DOI: 10.5281/zenodo.13925610
title: Loading Stability Benchmark for Pallet Loading Problems

description: Description

The dataset contains information about approx. 32.000 pallet loading problem (PLP) cargo layouts derived from a physical simulation with the MSC ADAMS software. The question of the study is to compare and benchmark multiple static stability algorithms: full base support, partial base support, static mechanical equilibrium, and physical simulation. As there are no real-world cargo loading datasets available, we decided to approximate real-world loading. We used a multibody simulator (MSC ADAMS) and simulated cargo loadings for a set of layouts. The benchmark simulation was adjusted in an iterative process, in which we visually tested simulations and incorporated insights from literature about physical cargo properties until we were satisfied with the plausibility of the results. However, the benchmark simulation depends on many parameters that need to be adjusted, and our adjustments might be unprecise. The dataset contains 2 sub-datasets: Dataset 1 is based on the ACLPP instances generated by Brandt & Nickel (2019). Dataset 2 is based on the instances from Ali et al. (2024). For every sub-dataset, we assembled three complexity scenarios with four stages. Scenario 1 is the easiest scenario, which assumes all items (boxes) have uniform density and no displaced center of mass (in relation to their geometric center). Scenario 2a moves the CoM now to a random position in the items' dimensions according to a Gaussian distribution around the item's geometric center. Scenario 2b now applies the same procedure as Scenario 2a but employs a uniform distribution.

Stages

Stage 0 ("0_input") are the raw data from both datasets. We did not include the raw data but provided the link to the dataset in the meta-information here.

Stage 1 ("1_AeULDs") are the input cargo items with itemLabel, weight, (box)-shape with width, height, depth, loading coordinate (x,y,z), sequence, and center of mass (x, y, z). We imposed a cap on the number of items of 20. If a ULD exceeds this threshold, we include only the first 20 items.

Stage 2 ("2_AeJobs") transfers the ULDs to an executable format and includes assessment information (i.e., stability approaches).

Stage 3 ("3_AeResults") are the results from the different static stability algorithms with a uniform static stability score between 0 (first item unstable) and 1 (all items stable) and a runtime. 

Stage 4 ("4_Benchmark") are the benchmark data from our multibody simulation. The first folder ("done_raw") is raw output of our ADAMS simulation, which tracks relevant physical characteristics such as angular momentum, angular velocity, acceleration, position, velocity (about the center of mass), translation, rotation, and contact forces with other items. We measured multiple observations per loading sequence, which all have an assigned time step. The total simulation length is 0.3 s. The second folder ("done_intermediate") now filters the raw data, such that we track the largest translation and rotation in x, y, and z- directions per loading step per item. We also calculate the maximal translation and rotation within the simulation. The third folder ("done") transforms the intermediate steps into a final quantified stability outcome, in case any item exceeds the threshold values for translation and rotation. The final outcome is normalized, such that 1 represents a stable cargo layout and 0 represents a layout in which the first item is unstable. Divide the number of stable loading steps by the total number of items in the cargo layout. The fourth folder ("done_sensitivity_analysis") computes the benchmark results for different epsilon_translations and epsilon_rotation values for sensitivity analyses. We filtered the data for the analysis, such that only ULDs with a minimal width, depth, and height of every item are included for the final analysis. Further, we filtered out ULDs that contained less than two items.

Stage 5 ("5_Final_results") contains aggregated results, such as the aggregated number of correct predictions, underestimations, overestimations, and sensitivity analyses results.

Further references

The paper (preprint) describing the study can be found here. The code for data generation, simulation, and analysis is in the GitHub Repository (also linked below).

Changelog:




Version
Change


0.0.3
This version fixes a bug during item dimension mapping in dataset 2 that made a re-simulation necessary. We imposed a cap on the number of items of 20. If a ULD exceeds this threshold, we include only the first 20 items. For the analysis, we included a minimal item level per ULD of 2. We set the minimal item dimensions to 10 (previously: 15). We removed macOS-specific files from the archive.