How to relax all variables of a model to be continuous

[carlosgmartin]

Is there a straightforward way to take a model object and relax all of its variables to be continuous?

For comparison, mip has a Model.relax method that does this.

[jajhall]

Yes, set the option

solve_relaxation = true

[ZedongPeng]

Hi @jajhall . Does solve_relaxation also work for presolve if I only want the presolved model? Thanks.

[jajhall]

No, and perhaps it should, so you'd have to set the integrality of all variables to HighsVarType::kContinuous (in C++)

[ZedongPeng]

Thank you @jajhall . I tried the following code, but it does not work. Could you give me an example to relax all variables in highspy?

    lp = model.getLp()
    for i in range(lp.num_col_):
        lp.integrality_[i] = highspy.HighsVarType.kContinuous
    model.passModel(lp)

[jajhall]

That relaxes all the variables in highspy. In what way does it not work?

[ZedongPeng]

Here is the code I tried and the output.

    model = highspy.Highs()
    model.readModel("2club200v15p5scn.mps")
    print("# of integer vars (before relaxation) = ", sum(v != highspy.HighsVarType.kContinuous for v in model.getLp().integrality_))

    lp = model.getLp()
    for i in range(lp.num_col_):
        lp.integrality_[i] = highspy.HighsVarType.kContinuous
    model.passModel(lp)

    print("# of integer vars (after relaxation) = ", sum(v != highspy.HighsVarType.kContinuous for v in model.getLp().integrality_))

Running HiGHS 1.11.0 (git hash: 364c83a): Copyright (c) 2025 HiGHS under MIT licence terms
Number of BV entries in BOUNDS section is 200
# of integer vars (before relaxation) =  200
# of integer vars (after relaxation) =  200

[jajhall]

The following works, but don't ask me why! I'm not a Python programmer. Previously the values of lp.integrality_ weren't changing if assigned in the loop.

That your reasonable approach doesn't work, and my approach - which, to me, looks equivalent to yours - does work, is a real indication of what a terrible language Python is!

Although the call to passModel was fine, note that if you have any odd behaviour, check the return status

model = highspy.Highs()
model.readModel("2club200v15p5scn.mps")
print("# of integer vars (before relaxation) = ", sum(v != highspy.HighsVarType.kContinuous for v in model.getLp().integrality_))

lp = model.getLp()
integrality = lp.integrality_
for i in range(lp.num_col_):
    integrality[i] = highspy.HighsVarType.kContinuous

lp.integrality_ = integrality

status = model.passModel(lp)

print(" model.passModel(lp) returns ", status)

print("# of integer vars (after relaxation) = ", sum(v != highspy.HighsVarType.kContinuous for v in model.getLp().integrality_))

[ZedongPeng]

Your code works as expected. Thank you @jajhall .
The reason might be related to how lp.integrality_ is implemented. Although it appears to be a mutable list, it may internally behave like an immutable or read-only structure due to the underlying C++ bindings.

[jajhall]

Your code works as expected. Thank you @jajhall . The reason might be related to how lp.integrality_ is implemented. Although it appears to be a mutable list, it may internally behave like an immutable or read-only structure due to the underlying C++ bindings.

That sounds far from obvious. It can't be just read-only, otherwise lp.integrality_ = integrality would fail - or am I being too rational!

[ZedongPeng]

One more question. I tried the code with the datt256_lp instance. The length of lp.integrality_ is zero. Is this expected?

import highspy

model = highspy.Highs()
model.readModel("datt256_lp.mps")
lp = model.getLp()
integrality = lp.integrality_
print("lp.integrality_ = ", len(lp.integrality_))

Running HiGHS 1.7.0 (git hash: 27ccfaa): Copyright (c) 2024 HiGHS under MIT licence terms
len(lp.integrality_) =  0

[jajhall]

One more question. I tried the code with the datt256_lp instance. The length of lp.integrality_ is zero. Is this expected?

This file is the LP relaxation of datt256 so, yes, the length of lp.integrality_ should be zero