Embedding Dual-Fixing into Probing

[Opt-Mucca]

Description

This implement the technique from https://link.springer.com/article/10.1007/s12532-026-00336-z

Locally I've observed 1.5% time improvement and 8% node improvement across all-optimal. It affects roughly 50% of the instances that solve under both settings. That seems to be a bit better than the numbers that are reported in the paper, and I'd chalk it up to (1) I'm using a 30min time limit (2) I happen to have randomly dropped some unlucky MIPLIB instances (3) My implementation is more efficient (4) I fixed some errors in the reference implementation that were missing some fixings.

Edit: Forgot good old (5). I've written incorrect code.

It seems to affect sub-mips extremely heavily, so introduces a lot of noise on instances that are racing for a primal solution. I'd not trust my results without extra testing from @fwesselm (There's not that many instances where the size of the presolved problem changes, and even for those that do, it's usually only a minor reduction)

@fwesselm I tested this before the last commit, so there's a small chance I broke something (I will test it again over the weekend). I realised that copying the object each time a domain is copied doesn't make sense because it's only used in presolve, and now have tried to get a bit fancy with the copy constructors of HighsDomain. Hopefully this shaves off another small time improvement.

Checklist

• I have read the contributing guidelines
• This PR targets the latest branch
• Tests are passing
• Documentation was updated where relevant
• This PR is not primarily AI-generated (per the AI contributions policy in CONTRIBUTING.md)

[Opt-Mucca]

@ZhaoWeiWang0319 feel like reviewing the code? I ended up changing a fair bit, but the core is the same.

[Opt-Mucca]

I clearly still have a bug given the failing tests..... Will fix that now

Edit: @ZhaoWeiWang0319 should now be good to review

[codecov]

Codecov Report

❌ Patch coverage is 96.13260% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 73.29%. Comparing base (f3a6291) to head (47deb3f).
⚠️ Report is 73 commits behind head on latest.

Files with missing lines	Patch %	Lines
highs/mip/HighsImplications.cpp	89.55%	14 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           latest    #3244      +/-   ##
==========================================
+ Coverage   73.21%   73.29%   +0.08%     
==========================================
  Files         445      445              
  Lines      107890   108381     +491     
  Branches    17278    17385     +107     
==========================================
+ Hits        78990    79438     +448     
- Misses      28624    28666      +42     
- Partials      276      277       +1     

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