What is the best way to separate out indices of a variable?

Specific Domains Optimization (Mathematical)
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1

Hi guys,

What do you recommend to do in this situation?

I have a set M consisting of three separate sets of vectors of various size. In other words M = [m_1, m_2, m_3] where m_i are vectors of different sizes. For instance m_1 could be 1:10 while m_2 = 22:65 and m_3 = 100:123(these are separate, no intersection in their elements).

with that, there need to have a variable x[i,j,m] to have some constraints as the following:

# N is a set which contains all net nodes 
# x,z are variables

x[i,j,m] >= z[i,j]    for all i,j in N and m in M

Now, we have another variables that are only defined on m_i like y[i,j,m_1]. So, at some points in some constraints, there’s only need to put condition over a subset of M (not all of its components). Similar to the following:

#I'm not writing like julia-- more like math version

sum(x[i,j,m] for i in N) <= y[i, m]   for all  j in N and m in m_1

I did try to do this by:

@constraint(model, [j in N, m in m_1], sum( x[i,j,m]  for i in N) <=  y[i, m] )

This is not working though. Do you know how to do this? having a variables that can act both over the whole set M and also act locally over just m_1 or just m_2
I’m not sure if the issue is variable either. What I need to find out is that how to have flexible variable x that can handle M and m_1 at the same time.

Thanks all!

2

I think you need something like this:

M = [1:2, 4:5, 7:8]
model = Model()
all_M = unique(reduce(vcat, M))
@variable(model, x[all_M])
@expression(model, sum(x[m] for m in all_M))
@expression(model, sum(x[m] for m in M[1]))

What probably happened is that it used m_1, m_2, an m_3 as the keys of the variable, not the values of the m_ vectors as the keys.

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4

I would say that the former is better for a single @variable declaration, since you’re not allocating an intermediate array (x_indices) but allowing JuMP to generate variables directly from your separate index sets. The latter is virtually equivalent but necessary if reusing an index set like x_indices in multiple locations.

There is the concept of generating values on demand in general in Julia: Generator Expressions.

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5

Thanks for your info and the link @jd-foster I’ll check it out!

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