This study uses independent exponential bracketing and integer binary search to find a ten-second boundary for each native solver version. A version stops expanding after its first failed size. It then searches smaller sizes between its last success and failure. The candidate and its adjacent sizes receive two runs; every knapsack size includes both profit variants. Failed confirmations remain recorded and can lower the reported boundary.

The displayed value is the largest sampled, confirmed size, not an absolute solver limit. Integer-programming difficulty is not monotonic in variable count. A larger untested instance can be easier than a smaller failed one. The report preserves observed reversals, unconfirmed discoveries, search ceilings and every actual input and decision. Missing outcomes are unknown, never synthetic failures or estimated completion times.

After both searches, timing points within the smaller confirmed boundary (plus its adjacent size) are shared where needed. The weaker version is not run across the stronger version's large-size range. Each curve uses only actual observations for that version. Discovery uses one run; confirmation uses two. A knapsack point summarizes both variants and all its runs, with the complete timing range. No full-cohort completion-time estimate is shown if any run is unfinished.

Recorded results

The local run records 162 measurements across 71 sampled inputs in 931.62 seconds, plus two loader probes. The measured tooling source is f724bd01795a87b2c310ba368c66d36bb09f660f. Every headline size passes two runs per version and every knapsack variant.

Category	Before confirmed	Optimized confirmed	Next tested failure (before / optimized)
Knapsack	33 items / 33 model variables	407 items / 407 model variables	34 / 408 in natural size units
Assignment	17 tasks / 289 model variables	17 tasks / 289 model variables	18 / 18 in natural size units
Facility location	8 sites / 136 model variables	8 sites / 136 model variables	9 / 9 in natural size units
Bin packing	17 items / 108 model variables	17 items / 108 model variables	18 / 18 in natural size units
Production planning	11 periods / 88 model variables	11 periods / 88 model variables	12 / 12 in natural size units
Routing	21 cities / 42 model variables	21 cities / 42 model variables	22 / 22 in natural size units
Weighted queens	23 queens / 92 model variables	23 queens / 92 model variables	24 / 24 in natural size units

Knapsack expands from 33 to 407 items (12.33 times the sampled size). At 33 items, the older correlated case takes 9.990 and 9.730 seconds; the boundary is sensitive to host timing. Both 407-item optimized variants complete near 28 ms. The other six confirmed capacities match.

One assignment timeout reports 25.724 seconds internally but 8.819 seconds externally. The host clocks disagreed; the cause is not established. That observation remains unfinished and has no completion-time estimate. Its second confirmation also reaches the limit with consistent clocks. No completed result has this discrepancy.

The complete portable record preserves raw results, inputs, decisions, untested cohorts and clock details. Earlier observations are not pooled into this adaptive experiment.

Models and interpretation

Inputs use deterministic extensions of the previous seeded model blocks. The new generator preserves their existing data where dimensions coincide. Facility location now has twice as many customers as candidate sites; bin packing uses ceil(items/3) candidate bins. These dimensions differ from some cases in the previous fixed suite, so this is a separate study.

Category	Natural size	Model variables	Search domain
Knapsack	Items n, both profit variants	n Binary	8..512
Assignment	Tasks/workers n	n*n Binary	3..32
Facility location	Sites n, customers 2*n	n+2nn Binary	2..16
Bin packing	Items n, bins b=ceil(n/3)	n*b+b Binary	4..32
Production planning	Periods n, eight options	8*n Binary	3..48
Circuit routing	Cities n	2*n integer, including cost columns	4..96
Weighted queens	Queens n	4*n integer, including diagonal/cost columns	4..32

Counts compare versions within one category, not difficulty across categories. The native driver and before/current runtime libraries are the same preserved products as the earlier seven-category study. There is no solver algorithm or ABI change in this experiment.

Every accepted solution is independently checked against its original model, objective and auxiliary values. Exact optimality is reported by the backend; this study does not independently recompute all reference optima. Matching reported objective and bound alone is not an independent optimality certificate. Cross-version and repeated optimum disagreements, better feasible peer solutions, contradictory peer bounds, malformed results and process failures reject the study instead of becoming a size boundary.

Execution and reproduction

Every solve uses Native/BAB, Exact, one thread, no starts, seed zero, zero gap allowances and a ten-second internal budget. Capture allows eleven seconds plus at most 0.5 seconds cleanup. The full invocation is bounded to 2,400 seconds, 480 subprocess attempts including loader probes, and 32 distinct sizes per category. Confirmation can reconsider a changed boundary at most six times. A ceiling or unfinished confirmation is reported as unresolved.

The generator, source hashes and search policy are fixed before measurement. Each deterministic input is saved and hashed before its first solve. Every attempt is recorded before launch; raw output, monotonic offsets, search choices and every failed confirmation are retained. Two loader probes establish the actual library cohorts, and final integrity checks cover source, driver, inputs and libraries. Preparation/validation occurs outside internal solve timing.

From the repository root, using the preserved local products:

python3 -B experiments/optimize/benchmark_boundaries.py \

--output-dir build/adaptive-boundaries/results

Choose a new output directory for another study. Existing directories are never overwritten. The runner builds or downloads nothing and does not resume or retry an interrupted solve. Sixteen focused generator/runner tests cover encodings, original validation, independent search behavior, confirmation and budget gates.

The complete portable results are linked from the benchmark page. Earlier fixed category results, capacity results and algorithm results remain separate checkpoints.