2D Bin Packing Research Articles

Integrating Heuristic Methods with Deep Reinforcement Learning for Online 3D Bin-Packing Optimization.

This study proposes a method named Hybrid Heuristic Proximal Policy Optimization (HHPPO) to implement online 3D bin-packing tasks. Some heuristic algorithms for bin-packing and the Proximal Policy Optimization (PPO) algorithm of deep reinforcement learning are integrated to implement this method. In the heuristic algorithms for bin-packing, an extreme point priority sorting method is proposed to sort the generated extreme points according to their waste spaces to improve space utilization. In addition, a 3D grid representation of the space status of the container is used, and some partial support constraints are proposed to increase the possibilities for stacking objects and enhance overall space utilization. In the PPO algorithm, some heuristic algorithms are integrated, and the reward function and the action space of the policy network are designed so that the proposed method can effectively complete the online 3D bin-packing task. Some experimental results illustrate that the proposed method has good results in achieving online 3D bin-packing tasks in some simulation environments. In addition, an environment with image vision is constructed to show that the proposed method indeed enables an actual robot manipulator to successfully and effectively complete the bin-packing task in a real environment.

Rapid prediction for the transient dispersion of leaked airborne pollutant in urban environment based on graph neural networks

Rapidly predicting airborne pollutant dispersion in urban is vital for ventilation design and evacuation planning. Computational fluid dynamics (CFD) simulations are commonly used to provide accurate predictions, but the computational cost is too high. Although graph neural networks (GNNs) provide fast predictions of flow fields by manipulating unstructured mesh on GPU, they suffer from high memory usage and accuracy decreases when applied to large-scale urban scenes. Moreover, it is difficult for GNNs to learn the coupled relationship between wind field and pollutant concentration field. We propose a multi-objective GNN model as CFD surrogate to rapidly predict the transient dispersion of airborne pollutant under the influence of complex wind field patterns in urban environment. Based on random urban layouts generated by a 2D bin packing algorithm, we employ a validated CFD model to construct a sample dataset of wind fields and concentration fields. We leverage graph pooling and multi-scale feature fusion to improve prediction accuracy, and subgraph partitioning of both wind field and concentration field to reduce GPU memory usage. The results show that our GNN model at its best runs 1–2 orders of magnitude faster than CFD simulation with accuracy evaluation metrics R2=0.92, and achieves 70 % GPU memory reduction.

PAAD: Panelization algorithm for architectural designs.

Due to the competitive nature of the construction industry, the efficiency of requirement analysis is important in enhancing client satisfaction and a company's reputation. For example, determining the optimal configuration of panels (generally called panelization) that form the structure of a building is one aspect of cost estimation. However, existing methods typically rely on rule-based approaches that may lead to suboptimal material usage, particularly in complex designs featuring angled walls and openings. Such inefficiency can increase costs and environmental impact due to unnecessary material waste. To address these challenges, this research proposes a Panelization Algorithm for Architectural Designs, referred to as PAAD, which utilizes a genetic evolutionary strategy built on the 2D bin packing problem. This method is designed to balance between strict adherence to manufacturing constraints and the objective of optimizing material usage. PAAD starts with multiple potential solutions within the predefined problem space, facilitating dynamic exploration of panel configurations. It approaches structural rules as flexible constraints, making necessary corrections in post-processing, and through iterative developments, the algorithm refines panel sets to minimize material use. The methodology is validated through an analysis against an industry implementation and expert-derived solutions, highlighting PAAD's ability to surpass existing results and reduce the need for manual corrections. Additionally, to motivate future research, a synthetic data generator, the architectural drawing encodings used, and a preliminary interface are also introduced. This not only highlights the algorithm's practical applicability but also encourages its use in real-world scenarios.

Optimizing Container Fill Rates for the Textile and Garment Industry Using a 3D Bin Packing Approach

The scarcity of empty containers presents a significant logistical challenge globally. To address this issue, this study proposes the application of the optimal box arrangement in a container with a 3D bin packing problem to enhance fill rates and accommodate the complex packing criteria of the textile and garment industry. The study’s objective is to optimize box stacking into containers by considering various factors such as multiple product types, diverse box sizes, varying container sizes, and prioritizing stacking according to purchase orders (PO). In tackling the NP-hard problem with the added constraint of PO-based stacking, this study advocates employing a genetic algorithm combined with a wall-building algorithm to address practical challenges. The genetic algorithm demonstrates optimal efficacy in solving large-scale optimization problems within specified timeframes, yielding high-quality results. In addition, normalization methods are applied to convert box sizes to pallet sizes, expediting problem-solving and facilitating the selection of appropriate container sizes, namely 20- or 40-feet. The research findings indicate that the proposed method achieved a container fill rate of up to 91.67% and minimized the number of containers used. Doi: 10.28991/HIJ-2024-05-02-017 Full Text: PDF

A Dynamic Multi-modal deep Reinforcement Learning framework for 3D Bin Packing Problem

The 3D bin packing problem, a notorious NP-hard combinatorial optimization challenge with wide-ranging practical implications, focuses on optimizing spatial allocation within a bin through the arrangement of boxes. Previous studies have shown promise in employing Neural Combinatorial Optimization to tackle such intractable problems. However, due to the inherent diversity in observations and the sparse rewards, current learning-based methods for addressing the 3D bin packing problem have yielded less-than-ideal outcomes. In response to this shortfall, we propose a novel Dynamic Multi-modal deep Reinforcement Learning framework tailored specifically for the 3D Bin Packing Problem, coined as DMRL-BPP. This framework stands apart from existing learning-based bin-packing approaches in two pivotal respects. Firstly, in order to capture the range of observations, we introduce an innovative dynamic multi-modal encoder, comprising dynamic boxes state and gradient height map sub-encoders, effectively modeling multi-modal information. Secondly, to mitigate the challenge of sparse rewards, we put forth a novel reward function, offering an efficient and adaptable approach for addressing the 3D bin packing problem. Extensive experimental results validate the superiority of our method over all baseline approaches, across instances of varying scales.

A GAN-based genetic algorithm for solving the 3D bin packing problem

The 3D bin packing problem is a challenging combinatorial optimization problem with numerous real-world applications. In this paper, we present a novel approach for solving this problem by integrating a generative adversarial network (GAN) with a genetic algorithm (GA). Our proposed GAN-based GA utilizes the GAN to generate high-quality solutions and improve the exploration and exploitation capabilities of the GA. We evaluate the performance of the proposed algorithm on a set of benchmark instances and compare it with two existing algorithms. The simulation studies demonstrate that our proposed algorithm outperforms both existing algorithms in terms of the number of used bins while achieving comparable computation times. Our proposed algorithm also performs well in terms of solution quality and runtime on instances of different sizes and shapes. We conduct sensitivity analysis and parameter tuning simulations to determine the optimal values for the key parameters of the proposed algorithm. Our results indicate that the proposed algorithm is robust and effective in solving the 3D bin packing problem. The proposed GAN-based GA algorithm and its modifications can be applied to other optimization problems. Our research contributes to the development of efficient and effective algorithms for solving complex optimization problems, particularly in the context of logistics and manufacturing. In summary, the proposed algorithm represents a promising solution to the challenging 3D bin packing problem and has the potential to advance the state-of-the-art in combinatorial optimization.

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.

A two‐stage solution method for the design problem of medium‐thick plates in steel plants

AbstractThe medium‐thick plate is an important type of steel product widely used in construction and engineering machinery. The orders are usually characterised by multiple specifications and small quantities. The plate design is an important part in the production process of medium‐thick plate, which includes the combination of sub‐plates and the size design of the motherboard. A multi‐objective model for medium‐thick plate design is proposed based on the 2D bin packing model, comprehensively considering spatial and size constraints of the plate production. A two‐stage genetic algorithm (TSGA) is developed to solve the proposed model. In the first stage, an improved GA is used to optimise the corresponding relationship between the sub‐plates and the slab, as well as the size of the motherboard. In the second stage, an exact algorithm based on the integer programming model is applied to calculate the order layout to minimise the surplus materials. To validate the proposed method, computational experiments are conducted based on actual production data from a steel plant. The experimental results show the effectiveness of the TSGA algorithm in solving the plate design problem.

Heuristics Integrated Deep Reinforcement Learning for Online 3D Bin Packing

Online 3D Bin Packing Problem (3D-BPP) has a wide range of industrial applications and there is an emerging research interest in learning optimal bin packing policy and deploying it for real logistics applications. From the heuristic methods to the deep reinforcement learning (DRL) methods, the previous works have proposed many solutions to solve the online 3D-BPP. However, none of them have studied what and how heuristics can be modelled into DRL to build a more effective and practical bin packing pipeline. In this work, we thoroughly investigate what heuristics can be used in online 3D-BPP and how to effectively integrate the heuristics with the DRL. First, we design 3 different heuristics based on the physical rules of the real world and the experiences of the human packers, including the Physics-Heuristics, the Packing-Heuristics and the Unpacking-Heuristics. Second, we model the 3 types of heuristics into the DRL framework and propose a novel heuristic DRL method to solve the online 3D-BPP. Extensive experimental results show that our method achieves state-of-the-art bin packing performance and the resulting real-world system is able to reliably finish the bin packing task in real logistics scenarios. Supplementary video is available at https://www.youtube.com/watch?v=x8GpmEELq18. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The rapid growth of e-commerce has significantly increased the burden of human packers in logistic warehouses, where the workers need to pick the products from a conveyor and pack them into bins (i.e. the online 3D bin packing). Thus it is of great importance to develop intelligent robotic systems to replace human labor, which is a long-standing topic in the field of control and automation science. This paper makes a substantial contribution to the related field by studying the online 3D bin packing in terms of both the theory and practice. On the one hand, the simulated experiments suggest that the presented algorithm significantly improves the space utilization of bin packing. On the other hand, the robotic system developed based on the proposed method can favourably finish the bin packing task in real logistics scenarios, demonstrating the practical use of our approach. Consequently, the approach proposed in this paper is totally applicable in logistic warehouses and is promising to drastically improve the working efficiency of the product packing in real warehouses. In the future, we will extend the presented approach to pack irregular-shaped objects and then facilitate more logistics applications.

Instance space analysis for 2D bin packing mathematical models

In this paper, we apply Instance Space Analysis (ISA) to study the two-dimensional bin-packing problem. We consider classical and newly-generated instances to test the performance of four mixed-integer programming (MIP) models from the literature. This is the first time ISA is used to compare MIP models. We set as a performance metric the time taken by the black-box MIP solver CPLEX to obtain a proven optimal solution when running each model. Our results provide a new perspective on the different models’ performance according to each instance’s features.

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.

BoxStacker: Deep Reinforcement Learning for 3D Bin Packing Problem in Virtual Environment of Logistics Systems.

Manufacturing systems need to be resilient and self-organizing to adapt to unexpected disruptions, such as product changes or rapid order, in supply chain changes while increasing the automation level of robotized logistics processes to cope with the lack of human experts. Deep Reinforcement Learning is a potential solution to solve more complex problems by introducing artificial neural networks in Reinforcement Learning. In this paper, a game engine was used for Deep Reinforcement Learning training, which allows visualization of view learning and result processes more intuitively than other tools, as well as a physical engine for a more realistic problem-solving environment. The present research demonstrates that a Deep Reinforcement Learning model can effectively address the real-time sequential 3D bin packing problem by utilizing a game engine to visualize the environment. The results indicate that this approach holds promise for tackling complex logistical challenges in dynamic settings.

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.

The 3D bin packing problem for multiple boxes and irregular items based on deep Q-network

The 3D bin packing problem for multiple boxes and irregular items based on deep Q-network

A Software Toolbox for Realistic Dataset Generation for Testing Online and Offline 3D Bin Packing Algorithms

Packing products into a pallet or other medium is an unavoidable activity for producing companies. In many cases, packing is based on operator experience and training using packing patterns that have worked before. Automated packing, on the other hand, requires a systematic procedure for devising packing solutions. In the scientific literature, this problem is known as 3D bin packing (3DBP) and many authors have proposed exact and heuristic solutions for many variations of the problem. There is, however, a lack of datasets that can be used to test and validate such solutions. Many of the available datasets use randomly generated products with extremely limited connection to real practice. Furthermore, they contain a reduced number of product configurations and ignore that packing relates to customers’ orders, which have specific relative mixes of products. This paper proposes a software toolbox for generating arbitrarily large datasets for 3DBPP based on real industry data. The toolbox was developed in connection with the analysis of a real dataset from the food and beverages sector, which enabled the creation of several synthetic datasets. The toolbox and the synthetic datasets are publicly available and can be used to generate additional data for testing and validating 3DBP solutions. The industry is increasingly becoming data dependent and driven. The ability to generate good quality synthetic data to support the development of solutions to real industry problems is of extreme importance. This work is a step in that direction in a domain where open data are scarce.

Compliant‐based robotic 3D bin packing with unavoidable uncertainties

AbstractRobotic 3D bin packing (R‐3dBPP), aiming to place deformed cases in various sizes in the container without fences, is a comprehensive application that includes perception, planning, execution, and hardware design. Traditional studies assume that the context of the real space must be accurately perceived and represented. However, disjunctions between the planner and reality are unavoidable in R‐3dBPP, especially with low‐cost sensors. As far as the author knows, there is no practical solution. In this paper, the above assumption is discarded and the typical types of uncertainties prevalent to guide the design of the algorithms are formulated. A new online bin‐packing algorithm is proposed, keeping deformed boxes stacked in close contact with each other, so that the whole pallet is kept stable by friction between the boxes and the container. In order to meet the requirement of close contact under the non‐negligible errors from sensors and planners, a compliant‐based motion planning system is introduced. It replaces the precision‐based feedback with a compliant end‐effector and accompanying motion strategies. Last but not least, a complete online bin‐packing robot system is developed and the system's performance under the influence of the uncertainties mentioned above through simulation and physical experiments is evaluated.

Ship–Infrastructure Cooperation: Survey on Infrastructure Scheduling for Waterborne Transportation Systems

Ship–infrastructure cooperation, i.e., infrastructure scheduling, is significant for optimizing the utilization of spatial-temporal resources of infrastructures and improving the efficiency and safety of waterborne transportation systems. This paper carries out a systematic review of the scheduling problems of the infrastructures in waterborne transportation systems, including locks, terminals, berths, and waterway intersections. The infrastructure scheduling problems are linked to the classical optimization problems, and a generalized infrastructure scheduling problem is formulated. For lock scheduling, the ship placement sub-problem aims at minimizing the number of lockages, which is a kind of classic 2D bin packing problem; the lockage scheduling sub-problem deals with chamber assignment and lockage operation planning, which is modeled as a single or parallel machine scheduling problem. For berth and terminal scheduling, the idea of queuing theory (for discrete terminal) and 2D bin packing (for continuous terminal) are usually applied. Most research aims at minimizing the waiting time of ships and focuses on the continuous dynamic terminal scheduling problems. As a special infrastructure, the waterway intersection receives little attention. Most research focuses on traffic conflicts and capacity problems. Future research directions are provided based on the review results and problems of infrastructure scheduling in practice.

Parameterized implementation of a triple refined modeling framework for mesoscale concrete

• A refined modeling framework for mesoscale concrete is developed using the parametric method. • The refined geometric aggregate models that consider micro/meso-scale morphology are generated. • The refined aggregate placement process is performed using the 3D BPT and Bullet physics engine. • The refined material assignment scheme is applied to describe random-continuous fields of material properties. As a typical heterogeneous composite material, concrete’s complex physical and mechanical behaviors on the macroscale are controlled by its mesoscale components and material properties. This paper aims to develop a refined modeling framework for mesoscale concrete using the parametric method, including the refined geometric aggregate model, refined aggregate placement process, and refined material assignment scheme. The geometric aggregates that consider micro/meso-scale morphology are first generated procedurally. Different degrees of mesh decimating operations are applied to the aggregates, and then the aggregate surface is smoothed by the Laplacian smoothing algorithm to build aggregate libraries of different resolutions. The numerical framework proposed by Huang et al. [39] is adopted in this work to conduct 3D bin packing and simulate the compaction and vibration process through the Bullet physics engine, so as to obtain the mesoscale geometric model with a high aggregate content. Furthermore, the material assignment schemes based on the statistical distribution and spatial correlation theory are applied to describe random-continuous fields of material properties. The chloride diffusion coefficient is used to illustrate the material assignment process. The triple refined modeling framework proposed in this paper provides a reference for high-fidelity parametric modeling of mesoscale concrete.

Multi-objective optimization of the 3D container stowage planning problem in a barge convoy system

Mainly motivated by the massification of flows in inland shipping, where several barges can be assembled in convoys to transport a large number of containers to and from the hinterland, we introduce an original extension of the Container Stowage Planning Problem (CSPP) (which we denote the 3D – barge Convoy Container Stowage Planning Problem (3D –CCSPP)). The requirements for stowing all containers in a barge convoy entail additional constraints related to both the containers and the convoy. In this paper, the 3D –CCSPP is dealt with, on the basis of its relation to the 3D Bin-Packing Problem (3D-BPP), in which the filled objects represent the containers, and the bins indicate the convoy barges. We consider the multi-objective aspect of the problem with three realistic functions to be optimized: shifting movements, the convoy stability and the number of real-used barges. This is a new and effective aspect considering the state of the art of CSPP in inland shipping. We develop a multi-objective mathematical formulation of the 3D-CCSPP and propose a novel adaptation of the multi-objective evolutionary algorithm NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) based on a set of heuristics introduced by the BPP resolution methods. Specific encoding method, generation of the initial population and genetic operators are designed based on the mathematical description of the problem. Extensive experiments are then carried out on a varied set of instances. The computational results demonstrate the effectiveness of the proposed approaches, they are evaluated using CPLEX solver and their performance is verified by a set of measurements which are adapted to the problem in real-world applications in relation to each objective function. Additional studies are carried out in sensitivity analysis to provide decision makers with a better knowledge of the problem. They can then choose, from the set of compromise solutions of the Pareto front, the most promising one for practical implementation based on their experience and preferences.