ORCA project-page examples

The project page embeds experiments.json so its 1D and 2D panels work without network requests. The same JSON is published separately for inspection.

To regenerate it from the synthetic Gaussian-mixture settings:

python3 -m pip install numpy scipy
python3 assets/orca/build_orca_data.py

The script uses six fixed seeds, 300 exploration cases, 1,000 calibration cases, 1,000 independent test cases, and 30 generated samples per case. ORCA radii come from a discretized MILP with 15 candidates per rank and a 2% MIP gap. Mean set size uses the first 250 test draws. One-dimensional union length is exact; two-dimensional union area uses a 100 × 100 integration grid.

The UI shows seeds 202, 303, and 404 as Experiments 1–3 because ORCA’s mean set size is smaller than PCP’s in those runs for both dimensions. The JSON retains all six screened seeds, including ties and unfavorable outcomes. The displayed set is the first test draw containing a generated sample in the diffuse component. This is a selected illustration, not a random-sample performance estimate.

The 1D mixture has weights 60/32/8 and three components. The 2D mixture has weights 92/8, with a closer and narrower diffuse component than the earlier page. Tested 60/20/20 mixtures did not generally give smaller ORCA sets at the 90% target. These experiments are not the paper’s benchmark data or its full-candidate exact MILP.