 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.     

LP-based bounds for the container and multi-container loading problem

New relaxations are developed in this paper for problems of optimal packing of small (rectangular-shaped) pieces within one or several larger containers. Based on these relaxations tighter bounds for the Container Loading Problem (CLP) and the Multi-Container Loading Problem (MCLP) are obtained.
The new relaxations for the CLP and MCLP lead to linear programming problems. A corresponding solution approach is discussed which is based on a column generation technique. Results of computational tests are also given.     

Some experiments with a simple tabu search algorithm for the manufacturer's pallet loading problem

The manufacturer's pallet loading problem consists in arranging, orthogonally and without overlapping, the maximum number of boxes with dimensions (l,w) or (w,l) onto a rectangular pallet with dimensions (L,W). This problem has been successfully handled by block heuristics, which generate loading patterns composed by one or more blocks where the boxes have the same orientation. A common feature of such methods is that the solutions provided are limited to the so-called first order non-guillotine patterns. In this paper we propose an approach based on the incorporation of simple tabu search (without longer-term memory structures) in block heuristics. Starting from an initial loading pattern, the algorithm performs moves that increase the size of selected blocks in the current pattern; as a result, other blocks are decreased, eliminated or created. Computational results indicate that the approach is capable of generating superior order optimal patterns for difficult instances reported in the literature.     

A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints

The capacitated vehicle routing problem with three-dimensional loading constraints combines capacitated vehicle routing and three-dimensional loading with additional packing constraints concerning, for example, unloading operations. An efficient hybrid algorithm including a tabu search algorithm for routing and a tree search algorithm for loading is introduced. Computational results are presented for all publicly available test instances. Most of the best solutions previously reported in literature have been improved while the computational effort is drastically reduced compared to other methods.     

An iterated construction approach with dynamic prioritization for solving the container loading problems

This paper addresses the single and multiple container loading problems, which forms the core engine of a warehouse management system we are contracted to implement for a Hong Kong logistics company. We propose to use dynamic prioritization to handle the awkward box types, whereas the box type with a higher priority is packed onto lower surfaces of the container for the single container case, or packed in earlier containers for the multiple container case. The solution found in one iteration of the algorithm is analyzed, and the priorities are updated and used in the next iteration. This approach provides very competitive results using standard benchmark data sets as compared with other methods. It helps to reduce the difficulty in system implementation and maintenance, because the algorithm is easy to understand for practitioners in the local industry, and it is applicable for both the single and multiple container loading problems at the same time. In addition, we find the existing test data for the multiple container loading problem to be deficient and supplement them by generating new test data consisting of 2800 test cases. Last but not least, our algorithm has been packaged into a software component with full graphical user interface and integrated into a warehouse management system for daily operations.     

考虑集装箱簇边装边卸的港口集卡调度模型求解

文章在集装箱装卸作业问题中,以集装箱簇为作业单位,分两阶段分析集装箱在岸桥集卡间的调度方案,以集卡空驶率最小与移动距离最短为目标,建立了整数规划模型。针对上述模型,文章利用启发式算法与自适应遗传算法对问题进行分析求解。最后通过配置不同集卡数量,将其移动总距离以及空驶效率进行比较,并与禁忌搜索算法相对比。试验结果表明,启发式自适应遗传算法的计算结果在空驶率以及移动总距离最小问题上有更优的解决方案。     

On the concept of density control and its application to a hybrid optimization framework: Investigation into cutting problems

The Generate-and-Solve (GS) methodology is a hybrid approach that combines a metaheuristic component with an exact solver. GS has been recently introduced in the literature in order to solve cutting and packing problems, showing promising results. The GS framework includes a metaheuristic engine (e.g., a genetic algorithm) that works as a generator of reduced instances of the original optimization problem, which are, in turn, formulated as mathematical programming problems and solved by an integer programming solver. In this paper, we present an extended version of GS, focusing primarily on the concept of a new Density Control Operator (DCO). The role of this operator is to adaptively control the dimension of the reduced instances in such a way as to allow a much steadier progress towards a better solution, thereby avoiding premature convergence. In order to assess the potentials of this novel version of the GS methodology, we conducted computational experiments on a set of difficult benchmark instances of the constrained non-guillotine cutting problem. The results achieved are quantitatively and qualitatively discussed in terms of effectiveness and efficiency, showing that the proposed variant of the GS hybridization framework is highly suitable when effectiveness is a major requirement.     

考虑动态平衡装卸的点对点取送货车辆路径优化

针对点对点取送货车辆路径优化问题,引入动态平衡、后进先出、三维装载等约束,以总路径最短为优化目标,构建多车多客户应用场景下的动态平衡装卸点对点取送货车辆路径优化模型;基于研究问题的特征,采用启发式插入法确定路径初始方案,设计节点交换和重新定位算子,构造路径邻域方案,并将动态平衡装卸纳入路径迭代过程,运用多重指标定序策略和三分空间策略,设计客户动态平衡装卸检算算法,并提出基于禁忌搜索的点对点取送货车辆路径优化算法,制订多车多客户取送货车辆路径方案的同时编制动态平衡装载方案。最后,通过标准算例验证方法的有效性,计算表明：所提方法能高效解决带动态平衡约束的点对点取送货车辆路径优化问题;在多车多客户应用场景下具有更强的寻优能力,求解效率更高。     

Ship routing and scheduling with cargo coupling and synchronization constraints

The purpose of this paper is to introduce and solve a planning problem faced by shipping companies operating in a special segment of tramp shipping called project shipping. Project shipping differs from other more traditional tramp segments because the cargoes are more unique and usually transported on a one-time basis. The special nature of the cargoes complicates the routing and scheduling. For instance, a cargo can be part of a process facility, but the shipping company cannot transport it unless other parts of the same facility are transported as well, even though these parts may have different origins. This creates an additional coupling constraint between the cargoes. In addition, the different parts might require synchronized delivery within some time window. We present a mathematical formulation for the problem and propose three alternative solution methods based on path flow formulations and a priori column generation. In one of the solution methods this is combined with a scheme for relaxing the complicating synchronization constraints and reintroducing them dynamically when needed. Computational results show that we are able to find optimal solutions to problems based on data obtained from a shipping company.