Three-dimensional Container Loading Problem Research Articles

Use of heuristic methods for the optimisation of truck loading in a steel company

The correct layout of goods, objects or cargo, in the container's available space is considered a complex task. The study was motivated by the need to implement a solution to optimise container use in a steel industry company in the South of Brazil. This article has contributed to synthesising research on the three-dimensional container loading problem, highlighting classifications, constraints, and algorithms used in its resolution. A framework is presented and may be used as a road map for practical implementation as used in this research. As a practical contribution, this article presents several instances of one actual case application. Results showed reducing of formatting loads processing time in comparison with the traditional company approach.

A differential evolution algorithm with ternary search tree for solving the three-dimensional packing problem

The three-dimensional packing problem, which is a strongly NP-hard problem and extremely difficult to solve in practice, is a typical issue in container loading. The container loading problem (CLP) is a combinatorial optimization problem with complex constraints. Its solution process is complicated, and the amount of computation is large. Although some studies used exact algorithms, they could not obtain the optimal solution in a reasonable time. Therefore, heuristic algorithms and intelligent optimization algorithms have become the preferred choice for solving the three-dimensional container loading problem (3D-CLP). Differential evolution algorithm (DE) is an efficient intelligent optimization algorithm, which has remarkable effect in dealing with optimization problems. In this paper, we propose a novel technique that combines a differential evolution algorithm with a ternary search tree model (TSTDE) to solve the 3D-CLP. TSTDE utilizes the ternary tree model to generate a set of suboptimal solutions as the initial population of DE. The improved differential evolution algorithm is used to search the feasible solution of the problem. In this paper, we used the Bischoff and Ratcliff instances to test the TSTDE algorithm, and the results solving the 3D-CLP were compared with those of other advanced algorithms. The experimental results verified the feasibility and superiority of TSTDE in handling the 3D-CLP.

An efficient method for the three-dimensional container loading problem by forming box sizes

This study focuses on a real-world case that is defined as an extension of the container loading problem (CLP) with weakly heterogeneous types of boxes. A company producing plastic cups wants to increase its efficiency in container loading operations. To solve the problem, a hybrid approach including a static rule to rank orders and integer nonlinear programming (INLP) models is developed. INLP models form box sizes according to the properties of the cups, and determine the position of the boxes in layers while simultaneously minimizing the layer-depth. The presented approach is tested on real-world cases and benchmark data sets. The results show that simultaneously forming boxes and solving the CLP increases the effectiveness of container loading operations.

Packing Boxes into Multiple Containers Using Genetic Algorithm

Container loading problems have been studied extensively in the literature and various analytical, heuristic and metaheuristic methods have been proposed. This paper presents two different variants of a genetic algorithm framework for the three-dimensional container loading problem for optimally loading boxes into multiple containers with constraints. The algorithms are designed so that it is easy to incorporate various constraints found in real life problems. The algorithms are tested on data of standard test cases from literature and are found to compare well with the benchmark algorithms in terms of utilization of containers. This, along with the ability to easily incorporate a wide range of practical constraints, makes them attractive for implementation in real life scenarios.

A heuristic modelling for three-dimensional container loading problem

In this research paper, we present a heuristic modelling of three-dimensional container loading problem (CLP) developed for a port. It considers the problem of loading containers with non-uniform size and presents a heuristic model. The objective of this work is to develop a computational system to prepare a near optimum container loading plans so that there will be maximum utilisation of container space and hence generation of more revenue. Research works reported in the literature mainly deals with in terms of weight restrictions, which is a simpler version of the problem that can be addressed by using dynamic programming method. Lack of completeness and uniqueness in their optimum solutions has led to the present work. In fact, CLP in terms of volume restrictions is a more interesting but difficult problem. This needs specific attention because sometimes volume is an important consideration than weight under the usual precedence constraints. Here we present a computational system of three-dimensional CLP developed for use in any typical port where, with a given number blocks, one can efficiently arrive at the desired solution.

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 Tree Search Algorithm for Solving the Container Loading Problem

This paper presents a tree search algorithm for the three-dimensional container loading problem (3D-CLP). The 3D-CLP is the problem of loading a subset of a given set of rectangular boxes into a rectangular container so that the packing volume is maximized. The method includes two variants: the full-support variant guarantees full support from below for all packed boxes, although this constraint is not taken into account by the nonsupport variant. The guillotine cut constraint is considered by both variants. The method is mainly based on two concepts. On the one hand, the block building approach is generalized. Not only are blocks of identical boxes in the same spatial orientation applied but also blocks of different boxes with small inner gaps. On the other hand, the tree search is carried out in a special fashion called a partition-controlled tree search. This makes the search both efficient and diverse, enabling a sufficient search width as well as a suitable degree of foresight. The approach achieves excellent results for the well-known 3D-CLP instances suggested by Bischoff and Ratcliff [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega 23(4) 377–390] with reasonable computing time.

A Hybrid Metaheuristic Algorithm for the Integrated Vehicle Routing and Three-Dimensional Container-Loading Problem

This paper examines a recently addressed practical variant of the capacitated vehicle routing problem (VRP) called the capacitated vehicle routing problem with 3-D loading constraints (3L-CVRP). This problem considers customer demand to be formed by 3-D rectangular items. Additional loading constraints often encountered in real-life applications of transportation logistics are imposed on the examined problem model. In addition to 3L-CVRP, we also introduce and solve a new practical problem version that was dictated by a transportation logistics company and covers cases in which transported items are manually unloaded from the loading spaces of the vehicles. Both problem versions are solved by a hybrid metaheuristic methodology that combines the strategies of tabu search (TS) and guided local search (GLS). The loading characteristics are tackled by employing a collection of packing heuristics. The proposed algorithm's robustness was tested for both problem versions, solving benchmark instances derived from the literature and new benchmark problems with diverse features in terms of customer set size and transported-item dimensions. It produced fine results, improving most of the best solutions that were previously reported.