perf(hybridz): accelerate objective-bound solving

[Kaijie-liu]

The final PR: Accelerates HybridZ solving.

[codecov]

Codecov Report

❌ Patch coverage is 86.78571% with 37 lines in your changes missing coverage. Please review.
✅ Project coverage is 75.82%. Comparing base (f1bc0f1) to head (7f8f847).

Files with missing lines	Patch %	Lines
act/back_end/solver/solver_hz.py	86.59%	37 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #114      +/-   ##
==========================================
+ Coverage   74.97%   75.82%   +0.85%     
==========================================
  Files          91       91              
  Lines       22230    22482     +252     
==========================================
+ Hits        16666    17048     +382     
+ Misses       5564     5434     -130     

Flag	Coverage Δ
bab	43.78% <7.14%> (-0.41%)	⬇️
backend-float32	47.06% <7.50%> (-0.44%)	⬇️
backend-float64	49.99% <64.64%> (+0.86%)	⬆️
frontend	31.04% <7.14%> (-0.27%)	⬇️
pipeline-fuzz	20.32% <7.14%> (-0.14%)	⬇️
pipeline-verify	41.64% <37.14%> (+0.21%)	⬆️

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Files with missing lines	Coverage Δ
act/back_end/hybridz_tf/tf_mlp.py	86.78% <100.00%> (+0.04%)	⬆️
act/back_end/solver/solver_hz.py	80.41% <86.59%> (+12.43%)	⬆️

... and 4 files with indirect coverage changes

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[yuleisui]

Need to fix the CI coverage.

[guanqin-123]

why we need this new 'private' class?

[Kaijie-liu]

This is the key of solver speedup. It keeps one HiGHS LP model live when checking multiple output objectives. The constraints stay the same, so rebuilding the model for every output row is wasteful. We only update the objective and reuse the model, then run MIP only for rows the LP cannot decide. It is private because only HZSolver uses it internally.

[guanqin-123]

What is multiple output?
And I assume it only belongs to HZSolver, and the rest of the other solvers are not accessible to it.