Fixing the value of some variables when defining it, not in the constraints

Specific Domains Optimization (Mathematical)
1

I’m very new to JuMP so this might be a trivial question.

We have a binary variable x_{ij}. We would like to set x_{ij} to be zero for some i and some j. So for example, nodes 1:10 cannot be assigned to nodes 1:5. So here’s what I did so far

for i = 1:10
    for j = 1:5
        @constraint(model, x[i, j] == 0)
    end
end

But I was wondering if this would increase the solution time and if there's a way to fix those variables when defining $x$ so the processing time is shorter?
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2

The @variable has keyword arguments lower_bound and upper_bound, if you set both to zero this will have the same effect as using a constraint to force equality to zero. There are also the JuMP.fix and JuMP.unfix. I do not believe any of these solutions should have a big impact on the solving time, but it is always good to profile your specific case.

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3

Hi @CactusHamster (I’m guessing you’re the same CactusHamster as modeling - Coding some parameters with index zero in Julia - Operations Research Stack Exchange :smile:).

To slightly elaborate on what @Henrique_Becker said,

for i=1:10, j=1:5
    @constraint(model, x[i, j] == 0)
end

will add 50 new linear constraints to your problem (rows to the constraint matrix). These should get pre-solved out by the solver, but it’s still work that needs to be done.

In contrast,

for i=1:10, j=1:5
    fix(x[i, j], 0.0)  # potentially with `; force = true` if there are other bounds
end

will set the lower and upper bounds of x[i, j] to 0.0. This will not add any new constraints so it might be a bit faster.

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