MIP Row and Objective Scaling

[akifcorduk]

mip_scaling_strategy.cu implements a GPU-accelerated row-scaling and objective-scaling strategy for MIP problems that improves numerical conditioning before solving.

Objective scaling (scale_objective): scales small objective coefficients up so the smallest nonzero magnitude reaches a minimum threshold (~1e-2), guarded by a max-coefficient cap to avoid blowing up large values.

Iterative row scaling (scale_problem): runs up to 8 iterations of per-row scaling to reduce the log2-spread of row infinity norms across the constraint matrix. Each iteration:

• Computes a median-based target norm (excluding big-M and zero-RHS rows for outlier robustness)
• Picks a per-row scaling factor clamped to [1/32, 32], with tighter [1/16, 1] limits for big-M rows and rows that are already numerically large
• Preserves integer coefficient integrality for integer variables by preferring power-of-two scaling factors (exact in IEEE 754) or integer-GCD-preserving multipliers
• Tracks cumulative scaling per row within a [1/256, 256] band
• Stops early when the spread improvement stalls below a relative tolerance

The current optimal setup is with only row scaling, that's why I have left row scaling only as default.

This also fixes a bug of setting lower bound of an approximate PDLP and Barrier solution. Now we set the bound only if the relaxation solution is fully feasible on absolute per row tolerances. With main+bug fix, number of infinite mip_gaps are 5-6 instances, with scaling it is only 1. So, scaling is able find 4-5 instances in with the absolute feasible root relaxation (does not necessarily mean basic solution in dual simplex).

Overall we are able to find 2 more optimal solutions compared to main + lower bound bug fix. And ~1% mip gap improvement.

Summary by CodeRabbit

• New Features

  • MIP row-scaling enabled by default for improved numeric robustness.
  • Solver returns partial results early when time limits are reached; time-limit enforcement is more proactive.
  • New selectable MIP scaling configurations with logging of the selected scaling setup.

• Bug Fixes

  • Fixed inconsistent unscaling and feasibility handling to prevent mismatched solution states.

• Chores

  • Removed a deprecated MIP configuration option.
  • Consolidated and replaced the scaling strategy; tests and build updated accordingly.

[chris-maes]

LGTM. Thanks Akif

[Iroy30]

lgtm on python

[akifcorduk]

/merge