Three-dimensional Bin Packing Research Articles

Online Three-Dimensional Bin Packing: A DRL Algorithm with the Buffer Zone

Abstract The online 3D bin packing problem(3D-BPP) is widely used in the logistics industry and is of great practical significance for promoting the intelligent transformation of the industry. The heuristic algorithm relies too much on manual experience to formulate more perfect packing rules. In recent years, many scholars solve 3D-BPP via deep reinforcement learning(DRL) algorithms. However, they ignore many skills used in manual packing, one of the most important skill is workers put the item aside if the item is packed improperly. Inspired by this skill, we propose a DRL algorithm with a buffer zone. Firstly, we define the wasted space and the buffer zone. And then, we integrate them into the DRL algorithm framework. Importantly, we compare the bin utilization with di erent thresholds of wasted space and di erent buffer zone sizes. Experimental results show that our algorithm outperforms existing heuristic algorithms and DRL algorithms.

Solving a 3D bin packing problem with stacking constraints

We consider a novel variant of the three-dimensional bin packing problem (3DBPP) arising from a maritime shipping port. Unlike the classical bin packing problem, our 3DBPP requires all items to be stacked vertically during the packing process. To tackle this problem effectively, we divide it into two subproblems: the stack packing problem (SPP) and the two-dimensional bin packing problem (2DBPP). We first formulate the SPP as an integer programming model to minimize the total bottom area of the stacks, which is further solved by a branch-and-price method. Then, in the 2DBPP, to pack all stacks into a minimum number of bins, we follow the left-down most extreme point placement strategy. An encoder–decoder model was developed to optimize the packing sequence and orientation of the stacks simultaneously. Industrial instances from shipping ports were collected and extended. The computational results show that our two-stage algorithm performs well in solving the stacking-constrained 3DBPP.

Optimizing e-commerce warehousing through open dimension management in a three-dimensional bin packing system.

In the field of e-commerce warehousing, maximizing the utilization of packing bins is a fundamental goal for all major logistics enterprises. However, determining the appropriate size of packing bins poses a practical challenge for many logistics companies. Given the limited research on the open-size 3D bin packing problem as well as the high complexity and lengthy computation time of existing models, this study focuses on optimizing multiple-bin sizes within the e-commerce context. Building upon existing research, we propose a hybrid integer programming model, denoted as the three dimensional multiple option dimensional rectangular packing problem (3D-MODRPP), to address the multiple-bin size 3D bin packing problem. Additionally, we leverage well-established hardware and software technologies to propose a 3D bin packing system capable of accommodating multiple bin types with open dimensions. To reduce the complexity of the model and the number of constraints, we introduce a novel assumption method for 0-1 integer variables in the overlap and rotation constraints. By applying this approach, we significantly streamline the computational complexity associated with the model calculations. Furthermore, we refine the dataset by developing a customized version based on the classical Three-Dimensional One-Size Dependent Rectangular Packing Problem (3D-ODRPP) dataset, leading to improved outcomes. Through comprehensive analysis of the research results, our model exhibits remarkable advancements in addressing the strong heterogeneous bin packing problem, the weak heterogeneous bin packing problem, the actual bin packing problem, and the bin packing problem with multiple bin types and open sizes. Specifically, it significantly reduces model complexity and computation time and increases space utilization. The system designed in this study paves the way for practical applications based on the proposed model, providing researchers with broader research prospects and directions to expand the scope of investigation in the field of 3D bin packing. Consequently, this system contributes to solving complex 3D packing problems, reducing space waste, and enhancing transportation efficiency.

Airfreight forwarder’s shipment planning: Shipment consolidation and containerization

This study focuses on an airfreight forwarder's shipment planning problem, while considering shipment consolidation and containerization in the international supply chain. Items belonging to different shipments from supplier's manufacturing warehouses are consolidated and loaded into Unit Loading Devices (ULDs) at outbound logistics hubs and to inbound logistics hubs by air transportation, where items are unloaded from the ULDs and distributed to the corresponding retailers by parcel delivery. A three-dimensional multiple bin size bin packing problem is considered, where items are consolidated and orthogonally loaded into ULDs of heterogeneous irregular shapes, where each item has a required latest allowable delivery time. A mixed integer programming model is formulated for the problem, which aims to determine the optimal route planning and feasible packing scheme for the transported items. This study develops a biased random-key genetic algorithm combining a three-dimensional bin packing heuristic to solve the problem. A two-phase greedy heuristic with a chaotic system is designed for the generation of initial population. Additionally, a catastrophe operator and a self-adaptive neighborhood search are put forward to further improve the performance of the algorithm. A numerical experiment is given to demonstrate the feasibility of formulation and effectiveness of algorithm by comparing with ILOG CPLEX, and managerial insights are provided.

BED-BPP: Benchmarking dataset for robotic bin packing problems

Many algorithms that were developed for solving three-dimensional bin packing problems use generic data for either experiments or evaluation. However, none of these datasets became accepted for benchmarking 3D bin packing algorithms throughout the community. To close this gap, this paper presents the benchmarking dataset for robotic bin packing problems (BED-BPP), which is based on realistic data. We show the variety of the dataset by elaborating an n-gram analysis. Besides, we propose an evaluation function, which contains a stability check that uses rigid body simulation. We demonstrated the application of our dataset on four different approaches, which we integrated in our software environment.

Hybrid approach for solving real-world bin packing problem instances using quantum annealers

Efficient packing of items into bins is a common daily task. Known as Bin Packing Problem, it has been intensively studied in the field of artificial intelligence, thanks to the wide interest from industry and logistics. Since decades, many variants have been proposed, with the three-dimensional Bin Packing Problem as the closest one to real-world use cases. We introduce a hybrid quantum-classical framework for solving real-world three-dimensional Bin Packing Problems (Q4RealBPP), considering different realistic characteristics, such as: (1) package and bin dimensions, (2) overweight restrictions, (3) affinities among item categories and (4) preferences for item ordering. Q4RealBPP permits the solving of real-world oriented instances of 3 dBPP, contemplating restrictions well appreciated by industrial and logistics sectors.

A hybrid biogeography-based optimization algorithm for three-dimensional bin size designing and packing problem

The three-dimensional bin packing problem (3D-BPP) plays a critical role in logistics activities. Prior studies focus on 3D-BPP in cases where bin size is predetermined. However, bin volume utilization can be improved significantly by optimizing bin size. In this study, we propose a novel three-dimensional bin size designing and packing problem (3D-BSDPP) and a hybrid biogeography-based optimization (HBBO) algorithm to address the problem by maximizing bin volume utilization by optimizing the bin size. The HBBO combines a differential evolution algorithm with basic biogeography-based optimization to improve exploration ability, and a novel local search strategy involving three specific local search operators is proposed to accelerate the HBBO convergence. Finally, a novel heuristic packing method is employed to find a high-quality packing solution. The proposed algorithm is evaluated through experiments carried out on a practical bin packing application. The results indicate that the proposed algorithm outperforms existing algorithms in solving the 3D-BSDPP.

An improved Harris Hawks Optimization algorithm for continuous and discrete optimization problems

Harris Hawks Optimization (HHO) is a population-based meta-heuristic optimization algorithm that has been used for the solution of test functions and real-world problems by many researchers. However, HHO has a premature convergence problem. The main motive of the novel approach in this paper is that the performance of an MHA could be improved by simplification and by modifying the way random parameters are determined. The proposed algorithm aims to solve both continuous and discrete optimization problems. HHO is improved in three stages. First, the method to determine the random parameters is modified. Second, the strategy of HHO to produce a new solution is updated. Third, the six-step decision mechanism of HHO is shortened to four. The proposed algorithm is compared to five recently published competitor algorithms by applying to the CEC2019 test functions and a three-dimensional bin packing problem (3D-BPP) dataset with 320 samples. All the algorithms are run on the same computer and the results of 30 independent studies are saved. Minimum, average, and standard deviation values and solution times of CEC2019 functions are used as comparison parameters. For the 3D-BPP, the number of bins and the solution time are used as comparison parameters for in the Wilcoxon test. The proposed algorithm performs better than the selected competitors in terms of its %5 significance level. Moreover, the algorithm proposed in the 3D-BPP data set is the most successful algorithm with its 9745 bins. Besides, the proposed algorithm is also compared to the four most popular algorithms in the literature. The results obtained confirm the validity of the proposed algorithm.

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

This paper proposes a matheuristic algorithm based on a column generation structure for the capacitated vehicle routing problem with three-dimensional loading constraints (3L–CVRP). In the column generation approach, the master problem is responsible for managing the selection of best-set routes. In contrast, the slave problem is responsible for solving a shorter restricted route problem (CSP, Constrained Shortest Path) for generating columns (feasible routes). The CSP is not necessarily solved to optimality. In addition, a greedy randomized adaptive search procedure (GRASP) algorithm is used to verify the packing constraints. The master problem begins with a set of feasible routes obtained through a multi-start randomized constructive algorithm (MSRCA) heuristic for the multi-container loading problem (3D–BPP, three-dimensional bin packing problem). The MSRCA consists of finding valid routes considering the customers' best packing (packing first-route second). The efficiency of the proposed approach has been validated by a set of benchmark instances from the literature. The results show the efficiency of the proposed approach and conclude that the slave problem is too complex and computationally expensive to solve through a MIP.

Multi-objective 3D bin packing problem with load balance and product family concerns

The classical three-dimensional bin packing problem (3D-BPP) orthogonally packs a set of rectangular items with varying dimensions into the minimum number of three-dimensional rectangular bins. While ensuring the minimum number of bins used, the safety of the logistic operations is addressed with the complementary load-balancing objective for which concepts such as orientation and stability are used in the literature though not at the same time. In this study, we extend the load-balanced 3D-BPP by combining both orientation and stability, and introducing a new concept called family unity which encourages packing a family of products (e.g., from the same order and with the same destination) together. Although item related concerns are very common in practice, there are no multi-objective studies in the bin packing literature that includes family unity concept. Therefore, this is the first study that proposes a multi-objective mixed integer programming model for the extended problem to determine the optimal packing plan that minimizes the number of bins used and the deviation of balance from the ideal barycenter while maximizing family unity ratio via a weighted objective function. A numerical example is provided to analyze the performance of the proposed model. Furthermore, a real-life container loading problem is solved and outputs of the study implies the practical advantages of including family unity and load-balance considerations in solving 3D-BPP problems.

Development of a Single Camera Machine Vision System for Automatic 3D Size Detection

The rapid growth of global e-commerce prompts the need of efficient warehouse handling and logistics, forcing manual operations to be replaced with automatic systems. An example of automated solutions is the smart packaging system for boxes which can simulate optimized box arrangements in order to save space. Even though three-dimensional bin packing problem has been studied widely to optimize box arrangement, only a few studies have been done to automatically detect box sizes. Box size detection is important to increase the effectiveness and efficiency of the packaging process as well as providing fast and accurate input for the box arrangement optimizer. Therefore, this paper presents the development of a machine vision system for automatic box size detection in 3D to support a smart packing simulator. The system uses a single camera and a platform covered with square grids prints. The box size detection algorithm was based on the localization of the platform area and it works by applying the bilateral filtering, binary thresholding and morphological image transform for the square grids feature extraction. To measure the box size, the length, width, and height of the boxes were detected by referencing it to the count of the square-grids. The volume of the boxes was further computed from the three-dimensional values obtained. The performance of the algorithm was then evaluated by calculating the error against the true value obtained from the manual measurements. The average accuracy for box size detection was 94.3% and analysis shows that the accuracy of the model was highly dependent on the size of the square grids on the platform. The result shows great potential of using a single camera system for automated 3D box size detection.

A heuristic and GRASP algorithm for three-dimensional multiple bin-size bin packing problem based on the needs of a spare-part company

A heuristic and GRASP algorithm for three-dimensional multiple bin-size bin packing problem based on the needs of a spare-part company

A heuristic and GRASP algorithm for three-dimensional multiple bin-size bin packing problem based on the needs of a spare-part company

A heuristic and GRASP algorithm for three-dimensional multiple bin-size bin packing problem based on the needs of a spare-part company

A Hybrid Chemical Reaction Optimization Algorithm for Solving 3D Packing Problem

This paper combines the chemical reaction optimisation algorithm with the greedy algorithm to solve the three-dimensional bin packing problem (3D-BPP). Traditionally, the 3D-BPP is solved with algorithms based on particle swarm optimisation, genetic algorithm, or simulated annealing algorithm, etc. The chemical reaction optimisation algorithm is proposed in recent years, which has the advantages of traditional simulated annealing algorithm and has a faster convergence speed. After making appropriate adjustments to the chemical reaction optimisation algorithm, the experiment was performed on classic 320 examples. The results show that the proposed algorithm outperforms the existing algorithms such as greedy variable neighbourhood descent (GVND) and biased random key genetic algorithm (BRKGA).

The Pallet Loading Problem: Three-dimensional bin packing with practical constraints

Pallet loading requires the solution of a three-dimensional bin packing problem (3DBPP) with additional requirements. In particular, vertical support and load bearing, which are not enforced in 3DBPP, are essential in practice. In this work, we provide a complete solution approach for pallet loading problems where practical constraints of vertical support, load bearing, planogram sequencing, and weight limits are fully accounted for. Using a layer based column generation approach, we tackle vertical support using second order cone programming, and satisfy load bearing through a graph representation to trace load distribution. Additionally, we use industry data to propose an instance generator that produces realistic items with practical attributes such as support surface, load capacity, weight, and planogram sequence number. Extensive numerical testing reveals the ability of the approach to find high quality solutions for industry size instances in fast computational times.

Three-Dimensional Bin Packing and Mixed-Case Palletization

Despite its wide range of applications, the three-dimensional bin-packing problem is still one of the most difficult optimization problems to solve. Currently, medium- to large-size instances are only solved heuristically and remain out of reach of exact methods. This is particularly true for its practical variant, the mixed-case palletization problem, where item support is needed. This and the lack of a realistic benchmark data set are identified as major research gaps by a recent survey. In this work, we propose a novel formulation and a column-generation solution approach, where the pricing subproblem is a two-dimensional layer-generation problem. Layers are highly desirable in practical packings as they are easily packable and can accommodate important practical constraints such as item support, family groupings, isle friendliness, and load bearing. Being key to the success of the column-generation approach, the pricing subproblem is solved optimally as well as heuristically and is enhanced by using item grouping, item replacement, layer reorganization, and layer spacing. We conduct extensive computational experiments and compare against existing approaches. We also use industrial data to train and propose a realistic data set. The proposed approach outperforms the best-performing algorithm in the literature on most instances and succeeds to solve practical size instances in very reasonable computational times.

A hybrid chaos firefly algorithm for three-dimensional irregular packing problem

<p style='text-indent:20px;'>The packing problem study how to pack multiple objects without overlap. Various exact and approximate algorithms have been developed for two-dimensional regular and irregular packing as well as three-dimensional bin packing. However, few results are reported for three-dimensional irregular packing problems. This paper will develop a method for solving three-dimensional irregular packing problems. A three-grid approximation technique is first introduced to approximate irregular objects. Then, a hybrid heuristic method is developed to place and compact each individual objects where chaos search is embedded into firefly algorithm in order to enhance the algorithm's diversity for optimizing packing sequence and orientations. Results from several computational experiments demonstrate the effectiveness of the hybrid algorithm.

BRKGA/VND Hybrid Algorithm for the Classic Three-dimensional Bin Packing Problem

The classic bin packing problem consists of packing a set of boxes with fixed orientation into the minimum number of bins. In this work we present a variable neighborhood descent (VND) inspired algorithm which improves the state-of-art biased random-key genetic algorithm (BRKGA), proposed in [6], for the three-dimensional bin packing problem. The constructive greedy heuristic method to pack the boxes uses an integer sequence to establish the order of boxes to be packed. The presented BRKGA/VND variant fills the initial and mutant population based on sorted box sequences. The devised hybrid method shows significantly superior average fitness through the generations, therefore, solutions with high quality are found faster. The novel approach is tested with a standard set of 320 instances. The computational experiment demonstrate that BRKGA/VND produces equal or better results compared to other state-of-art algorithms proposed in the literature. The empirical data shows that BRKGA/VND hybrid variant systematically produces high quality solutions at fewer iterations compared to the results attained by BRKGA.

A column generation-based heuristic for the three-dimensional bin packing problem with rotation

This paper addresses a three-dimensional bin packing problem (3D-BPP) with rotation. The aim is finding the best way of packing 3D items into bins to increase the packing factor with the purpose of minimizing the number of bins. No restrictions apply to the orientation of the items, in which case items can be rotated both vertically and horizontally. 3D-BPP is solved by using a column generation (CG) technique-based heuristic. To generate new columns, fast CG is carried out by applying a heuristic pricing method, in which items with most negative reduced cost are sequentially positioned into bins based on an extreme point concept. The CG technique outperforms the best significant techniques in the literature in terms of solution quality. We also provide the new lower bounds for 3D-BPP with no rotation using CG technique.

A MIP-based slicing heuristic for three-dimensional bin packing

The mixed-case palletization problem is a common problem in warehousing and logistics where boxes of rectangular shapes are stacked on top of each other to form pallets. The problem shares common features with three-dimensional bin packing but requires boxes to be adequately supported. We propose a mixed integer programming formulation that maximizes the density of the bottom layers and the compactness of the pallet to ensure stability for top layers. We use a relative-position formulation with slicing that minimizes height, maximizes the fill rate of slices, and pushes boxes towards the vertical axis in order to consolidate fragmented space. Apart from common non-overlap and dimension-related constraints, we explicitly model the fill rates and force lower slices to have an equal or higher density than upper slices. As expected, the formulation could only handle small instances. To tackle larger instances, we embedded the formulation in an iterative approach that packs subsets of boxes sequentially. The approach was found to provide stable pallets and to outperform the branch-and-bound approach of Martello et al. (Oper Res 48(2):256–267, 2000).