Conditional Constraint Construction Based on Input Data Presence/Absence of Set Combinations in Julia JUMP

Specific Domains Optimization (Mathematical)
2

This question has come up a few times recently (Suggestions for documentation improvements · Issue #2348 · jump-dev/JuMP.jl · GitHub), so I definitely need to write some guidance on transitioning from GAMS to JuMP.

Can you provide a reproducible example of what you currently have, as well as the input data file? I’ll have a go to see how I would write your model.

Transitioning from GAMS to JuMP is a little complicated, because of the way we differ in handling data.

For example, GAMS lets you create “dense” sets and variables, and then index them using for-if loops. This means a direct translation of your GAMS code would try to look like:

model = Model()
@variable(model, x[A, B])
@constraint(model, [a in A], sum(x[a, b] for b in B if something(a, b)) == 1)

If there are very few values of a and b for which something(a, b) is true (that is, x is sparse), then this approach is inefficient because it requires a loop over every element in B for every element in A, just to throw away most of the work because something(a, b) == false.

The for-if approach works in GAMS because behind the scenes, GAMS translates this into a much more efficient format using relational algebra. But the for-if approach doesn’t work in JuMP because we don’t do the translation.

One approach is to only create variables for which the result is non-zero:

a_to_b = Dict(a => [] for a in A)
for a in A, b in B
    if something(a, b)
        push!(a_to_b[a], b)
    end
end
model = Model()
@variable(model, x[a in A, b in a_to_b[a]])
@constraint(model, [a in A], sum(x[a, b] for b in a_to_b[a]) == 1)

The other approach is to change your data structure to something like a DataFrame:

import DataFrames
df = DataFrames.DataFrame([(a = a, b = b) for a in A, b in B if something(a, b)])
model = Model()
df.x = @variable(model, x[1:size(df, 1)])
for gdf in DataFrames.groupby(df, [:a])
    @constraint(model, sum(gdf.x) == 1)
end

Here are some other links:

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