Constraint-Aware 3D Container Loading via Recursive Space Partitioning and Annealed Permutation Search
Abstract
We describe a production orthogonal 3D container loading system that combines three techniques: (1) a recursive space-partition placement that subdivides containers through nested sub-container narrowing, preserving parent-region dimensions for constraint checking, (2) a beam-augmented annealed search over item permutations, where a deterministic placer enforces all constraints internally so that every candidate ordering decodes to a valid packing, and (3) a deterministic compaction post-pass that reclaims gravity and slide gaps while preserving a >75% bottom-face support rule.
On heterogeneous mid-size item sets, cost-function rebalancing improved packing compactness from 0.45 to 0.72 (a 62% gain). On a production 40-foot container load of 730 items across two box types, the system achieves 82% volume utilization.
Download PDF →Key results
| Metric | Before | After | Change |
|---|---|---|---|
| S3 compactness (16 mixed items) | 0.454 | 0.688 | +51% |
| S4 compactness (20 heterogeneous) | 0.448 | 0.724 | +62% |
| S11 compactness (24 mixed-priority) | 0.736 | 0.883 | +20% |
| Production load (730 items) | 82% utilization | 0 unplaced | |
| Run-to-run variance (S4) | 0.41–0.57 | 0.724 | Eliminated |
Contributions
Recursive space-partition placement. A deterministic strategy that maintains nested sub-containers rather than enumerating candidate positions. Each placement narrows a sub-container along the width axis; later placements inherit the parent's full height and length. This preserves constraint-checking context that disjoint partitioning methods lose.
Beam-augmented annealed permutation search. The search mutates item orderings, not positions. Eight concurrent mutation strategies per temperature step. Constraints are enforced inside the deterministic placer; every candidate ordering decodes to a valid result.
Grounding-aware compaction. A post-pass that drops and slides items toward the origin, validating each move against a >75% bottom-face support threshold. Converges in 2–4 sweeps and eliminates run-to-run variance.
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