[Pyomo.DoE] Add simultaneous design of multiple experiments

[smondal13]

Fixes # .

Summary/Motivation:

This PR adds a new DesignOfExperiments.optimize_experiments() API in pyomo/contrib/doe/doe.py to support simultaneous optimization of multiple experiments in one workflow. The motivation is to provide a multi-experiment DoE interface with stronger initialization options, clearer mode handling (template vs. user-initialized experiments), and richer diagnostics/results than the existing single-experiment path.

Changes proposed in this PR:

• Added API optimize_experiments() for multi-experiment DoE optimization.
• Added Cholesky-based D- and A-optimality objective and Greybox-based D-, A-, E-, and ME- optimality objective
• Implemented two operating modes:
  • Template mode: pass one experiment and set n_exp.
  • User-initialized mode: pass a list of experiments; n_exp is inferred/validated.
• Added optional LHS-based initialization (initialization_method="lhs") with controls for:
  • sample count, seed, candidate evaluation parallelism, combination fim metric scoring parallelism,
  • worker count, chunk size, parallel threshold, and optional wall-clock budget.
• Added symmetry-breaking constraints for multi-experiment solves:
  • supports user-specified variable through sym_break_cons suffix,
  • falls back to the first experiment input with a diagnostic warning when not provided.
• Expanded output for this API:
  • per-scenario and per-experiment results (designs, outputs, measurement errors, FIM/sensitivities),
  • aggregated FIM metrics, timings, settings, names, diagnostics, and structured run_info.
• Added JSON-safe serialization via _DoEResultsJSONEncoder for numpy/Pyomo-enum values when writing results_file.

Note:

• Added new documentation.md which describes the API. This documentation is to help the reviewers to understand the API and will not be merged into Pyomo:main

Remove before merging

• documentation.md
• rb_multi.py

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[smondal13]

@blnicho @mrmundt All the tests are passing except win/3.11 with

INFO: The following extensions were downloaded:
    [FAIL]  gjh
    [ OK ]  mcpp

[smondal13]

@mrmundt and @blnicho , all the comments are addressed, and all the tests are passing now.

[slilonfe5]

@mrmundt @blnicho, Shuvo has addressed all the comments. This looks pretty good to me. Any final review would be appreciated; otherwise, I think we are good to go.

[codecov]

Codecov Report

❌ Patch coverage is 91.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 90.15%. Comparing base (3603b1e) to head (a20061b).
⚠️ Report is 6 commits behind head on main.

Files with missing lines	Patch %	Lines
pyomo/contrib/doe/grey_box_utilities.py	91.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3866      +/-   ##
==========================================
+ Coverage   90.11%   90.15%   +0.03%     
==========================================
  Files         909      909              
  Lines      108580   109236     +656     
==========================================
+ Hits        97847    98477     +630     
- Misses      10733    10759      +26     

Flag	Coverage Δ
builders	28.98% <91.66%> (-0.12%)	⬇️
default	86.17% <91.66%> (?)
expensive	34.97% <91.66%> (?)
linux	87.68% <91.66%> (-1.93%)	⬇️
linux_other	87.68% <91.66%> (+0.05%)	⬆️
oldsolvers	27.90% <8.33%> (-0.15%)	⬇️
osx	83.09% <8.33%> (+0.03%)	⬆️
win	85.44% <91.66%> (+0.07%)	⬆️

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[adowling2]

@smondal13 This PR is now showing merge conflicts.

[adowling2]

I think this is practically ready. I requested a few small comments. Also, there is a merge conflict (I think).

[smondal13]

I think this is practically ready. I requested a few small comments. Also, there is a merge conflict (I think).

@adowling2 I have addressed your comments. @adowling2 @mrmundt, I have resolved the conflicts. The conflicts were from @adowling2's recent PR #3867 merge into Pyomo:main.

[smondal13]

@mrmundt @blnicho, the following two tests are failing. I think these two are not part of my PR

=========================== short test summary info ============================
FAILED pyomo/contrib/iis/tests/test_iis.py::TestIIS::test_write_iis_any_solver - SystemError: <method 'write' of '_io.FileIO' objects> returned a result with an exception set
FAILED pyomo/contrib/iis/tests/test_iis.py::TestIIS::test_write_iis_cplex - SystemError: <method 'write' of '_io.FileIO' objects> returned a result with an exception set

[blnicho]

@smondal13 those failures were resolved in #3965 and I merged main into your PR to pick up the fix.

[smondal13]

@blnicho @mrmundt this one is failing due to download issue

downloaded:
[FAIL] gjh
[ OK ] mcpp
Error: Process completed with exit code 1.

[smondal13]

@blnicho @mrmundt Two tests are failing in this PR, which are not related to the PR.