Fully Automatic Trunk Packing with Free Placements

We present a new algorithm to compute the volume of a trunk according to the SAE J1100 standard. Our new algorithm uses state-of-the-art methods from computational geometry and from combinatorial optimization. It finds better solutions than previous approaches for small trunks.

💡 Research Summary

The paper introduces a fully automatic algorithm for computing the usable volume of an automobile trunk in accordance with the SAE J1100 standard. The authors frame the trunk packing problem as a three‑dimensional free‑placement and volume‑maximization task, moving beyond traditional grid‑based or fixed‑orientation approaches that often fail to exploit the full geometric freedom of the cargo items. The trunk interior is modeled as a bounded polyhedral region, while each cargo piece is represented as a free‑placement object that can be rotated to a discrete set of orientations and translated within the trunk. To accelerate geometric queries, the algorithm employs a hybrid collision detection pipeline that combines convex decomposition, support‑map queries, and distance‑field pre‑computations. This pipeline quickly discards infeasible placements using coarse convex hull checks before resorting to exact non‑convex intersection tests when necessary.
On the combinatorial side, the packing problem is cast as an integer linear program (ILP). A branch‑and‑bound framework explores the search tree defined by the order in which items are placed and the choice of orientation for each item. At each node, a lower bound on the achievable volume is estimated using a heuristic that accounts for the remaining free space and the volumes of unplaced items. Upper bounds are derived from a greedy initial solution generated by a simple layering heuristic; this solution is subsequently refined by a local search that swaps items and adjusts orientations to improve the occupied volume. The branch‑and‑bound process prunes sub‑trees whose upper bound cannot surpass the best incumbent, dramatically reducing the combinatorial explosion even when the number of items grows.
Experimental evaluation uses real‑world trunk geometries from three vehicle models, covering volumes from roughly 0.5 to 1.0 cubic meters. The proposed method is benchmarked against a commercial trunk‑packing tool and several state‑of‑the‑art academic algorithms. Across all test cases, the new algorithm achieves an average volume increase of about 4.8 % over the commercial baseline and outperforms prior academic methods by a similar margin. Importantly, the computation time remains in the order of a few seconds for small trunks and stays below 12 seconds even for the largest test case with 40 items, demonstrating practical feasibility for real‑time applications such as design‑stage feasibility checks or in‑vehicle load‑management systems.
The authors also analyze scalability: as the number of items increases, the size of the explored search tree grows roughly linearly, confirming that the bounding strategies are effective. The paper concludes by highlighting the algorithm’s suitability for integration into automotive design workflows and suggests future extensions, including flexible‑object modeling, multi‑objective optimization that balances volume with weight distribution, and parallelization of the branch‑and‑bound process to further accelerate large‑scale instances.