Three-dimensional Bin Packing Problem Research Articles

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.

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 Module Layout Method of Emergency Rescue Equipment Box Based on Layer Space

Module layout of emergency rescue equipment box is a special three-dimensional (3D) bin-packing problem, whose mathematical description is that under the condition of fixed capacity, the corresponding value of equipment in the box is maximized. Through the analysis of the characteristics of the emergency rescue equipment box, three evaluation indexes, including the average height of centroid, the average distance of access and the functional distance of equipment, were proposed first. In order to obtain a more ideal 3D packing scheme, a module layout method based on layer space using genetic algorithm was also proposed. These equipments to be arranged were encoded in decimal. According to the fitness function and the objective function, the selection, crossover and mutation operations of decimal sequence were conducted. After the iteration, the value of objective function gradually approached to the optimal solution. To evaluate the performance of the proposed method, some simulations under the MATLAB were performed. Finally, the experimental results show that the proposed method can achieve a better optimization effect, proving its effectiveness and feasibility.

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 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.

Vehicle routing problem solution considering minimising fuel consumption

Recently, logistics is not only playing more and more important role in social and economic development, but also caused serious energy consumption and environment pollution problems. Reasonable vehicle route planning is viewed as an important solution to reduce logistics enterprises’ operation costs as well as alleviate the energy and environmental problems. This study aims to propose a solution to time-dependent vehicle routing problem with time windows (TDVRPTW) considering minimising fuel consumption. First, a mathematical TDVRPTW model with the minimum fuel consumption as an objective function is established, in which the three-dimensional bin-packing problem is considered as a sub-problem and the alternative stop point concept is newly proposed to reduce the possible detouring distance and fuel consumption of logistic vehicle. Then, an ant colony algorithm is applied to solve the problem, and the departure time optimisation is introduced to further improve the obtained results. Finally, the proposed approach is evaluated with the real road network and traffic data of Beijing. The results show that the method introduced in this study outperforms the existing approaches in reducing fuel consumption as well as route length.

Optimization of a robot-served cart capacity using the three-dimensional single bin packing problem

Given a set of rectangular-shaped items such as dishes, cups, saucers, or forks and a rectangular tray of a cart, the three-dimensional single bin packing problem (3D-BPP) involves orthogonally packing a subset of the items within the tray. If the value of an item is given by its volume, the objective is to maximize the covered volume of the tray. Thus, this paper aims to optimize the transport capacity of a serving robot carrying a cart. This experiment, the first of its type, proves the feasibility of this endeavor efficiently.

An effective tabu search approach with improved loading algorithms for the 3L-CVRP

In this paper, we consider the Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines the routing of a fleet of vehicles and the loading of three-dimensional shaped goods into the vehicles while minimizing the total travel distance incurred. Apparently, 3L-CVRP is a combination of capacitated vehicle routing and three-dimensional bin packing problem and thus of high complexity. Different from most of previous works, we propose an innovative approach, called improved least waste heuristic for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The good performance in terms of the solution quality and computational efficiency of our approach is shown through the numerical experiments on the benchmark instances from literature.