Benchmark

Every number below is a distribution over seeds and a paired comparison over tasks. No single lucky run is reported. 33,523 front plans were re-validated when this summary was built; the build refuses to write if any fails.

RQ1 — Which algorithms most reliably produce valid plans?

"Valid share of evaluations" is validCount / full evaluations. Constructive methods (greedy, CP) only evaluate complete constructions, so their share is ~100 % by design and their cost sits in candidate checks; compare methods on runs-with-a-valid-plan, valid plans per run and hypervolume instead. Runtime includes the (small, fixed-cost) convergence-trace sampling; it is not purified to algorithm-only compute time in this run. Green rows: best median HV in the tier.

RQ2 — Which methods best explore Pareto trade-offs?

Hypervolume (exact, 5 headline objectives normalised per task) captures both convergence and spread. The paired table gives task-level wins/losses on per-task median HV and Holm-adjusted two-sided Wilcoxon signed-rank p-values over 28 tasks. Exclusive contribution to the union front is on the Pareto page.

Convergence (mean archive hypervolume vs budget)

RQ3 — How does performance degrade as constraints increase?

Each point is one task. Rooms and constraint count grow across tiers; the L and U boundaries and accessibility clearances add hard constraints. Run-level validity and hypervolume per method against the constraint count:

Fill = sum of minimum room areas / boundary area. Red cells: no seed produced a valid plan within budget.

RQ4 — Do generative / ML-style methods outperform classical optimisation after validity?

The only "differentiable/ML-style" condition is analytic placement (gradient descent on a smooth penalty energy with legalisation), included because it is a classical technique from VLSI placement, not because it is learned. The LLM condition runs only when an endpoint is configured (it was not part of this canonical run; see Methods for why). On the runs above, analytic placement solved 41% of runs with median HV 0.000, versus 80% / 0.292 for constraint search and 92% / 0.363 for greedy-seeded SA.

RQ5 — How sensitive are conclusions to objective weighting?

300 Dirichlet(1) weight vectors over the five headline objectives. For each (weight, task) the method whose per-seed fronts hold the best scalarised plan (median over seeds) wins. Rank stability is Kendall τ between the algorithm ranking under uniform weights and under each random weighting.

Per-task detail