Online 3D Bin Packing Problem (3D-BPP) has widespread applications in industrial automation. Existing methods usually solve the problem with limited resolution of spatial discretization, and/or cannot deal with complex practical constraints well. We propose to enhance the practical applicability of online 3D-BPP via learning on a novel hierarchical representation, packing configuration tree (PCT). PCT is a full-fledged description of the state and action space of bin packing which can support packing policy learning based on deep reinforcement learning (DRL). The size of the packing action space is proportional to the number of leaf nodes, making the DRL model easy to train and well-performing even with continuous solution space. We further discover the potential of PCT as tree-based planners in deliberately solving packing problems of industrial significance, including large-scale packing and different variations of BPP setting. A recursive packing method is proposed to decompose large-scale packing into smaller sub-trees while a spatial ensemble mechanism integrates local solutions into global. For different BPP variations with additional decision variables, such as lookahead, buffering, and offline packing, we propose a unified planning framework enabling out-of-the-box problem solving. Extensive evaluations demonstrate that our method outperforms existing online BPP baselines and is versatile in incorporating various practical constraints. The planning process excels across large-scale problems and diverse problem variations. We develop a real-world packing robot for industrial warehousing, with careful designs accounting for constrained placement and transportation stability. Our packing robot operates reliably and efficiently on unprotected pallets at 10 seconds per box. It achieves averagely 19 boxes per pallet with 57.4% space utilization for relatively large-size boxes.
Recently, deep reinforcement learning (DRL) has achieved promising results in solving online 3D Bin Packing Problems (3D-BPP). However, these DRL-based policies may perform poorly on new instances due to distribution shift. Besides generalization, we also consider adaptation, completely overlooked by previous work, which aims at rapidly finetuning these policies to a new test distribution. To tackle both generalization and adaptation issues, we propose Adaptive Selection After Pruning (ASAP), which decomposes a solver's decision-making into two policies, one for pruning and one for selection. The role of the pruning policy is to remove inherently bad actions, which allows the selection policy to choose among the remaining most valuable actions. To learn these policies, we propose a training scheme based on a meta-learning phase of both policies followed by a finetuning phase of the sole selection policy to rapidly adapt it to a test distribution. Our experiments demonstrate that ASAP exhibits excellent generalization and adaptation capabilities on in-distribution and out-of-distribution instances under both discrete and continuous setup.
Designing effective policies for the online 3D bin packing problem (3D-BPP) has been a long-standing challenge, primarily due to the unpredictable nature of incoming box sequences and stringent physical constraints. While current deep reinforcement learning (DRL) methods for online 3D-BPP have shown promising results in optimizing average performance over an underlying box sequence distribution, they often fail in real-world settings where some worst-case scenarios can materialize. Standard robust DRL algorithms tend to overly prioritize optimizing the worst-case performance at the expense of performance under normal problem instance distribution. To address these issues, we first introduce a permutation-based attacker to investigate the practical robustness of both DRL-based and heuristic methods proposed for solving online 3D-BPP. Then, we propose an adjustable robust reinforcement learning (AR2L) framework that allows efficient adjustment of robustness weights to achieve the desired balance of the policy's performance in average and worst-case environments. Specifically, we formulate the objective function as a weighted sum of expected and worst-case returns, and derive the lower performance bound by relating to the return under a mixture dynamics. To realize this lower bound, we adopt an iterative procedure that searches for the associated mixture dynamics and improves the corresponding policy. We integrate this procedure into two popular robust adversarial algorithms to develop the exact and approximate AR2L algorithms. Experiments demonstrate that AR2L is versatile in the sense that it improves policy robustness while maintaining an acceptable level of performance for the nominal case.
The 3D Bin Packing Problem (3D-BPP) is one of the most demanded yet challenging problems in industry, where an agent must pack variable size items delivered in sequence into a finite bin with the aim to maximize the space utilization. It represents a strongly NP-Hard optimization problem such that no solution has been offered to date with high performance in space utilization. In this paper, we present a new reinforcement learning (RL) framework for a 3D-BPP solution for improving performance. First, a buffer is introduced to allow multi-item action selection. By increasing the degree of freedom in action selection, a more complex policy that results in better packing performance can be derived. Second, we propose an agnostic data augmentation strategy that exploits both bin item symmetries for improving sample efficiency. Third, we implement a model-based RL method adapted from the popular algorithm AlphaGo, which has shown superhuman performance in zero-sum games. Our adaptation is capable of working in single-player and score based environments. In spite of the fact that AlphaGo versions are known to be computationally heavy, we manage to train the proposed framework with a single thread and GPU, while obtaining a solution that outperforms the state-of-the-art results in space utilization.
We tackle the Online 3D Bin Packing Problem, a challenging yet practically useful variant of the classical Bin Packing Problem. In this problem, the items are delivered to the agent without informing the full sequence information. Agent must directly pack these items into the target bin stably without changing their arrival order, and no further adjustment is permitted. Online 3D-BPP can be naturally formulated as Markov Decision Process (MDP). We adopt deep reinforcement learning, in particular, the on-policy actor-critic framework, to solve this MDP with constrained action space. To learn a practically feasible packing policy, we propose three critical designs. First, we propose an online analysis of packing stability based on a novel stacking tree. It attains a high analysis accuracy while reducing the computational complexity from $O(N^2)$ to $O(N \log N)$, making it especially suited for RL training. Second, we propose a decoupled packing policy learning for different dimensions of placement which enables high-resolution spatial discretization and hence high packing precision. Third, we introduce a reward function that dictates the robot to place items in a far-to-near order and therefore simplifies the collision avoidance in movement planning of the robotic arm. Furthermore, we provide a comprehensive discussion on several key implemental issues. The extensive evaluation demonstrates that our learned policy outperforms the state-of-the-art methods significantly and is practically usable for real-world applications.
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.
We propose a Deep Reinforcement Learning (Deep RL) algorithm for solving the online 3D bin packing problem for an arbitrary number of bins and any bin size. The focus is on producing decisions that can be physically implemented by a robotic loading arm, a laboratory prototype used for testing the concept. The problem considered in this paper is novel in two ways. First, unlike the traditional 3D bin packing problem, we assume that the entire set of objects to be packed is not known a priori. Instead, a fixed number of upcoming objects is visible to the loading system, and they must be loaded in the order of arrival. Second, the goal is not to move objects from one point to another via a feasible path, but to find a location and orientation for each object that maximises the overall packing efficiency of the bin(s). Finally, the learnt model is designed to work with problem instances of arbitrary size without retraining. Simulation results show that the RL-based method outperforms state-of-the-art online bin packing heuristics in terms of empirical competitive ratio and volume efficiency.
We solve a challenging yet practically useful variant of 3D Bin Packing Problem (3D-BPP). In our problem, the agent has limited information about the items to be packed into the bin, and an item must be packed immediately after its arrival without buffering or readjusting. The item's placement also subjects to the constraints of collision avoidance and physical stability. We formulate this online 3D-BPP as a constrained Markov decision process. To solve the problem, we propose an effective and easy-to-implement constrained deep reinforcement learning (DRL) method under the actor-critic framework. In particular, we introduce a feasibility predictor to predict the feasibility mask for the placement actions and use it to modulate the action probabilities output by the actor during training. Such supervisions and transformations to DRL facilitate the agent to learn feasible policies efficiently. Our method can also be generalized e.g., with the ability to handle lookahead or items with different orientations. We have conducted extensive evaluation showing that the learned policy significantly outperforms the state-of-the-art methods. A user study suggests that our method attains a human-level performance.
In this paper, a new type of 3D bin packing problem (BPP) is proposed, in which a number of cuboid-shaped items must be put into a bin one by one orthogonally. The objective is to find a way to place these items that can minimize the surface area of the bin. This problem is based on the fact that there is no fixed-sized bin in many real business scenarios and the cost of a bin is proportional to its surface area. Our research shows that this problem is NP-hard. Based on previous research on 3D BPP, the surface area is determined by the sequence, spatial locations and orientations of items. Among these factors, the sequence of items plays a key role in minimizing the surface area. Inspired by recent achievements of deep reinforcement learning (DRL) techniques, especially Pointer Network, on combinatorial optimization problems such as TSP, a DRL-based method is applied to optimize the sequence of items to be packed into the bin. Numerical results show that the method proposed in this paper achieve about 5% improvement than heuristic method.
A 3D flexible bin packing problem (3D-FBPP) arises from the process of warehouse packing in e-commerce. An online customer's order usually contains several items and needs to be packed as a whole before shipping. In particular, 5% of tens of millions of packages are using plastic wrapping as outer packaging every day, which brings pressure on the plastic surface minimization to save traditional logistics costs. Because of the huge practical significance, we focus on the issue of packing cuboid-shaped items orthogonally into a least-surface-area bin. The existing heuristic methods for classic 3D bin packing don't work well for this particular NP-hard problem and designing a good problem-specific heuristic is non-trivial. In this paper, rather than designing heuristics, we propose a novel multi-task framework based on Selected Learning to learn a heuristic-like policy that generates the sequence and orientations of items to be packed simultaneously. Through comprehensive experiments on a large scale real-world transaction order dataset and online AB tests, we show: 1) our selected learning method trades off the imbalance and correlation among the tasks and significantly outperforms the single task Pointer Network and the multi-task network without selected learning; 2) our method obtains an average 5.47% cost reduction than the well-designed greedy algorithm which is previously used in our online production system.