When I use the quadratic_marginal_cost attribute in PyPSA in combination with HiGHS, I

This is weird, as all the tests seem to be fine. Things like <div class="highlight

`linopy` does not pass quadratic objective terms to HiGHS about linopy HOT 3 CLOSED

fneum commented on June 20, 2024

`linopy` does not pass quadratic objective terms to HiGHS

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Comments (3)

FabianHofmann commented on June 20, 2024

This is weird, as all the tests seem to be fine. Things like

m = linopy.Model()

lower = pd.Series(0, range(10))
x = m.add_variables(lower, name="x")
y = m.add_variables(lower, name="y")

m.add_constraints(x + y >= 10)

m.add_objective(- 2 * x + y + x * x)

m.solve(solver_name="highs")

yield the same result for highs and gurobi. and also the model definition seems totally fine when running test for pypsa networks (however it does not solve with highs). Did it explicitly say that it is trying to solve a LP in your case? and are the dual non-zero?

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fneum commented on June 20, 2024

I think I understand this now.

Let's take a simple LP file with quadratic terms:

min

obj:

-4 x0 -6 x1 + [ + 4 x0 * x0 + 12 x1 * x1 ] / 2

s.t.

c0: +1 x0 +2 x1 >= +4

bounds

+0 <= x0 <= +4
+0 <= x1 <= +4
end

If we run

import highspy
h = highspy.Highs()
h.readModel("test-highs.lp")
h.run()

we get the correct solution:

Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d-dirty]
Copyright (c) 2023 HiGHS under MIT licence terms
<HighsStatus.kOk: 0>
0, 16.000001, 0, 0.000281, 0.000000, 0, 0.000000, 0.000000
4, -0.071428, 1, 0.000331, 0.000000, 0, 0.000000, 1.000000
Model   status      : Optimal
QP ASM    iterations: 4
Objective value     : -7.1428571429e-02
HiGHS run time      :          0.00

However, if we specify "ipm" as solver:

import highspy
h = highspy.Highs()
h.readModel("test-highs.lp")
h.setOptionValue("solver", "ipm")
h.run()

we get a different result:

Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d-dirty]
Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
0 rows, 0 cols, 0 nonzeros
0 rows, 0 cols, 0 nonzeros
Presolve : Reductions: rows 0(-1); columns 0(-2); elements 0(-2) - Reduced to empty
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Objective value     : -4.0000000000e+01
HiGHS run time      :          0.00

I always assumed that HiGHS would be using the same IPM solver for linear as for quadratic problems, but this does in fact not seem to be the case (ERGO-Code/HiGHS#766). The documentation of HiGHS also notes that implicitly:

solver

Solver option: "simplex", "choose" or "ipm". If "simplex"/"ipm" is chosen then, for a MIP (QP) the integrality constraint (quadratic term) will be ignored
Type: string
Default: "choose"

So, no problem with linopy.

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FabianHofmann commented on June 20, 2024

Great that you cleared that up!

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