Online 3D bin packing with a bounded buffer requires irreversible item-selection and placement decisions under limited knowledge of future arrivals. Feasibility alone is insufficient, as feasible actions can produce different residual-space structures and subsequent packing opportunities. A central architectural question is how to allocate spatial reasoning between item selection and placement evaluation. We propose Spatial Affordance Retrieval (SAR), a novel learning-based framework that coordinates global item-space matching with geometry-aware placement ranking. A voxel-token spatial encoder represents 3D container occupancy, enabling a picker to match buffered items to the residual space without requiring item-specific placement proposals as inputs. After item selection, a loader ranks feasible rotation-position candidates using candidate geometry, local geometric features (LGF), and inter-candidate comparison, without directly accessing global spatial tokens. The feasible candidate set connects the two stages, which are jointly optimized under a shared long-horizon packing return. On the Random, JD, and SF datasets, the best SAR variants improve utilization over the strongest evaluated online baselines by 0.96-4.20 percentage points under the no-buffer setting (K=1). With a buffer (K=5), the best utilization rates across SAR variants reach 93.55%, 91.04%, and 90.41%, respectively. Ablations support the complementary roles of global item-space matching and geometry-aware placement evaluation, counterfactual analysis suggests that learned item selection favors greater future packing potential, and experiments demonstrate compatibility with multiple candidate generators.
Figures & tables
Figure 1: Illustration of the buffered online 3D-BP scenario. Items arrive on a conveyor and enter a limited buffer. The policy selects which item to pack and its orientation and position in the container. The robot arm visualizes the selected item’s transfer and placement.
Figure 2: Empirical observations. (a) Across item-size distributions, smaller items are associated with higher packed-item counts (longer packing trajectories) and higher final utilization, whereas larger items exhibit the opposite pattern. (b) As packing progresses, feasible placement candidates become fewer and more spatially aggregated, increasing the need for fine-grained candidate evaluation.
Method
Type
Item visibility
Item order
Learned decisions
Spatial representation
Placement evaluation
Training
PackIt ( Goyal and Deng, 2020 )
Offline
Global
Adjustable
Item
3D voxel grid
Handcrafted; BLBF placement with Aligned rotation
PPO
TAP-Net ( Hu et al., 2020 )
Offline
Global
Adjustable
(Item, rotation)
2D height map
Handcrafted criteria inside the heuristic; no learned evaluation
Policy gradient; heuristic packing
Attend2Pack ( Zhang et al., 2021 )
Offline
Global
Adjustable
Item, (rotation, position)
2D frontier map
Implicit; from oriented dimensions and frontier geometry
REINFORCE with rollout baseline
PCT ( Zhao et al., 2022a )
Online
Local
Fixed
(Rotation, position)
Tree structure
Implicit; from placed-item and candidate-node geometry
ACKTR
Zhao et al. ( Zhao et al., 2022b )
Online
Local
Fixed
Rotation, position
2D height map
Implicit; from height-map geometry; stacking tree for feasibility
Constrained ACKTR
GOPT ( Xiong et al., 2024 )
Online
Local
Fixed
(Rotation, position)
2D height map
Implicit; from free-space and item–space relations
PPO
Table 1: Comparison of representative packing policies. Item visibility is global when the policy observes the complete item set and local when it observes only the current item or a bounded buffer. Item order is fixed or adjustable during packing. Learned decisions are listed in the order item, rotation, and position, where a parenthesized group denotes joint selection and a comma between groups denotes separate stages; decisions not learned by the policy itself are omitted. Entries refer to the formulations discussed in the text.
Figure 3: Overview of the proposed Spatial Affordance Retrieval (SAR) framework. A 3D CNN with max pooling and self-attention encodes the container voxel grid Ot (top left) into spatial tokens Zt , and an item encoder embeds the buffered items Bt (bottom left) into Ut . The picker computes scaled dot-product scores between item embeddings (Q) and these tokens (K), averages the scores, and softmax-normalizes them into the item-selection policy πθpicker(bt,i∣st) ; a critic additionally estimates the state value Vψ(st) for training. Given the selected item, heuristic placement generation enumerates rotation–position candidates, filters them by stability, and computes Local Geometric Features (LGF; support, compactness, height, and surface fit), forming the feasible placement set Ct(bt,i) (middle). For fine-grained placement evaluation, the loader encodes these candidates into tokens Yt0 , refines them by self-attention into Yt2 , and scores them by scaled dot-products between placement queries {qt,j}j=1J (Q) and the refined keys (K), yielding the placement policy πθloader(ct,j∣st,bt) that determines the final orientation and position (right). The selected item determines the loader’s feasible candidate set, and both stages are trained under a shared return.
Dataset 1
Dataset 2
Dataset 3
Method
util. ↑
std. ↓
num.
time ↓
util. ↑
std. ↓
num.
time ↓
util. ↑
std. ↓
num.
time ↓
Heuristic
Random
39.53
9.17
16.65
<0.1s
37.30
9.33
9.84
<0.1s
34.22
10.15
7.28
<0.1s
MACS
63.01
9.54
24.99
<0.1s
61.35
9.27
14.97
<0.1s
61.96
11.09
12.41
<0.1s
LSAH
62.56
9.95
24.78
<0.1s
55.82
11.49
14.27
<0.1s
56.48
9.381
11.62
<0.1s
BR
54.34
10.57
22.02
<0.1s
53.65
10.21
13.39
<0.1s
54.82
10.36
11.24
<0.1s
Table 2: Performance comparisons. {util.} denotes space utilization of the environment (%); {std.} denotes standard deviation of space utilization ( ×10−2 ); {num.} denotes the average number of packed items per episode; {time} denotes the average decision time per step. SAR1 denotes K=1 . SAR5 denotes K=5 . All learning-based methods were set R=10,Nori=6 . Bold and underlined entries indicate the best and second-best results within each setting.
Figure 4: Packing progression of one episode on D2 .
Figure 5: Sensitivity Analysis and ablation studies. (a) Performance across the three datasets. (b) Effect of K on D1 . (c) Ablation studies on space utilization during training.
Spatial Encoder
Picker
Loader
util. ↑
std. ↓
num.
(H/L)
(H/L)
(H/L)
1/1
1/1
1/1
93.46
3.80
38.92
1/1
4/1
1/1
93.50
3.52
38.95
4/1
1/1
1/1
93.24
3.55
38.43
1/1
1/1
4/1
93.46
3.28
38.56
1/2
1/1
1/1
93.05
3.66
38.98
Table 5: Performance under different attention configurations. H/L denotes the number of attention heads/layers. Util. denotes space utilization (%), std. denotes its standard deviation ( ×10−2 ), and num. denotes the average number of packed items per episode.
Table 6: Attention-component ablation. ✓ and × indicate enabled and disabled components, respectively. Each metric is reported as an absolute result and an adjacent Δ column showing its change from Full. Util. denotes space utilization (%), std. denotes its standard deviation ( ×10−2 ), and num. denotes the average packed-item count.
Figure 7: Reference candidate construction on a valid ground-level packing. (a) EMS aligns the item with the corners of valid empty spaces. (b) CP extracts positions where the projected item silhouette transitions from a vertical to a horizontal boundary segment. (c) EP shows the raw anchors retained by the reference implementation’s sequential 2D projection routine. (d) EV combines item and container boundary alignments, converted to FLB coordinates for the candidate footprint, at each relevant boundary height within the vertical span of nt . Red points denote retained candidate FLB anchors from the z=0 construction plane for an item whose bottom face spans 3 grid cells along both the x and y axes (a 3×3 footprint). These anchors are shown before height lifting and physics checks; the EP anchor at (3,0) is lifted above the yellow item.
Figure 8: Top-view illustration of the incremental candidate-generation variants. Blue points denote top-face candidates, and orange points denote bottom-perimeter candidates. Points lie on integer grid intersections and show the (x,y) coordinates of voxel lower corners used as candidate FLB anchors for subsequent items. V1 densely samples the top face and perimeter edges, whereas V2 retains only their corner and endpoint representatives.
Figure 9: Training dynamics under different placement-generation schemes. Each curve shows the space utilization from one training run after exponential smoothing with a factor of 0.99. Final policy evaluation results are reported in Table 8 .
Figure 10: Episode-averaged model advantage (percentage points) under Leaf-Max and Leaf-Mean. Positive and negative values favor the selected and unselected items, respectively; zero denotes equal outcomes.
Dataset 1
Dataset 2
Dataset 3
Method
util. ↑
std. ↓
num.
util. ↑
std. ↓
num.
util. ↑
std. ↓
num.
zero-shot
93.69
3.88
37.99
76.44
8.00
22.24
72.34
8.47
17.56
fine-tuned
87.42
5.72
37.24
89.22
4.65
25.04
86.69
5.57
21.53
Table 8: Generalization performance under zero-shot and fine-tuned settings. Util. denotes space utilization (%), std. denotes its standard deviation ( ×10−2 ), and num. denotes the average packed-item count. Underlined values correspond to source-domain evaluation of Model A.
Figure 11: Cross-dataset space utilization under zero-shot and fine-tuned settings.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure A.1: Item types in the three datasets. Each cube is rendered at the relative dimensions of one item type within a unit container and labeled by its dimensions in ascending order. (a) Dataset 1 ( D1 ), (b) Dataset 2 ( D2 ), and (c) Dataset 3 ( D3 ).
The online three-dimensional bin packing problem (3D-BPP) is a longstanding challenge in logistics and industrial palletizing. Recent learning-based methods use a learned policy to select among feasible candidate placements. Performance depends on the candidate generator and representation, especially in industrial settings where packings must be space-efficient, stable, compact, and balanced. However, prior work has mainly optimized the policy, while candidate generation and representation remain largely geometry-driven. We address this gap with OPAL, an operationally guided placement-aware learning framework for industrial online 3D-BPP which combines an Operationally Guided Empty-Maximal-Space generator (OG-EMS), an operational representation for each candidate placement, and a masked ranking policy trained with proximal policy optimization. OG-EMS evaluates multiple anchors within each free-space region and prioritizes low, well-supported, compact, and spatially diverse placements. An xLSTM-based Placement Encoder models dependencies among geometric and operational candidate attributes, while a lightweight recurrent core combines the resulting embeddings with the current item and pallet state to rank feasible actions. On the BED-BPP benchmark, OPAL achieves a mean space utilization of 0.49, with improvements of 15.1% from operationally guided candidate generation and 6.3% from learned ranking, while maintaining robust inference-time performance.
Dheeraj Poolavaram, Aanchal Rajesh Chugh, Sebastian Dorn
TTZ Landsberg am Lech, Technische Hochschule Augsburg, Augsburg, Germany
Robotic bin packing is widely deployed in warehouse automation, with current systems achieving robust performance through heuristic and learning-based strategies. These systems must balance compact placement with rapid execution, where selecting alternative items or reorienting them can improve space utilization but introduce additional time. We propose a selection-based formulation that explicitly reasons over this trade-off: at each step, the robot evaluates multiple candidate actions, weighing expected packing benefit against estimated operational time. This enables time-aware strategies that selectively accept increased operational time when it yields meaningful spatial improvements. Our method, STEP (Space-Time Efficient Packing), uses a preference-conditioned, Transformer-based reinforcement learning policy, and allows generalization across candidate set sizes and integration with standard placement modules. It achieves a 44% reduction in operational time without compromising packing density. Additional material is available at https://step-packing.github.io.
Nikita Sarawgi, Omey M. Manyar, Fan Wang +3
Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA. · Amazon Robotics, North Reading, MA, USA.
The online 3D bin packing problem is important in logistics, warehousing and intelligent manufacturing, with solutions shifting to deep reinforcement learning (DRL) which faces challenges like low sample efficiency. This paper proposes a diffusion reinforcement learning-based algorithm, using a Markov decision chain for packing modeling, height map-based state representation and a diffusion model-based actor network. Experiments show it significantly improves the average number of packed items compared to state-of-the-art DRL methods, with excellent application potential in complex online scenarios.
Jie Han, Tong Li, Qingyang Xu +3
School of Mechanical, Electrical, and Information Engineering, Shandong University, Weihai 264209, China · Shandong Key Laboratory of Intelligent Electronic Packaging Testing and Application, Shandong University, Weihai 264209, China