chore(bench): a benchmark that times interior point without crossover against simplex on the ladder

[FBumann]

Prompt: Add stacked PRs about the new things we discussed

#1879 merged into its stacked base after that base had already landed, so it never reached main. This PR re-lands it; the follow-up that asked for it was "Fiy it". A later follow-up dropped the how-to: "Do we really want this in the docs?" → "Drop it".

Note

The following content was generated by AI.

bench/crossover.py times HiGHS three ways on a ladder rung: simplex, interior point with crossover, and without. On rung m, no crossover was fastest only on transport, by 13%. No docs or src/ change.

What it is, and what changed from #1879

• bench/crossover.py solves a case's rung three ways: HiGHS's own choice (simplex on these LPs), interior point with crossover, and interior point without. It prints the solve seconds (diagnostics().seconds['solve']: the solve alone, not the build), whether the answer has duals, and the objective's gap relative to simplex. It is not an arm, and it writes no results file. bench/test_harness.py checks that the three ways reach one optimum on dispatch 2xs.
• No how-to. docs(solvers): how to solve an LP by interior point without crossover, and when it paid on the benchmark models #1879 added "Solve an LP by interior point without crossover" to docs/howto/solvers.md. It is dropped here. The one fact specific to specsolve, that such an answer carries no basis, is already in docs/howto/warm-start.md. The rest was each solver's own option names and a verdict of "measure on your own model". With it went the changelog line, and the type is now chore.
• Changed for refactor(api): keep= is gone, and a re-solve carries on from where the last solve ended unless start=None says otherwise #1884. keep= is gone, so each way now gets a model built for it, and no solver state crosses from one way to the next.

Measured on main: HiGHS, rung m, solve seconds

Method: python -m bench.crossover dispatch nodal transport storage --sizes m, then transport nodal again, at 45c540c (main dc2935e plus this branch, whose src/ is main's). Each run started after the 1-minute load average fell below 0.5 on 4 cores, and nothing else ran on the box. transport and nodal ran twice, and their cells are the range.

case	simplex	interior point with crossover	without crossover
dispatch	8.71 s	9.91 s	9.24 s
nodal	3.81–3.93 s	1.94–2.01 s	39.2–41.2 s
transport	33.6–34.0 s	32.1–33.6 s	28.9–29.6 s
storage	72.1 s	228.0 s	207.3 s

On transport, the means are 29.25 s without crossover and 33.81 s for simplex: 13% less. On nodal, the means are 40.19 s without crossover and 1.98 s with it: 20 times as long. Every answer had duals. The largest objective gap to simplex was 6.7e-9 relative (dispatch, without crossover).

#1879 measured the same ranking on every case, on an earlier machine and polars 1.x: 14% on transport, 28 times on nodal.

Full output

dispatch m (2.17995e+09):  simplex 8.708           ipm 9.910 (-4.4e-16)            no crossover 9.236 (+6.7e-09)
nodal m (3.07336e+09):     simplex 3.934 / 3.805   ipm 1.940 / 2.013 (0)           no crossover 41.181 / 39.193 (+4.2e-12)
transport m (9.76456e+08): simplex 33.602 / 34.024 ipm 33.574 / 32.122 (+1.2e-16)  no crossover 28.893 / 29.613 (+1.6e-11)
storage m (9.62692e+08):   simplex 72.095          ipm 228.046 (-5.0e-16)          no crossover 207.286 (+3.1e-09)

Verification

On 94828e9: pixi run check (5325 passed, 566 skipped, 1 xfailed) and pixi run test-bench --i-know-another-is-running (264 passed, 16 skipped). The load guard was overridden because check had just loaded the box, and the harness tests assert correctness, not time.

Deliberately not done

• Gurobi and Xpress are not measured: their bundled licences stop well below rung m.
• Rung l is not measured: storage at m already takes over three minutes for interior point.

🤖 Generated with Claude Code

https://claude.ai/code/session_01GLBvwp6NU7YjszFz5QMRf1

[read-the-docs-community]

Documentation build overview

📚 specsolve | 🛠️ Build #35019228 | 📁 Comparing 94828e9 against latest (8c7bd4b)

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[codspeed]

Merging this PR will not alter performance

✅ 67 untouched benchmarks
⏩ 307 skipped benchmarks¹

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_{Comparing claude/festive-carson-8x46sq-crossover (94828e9) with main (35357c7)²}

Footnotes

1. 307 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

2. No successful run was found on main (76c77c3) during the generation of this report, so 35357c7 was used instead as the comparison base. There might be some changes unrelated to this pull request in this report. ↩