Adjust basis repair for super basic variables. Repeat root solve if cuts make it infeasible

[chris-maes]

Fixes an issue on neos-4413714-turia where basis repair was called during dual push, and the slack needed was superbasic.

Fixes an issue where cbs-cta was incorrectly classified as infeasible after cuts were added.

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[coderabbitai]

📝 Walkthrough

Walkthrough

Extended basis repair to track superbasic variables, added superbasic classification and propagation across crossover/primal/dual flows, updated basis repair/update call sites to accept a superbasic_list, and adjusted branch-and-bound root recovery and iteration/objective accounting.

Changes

Cohort / File(s)	Summary
Basis repair API & impl cpp/src/dual_simplex/basis_solves.hpp, cpp/src/dual_simplex/basis_solves.cpp	basis_repair signature now accepts std::vector<i_t>& superbasic_list. Implementation builds a superbasic_map, handles replacements into nonbasic or superbasic lists, updates swapped variable statuses (NONBASIC/SUPERBASIC), marks replaced column BASIC, and adjusts assertions to include superbasic counts.
Basis update & repair call sites cpp/src/dual_simplex/basis_updates.cpp, cpp/src/dual_simplex/primal.cpp	Introduced a local superbasic_list and updated calls to basis_repair to pass the new parameter (e.g., on initial factorization failure and in primal_phase2).
Crossover & superbasic management cpp/src/dual_simplex/crossover.cpp	Added find_primal_superbasic_variables(...) to classify and produce superbasic_list. Recomputed and propagated superbasic_list at multiple points (after repairs/updates and in push routines) and replaced ad-hoc superbasic removals with explicit recomputation/maintenance.
Branch-and-bound root recovery cpp/src/dual_simplex/branch_and_bound.cpp	Reordered updates to total_lp_iters and root_objective_. Added a recovery path that attempts a scratch re-solve with an advanced-basis solver when root cut status is non-OPTIMAL; updates status, iteration counts, and objective on successful recovery.

Estimated code review effort

🎯 4 (Complex) | ⏱️ ~45 minutes

🚥 Pre-merge checks | ✅ 2 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 0.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly summarizes the two main changes: handling superbasic variables in basis repair and repeating root solve when cuts cause infeasibility issues.

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[coderabbitai]

Actionable comments posted: 0

Caution

Some comments are outside the diff and can’t be posted inline due to platform limitations.

⚠️ Outside diff range comments (1)

cpp/src/dual_simplex/basis_solves.cpp (1)

627-628: ⚠️ Potential issue | 🟡 Minor

Assertion may fail when superbasic variables exist.

The assertion assert(nonbasic_list.size() == n - m) assumes all non-basic variables are in nonbasic_list. However, with the introduction of superbasic support, when superbasic_list is non-empty, this invariant breaks since nonbasic_list.size() + superbasic_list.size() == n - m.

🐛 Proposed fix

 const i_t m = A.m;
 const i_t n = A.n;
 assert(basis_list.size() == m);
-assert(nonbasic_list.size() == n - m);
+assert(nonbasic_list.size() + superbasic_list.size() == n - m);

[chris-maes]

/ok to test a3740e0

[aliceb-nv]

Thank you so much Chris!

[chris-maes]

/ok to test 65af246

[chris-maes]

/ok to test d19b30f

[coderabbitai]

Actionable comments posted: 1

🤖 Fix all issues with AI agents

In `@cpp/src/dual_simplex/branch_and_bound.cpp`:
- Around line 2006-2025: When the recovery solve in
solve_linear_program_with_advanced_basis succeeds, update the cached root
objective and iteration counts: after detecting scratch_status ==
lp_status_t::OPTIMAL (inside the block that sets cut_status =
convert_lp_status_to_dual_status(scratch_status)), recompute root_objective_
from the recovered root_relax_soln_ (so local_lower_bounds_.assign(...,
root_objective_) uses the fresh value) and add the iterations performed by the
recovery solve to exploration_stats_.total_lp_iters; ensure any other derived
quantities depending on the root solution (e.g., gap calculations reported
later) are consistent with the new root_objective_.

[chris-maes]

/ok to test 48b9e88

[coderabbitai]

Actionable comments posted: 1

🤖 Fix all issues with AI agents

In `@cpp/src/dual_simplex/branch_and_bound.cpp`:
- Around line 1994-1996: The iteration count is coming from the out-parameter
iter returned by dual_phase2_with_advanced_basis, not from
root_relax_soln_.iterations, so replace uses of root_relax_soln_.iterations for
accounting with iter and then store iter into root_relax_soln_.iterations;
specifically update exploration_stats_.total_lp_iters to add iter instead of
root_relax_soln_.iterations and set root_relax_soln_.iterations = iter after
calling dual_phase2_with_advanced_basis so future code sees the populated value.

[chris-maes]

/ok to test 4e1d35c

[chris-maes]

/merge