test unit invariance of objective function coefficient

[luke-kiernan]

What the title says: put the same physical data in different unit systems and check that we get the same objective function coefficient in each case.

[Copilot]

Pull request overview

Adds regression tests to ensure objective-function coefficients derived from linear and quadratic cost curves are invariant to the unit system used to express the same underlying physical costs (natural units vs system-base vs device-base), strengthening correctness around unit conversions in objective construction.

Changes:

• Add unit-system invariance test coverage for CostCurve{LinearCurve} objective coefficients.
• Add unit-system invariance test coverage for CostCurve{QuadraticCurve} linear and quadratic objective coefficients.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
test/test_linear_curve.jl	Adds a testset verifying linear-cost objective coefficients match across NATURAL_UNITS, SYSTEM_BASE, and DEVICE_BASE representations of the same physical rate.
test/test_quadratic_curve.jl	Adds a testset verifying both linear and quadratic objective coefficients match across NATURAL_UNITS, SYSTEM_BASE, and DEVICE_BASE representations of the same physical quadratic cost.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[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_2026-07-21T19-38-15.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   0.0253   0.0039

NLP (Uno)       -     40     105      0     0.956760   0.0000         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0011   0.0010

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   0.0049   1.4221
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   0.0052   6.0257
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  21.4280

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   1.3931
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   5.9888
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   0.0026  14.4101

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   0.0032   4.6955
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   0.0031  10.7444
Bin2+Saw        8    550    1915    240     0.956996   0.0247    0.0072     0.956927  7.52e-02  1.68e-01  1.37e+02  2.09e+02   0.0037  40.5603

HybS+sSOS       4    310    1165      0     0.812261  15.1030    0.0000     0.812261  5.52e-01  1.00e+00  2.04e+02  2.97e+02   0.0064   2.1499
HybS+sSOS       6    410    1545      0     0.891208   6.8515    0.0000     0.891208  5.49e-01  1.00e+00  3.69e+02  7.09e+02   0.0065   3.9635
HybS+sSOS       8    510    1925      0     0.934789   2.2965    0.0087     0.934707  5.48e-01  1.00e+00  3.47e+02  5.22e+02   0.0072  12.5145

HybS+mSOS       4    390    1345     80     0.812261  15.1030    0.0046     0.812224  5.52e-01  1.00e+00  2.04e+02  2.97e+02   0.0030   2.3382
HybS+mSOS       6    530    1805    120     0.891208   6.8515    0.0000     0.891208  5.49e-01  1.00e+00  3.69e+02  7.09e+02   0.0034   5.0127
HybS+mSOS       8    670    2265    160     0.934789   2.2965    0.0047     0.934744  5.48e-01  1.00e+00  3.47e+02  5.22e+02   0.0038  12.9876

HybS+Saw        4    390    1525     80     0.951869   0.5113    0.0021     0.951849  5.48e-01  1.00e+00  2.16e+03  4.23e+03   0.0033  10.9093
HybS+Saw        6    530    2105    120     0.956386   0.0391    0.0099     0.956291  5.48e-01  1.00e+00  4.57e+02  7.57e+02   0.0039  26.8631

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_2026-07-21T19-43-51.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   0.0249   0.0037

NLP (Uno)       -     40     105      0     0.956760   0.0000         -            -  0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.0011   0.0010

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   0.0051   1.4134
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   0.0053   6.0046
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   0.0055  21.3921

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   0.0020   1.3875
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   0.0021   5.9744
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   0.0022  14.3725

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   0.0027   4.6542
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   0.0032  10.6184
Bin2+Saw        8    550    1915    240     0.956996   0.0247    0.0072     0.956927  7.52e-02  1.68e-01  1.37e+02  2.09e+02   0.0037  40.2537

HybS+sSOS       4    310    1165      0     0.812261  15.1030    0.0000     0.812261  5.52e-01  1.00e+00  2.04e+02  2.97e+02   0.0064   2.1384
HybS+sSOS       6    410    1545      0     0.891208   6.8515    0.0000     0.891208  5.49e-01  1.00e+00  3.69e+02  7.09e+02   0.0068   3.9458
HybS+sSOS       8    510    1925      0     0.934789   2.2965    0.0087     0.934707  5.48e-01  1.00e+00  3.47e+02  5.22e+02   0.0070  12.4340

HybS+mSOS       4    390    1345     80     0.812261  15.1030    0.0046     0.812224  5.52e-01  1.00e+00  2.04e+02  2.97e+02   0.0028   2.3279
HybS+mSOS       6    530    1805    120     0.891208   6.8515    0.0000     0.891208  5.49e-01  1.00e+00  3.69e+02  7.09e+02   0.0033   4.9988
HybS+mSOS       8    670    2265    160     0.934789   2.2965    0.0047     0.934744  5.48e-01  1.00e+00  3.47e+02  5.22e+02   0.0037  12.9418

HybS+Saw        4    390    1525     80     0.951869   0.5113    0.0021     0.951849  5.48e-01  1.00e+00  2.16e+03  4.23e+03   0.0032  10.8696
HybS+Saw        6    530    2105    120     0.956386   0.0391    0.0099     0.956291  5.48e-01  1.00e+00  4.57e+02  7.57e+02   0.0039  26.8115