Precompilation workload

[jd-lara]

We can precompile certain aspects like the code to create containers without the system.

[github-actions]

Performance Results
Main

Network: 10 nodes, 13 edges, 3 cost segments
Generators: 5, Demands: 5
Loss coefficients (a, b, c) per generator:
  n1: a=0.007287  b=0.005968  c=0.003850
  n2: a=0.001094  b=0.009002  c=0.007028
  n3: a=0.007897  b=0.008552  c=0.003001
  n4: a=0.008179  b=0.002530  c=0.009637
  n5: a=0.009778  b=0.009934  c=0.009099

Solver logs: /home/runner/work/InfrastructureOptimizationModels.jl/InfrastructureOptimizationModels.jl/main/test/performance/logs/solver_2026-07-24T12-50-24.log

==============================================================================================================================================
Bilinear Approximation Benchmarks
  Refinement = depth for all methods
==============================================================================================================================================
Method          R   Vars Constrs   Bins    Objective   Gap(%) MIPGap(%)     LowerBnd  rmse δbi   max δbi   rmse δq    max δq  build_t  solve_t
----------------------------------------------------------------------------------------------------------------------------------------------
NLP (Ipopt)     -     40     105      0     0.956760        -         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0319   0.0045

NLP (Uno)       -     40     105      0     0.956760   0.0000         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0013   0.0011

Bin2+sSOS       4    190     535      0     1.180700  23.4061    0.0000     1.180700  8.07e-02  1.41e-01  2.49e+01  5.48e+01   0.0053   1.7688
Bin2+sSOS       6    250     655      0     1.098175  14.7806    0.0000     1.098175  1.26e-01  2.86e-01  5.47e+00  9.07e+00   0.0057   7.3457
Bin2+sSOS       8    310     775      0     1.053069  10.0661    0.0088     1.052976  8.62e-02  2.43e-01  4.18e+01  9.32e+01   0.0057  26.0702

Bin2+mSOS       4    310     805    120     1.180700  23.4061    0.0000     1.180700  8.07e-02  1.41e-01  2.49e+01  5.48e+01   0.0024   1.7164
Bin2+mSOS       6    430    1045    180     1.098175  14.7806    0.0092     1.098074  1.26e-01  2.86e-01  5.47e+00  9.07e+00   0.0025   7.3196

This branch

Network: 10 nodes, 13 edges, 3 cost segments
Generators: 5, Demands: 5
Loss coefficients (a, b, c) per generator:
  n1: a=0.007287  b=0.005968  c=0.003850
  n2: a=0.001094  b=0.009002  c=0.007028
  n3: a=0.007897  b=0.008552  c=0.003001
  n4: a=0.008179  b=0.002530  c=0.009637
  n5: a=0.009778  b=0.009934  c=0.009099

Solver logs: /home/runner/work/InfrastructureOptimizationModels.jl/InfrastructureOptimizationModels.jl/branch/test/performance/logs/solver_2026-07-24T12-52-50.log

==============================================================================================================================================
Bilinear Approximation Benchmarks
  Refinement = depth for all methods
==============================================================================================================================================
Method          R   Vars Constrs   Bins    Objective   Gap(%) MIPGap(%)     LowerBnd  rmse δbi   max δbi   rmse δq    max δq  build_t  solve_t
----------------------------------------------------------------------------------------------------------------------------------------------
NLP (Ipopt)     -     40     105      0     0.956760        -         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0309   0.0044

NLP (Uno)       -     40     105      0     0.956760   0.0000         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0012   0.0012

Bin2+sSOS       4    190     535      0     1.180700  23.4061    0.0000     1.180700  8.07e-02  1.41e-01  2.49e+01  5.48e+01   0.0057   1.7607
Bin2+sSOS       6    250     655      0     1.098175  14.7806    0.0000     1.098175  1.26e-01  2.86e-01  5.47e+00  9.07e+00   0.0058   7.3464
Bin2+sSOS       8    310     775      0     1.053069  10.0661    0.0088     1.052976  8.62e-02  2.43e-01  4.18e+01  9.32e+01   0.0058  26.2324

Bin2+mSOS       4    310     805    120     1.180700  23.4061    0.0000     1.180700  8.07e-02  1.41e-01  2.49e+01  5.48e+01   0.0024   1.7370
Bin2+mSOS       6    430    1045    180     1.098175  14.7806    0.0092     1.098074  1.26e-01  2.86e-01  5.47e+00  9.07e+00   0.0025   7.4007
Bin2+mSOS       8    550    1285    240     1.053069  10.0661    0.0045     1.053021  8.62e-02  2.43e-01  4.18e+01  9.32e+01   0.0025  17.8432

Bin2+Saw        4    310    1075    120     0.985823   3.0376    0.0000     0.985823  1.08e-01  2.49e-01  1.11e+02  2.44e+02   0.0031   5.7855
Bin2+Saw        6    430    1495    180     0.958677   0.2004    0.0077     0.958603  7.52e-02  1.68e-01  8.94e+01  1.71e+02   0.0037  13.2096

[odow]

See one problem with this is that it is precompiling a bunch of methods for _WorkloadVariable, which will never be used in any user's script.

[jd-lara]

yeah, we need another strategy here. Perhaps the precompilation workload can use PSY or we can make better methods that can be precompiled correctly with appropriate typing