How to create multidimensional sets in JuMP/Julia as in GAMS

Domains Optimization (Mathematical)
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#1

In GAMS, we can create multidimensional sets as follows

Set i       "mining regions"     / china, ghana, ee+ussr, s-leone /
    n       "ports"              / accra, freetown, leningrad, shanghai /
    in(i,n) "mines to ports map" / china  .shanghai
                                   ghana  .accra
                                   ee+ussr.leningrad
                                   s-leone.freetown /;

How can I do the same in JuMP/Julia?

#2

Usually I’d suggest a vector of symbols, but since your regions contain characters like + and - probably a vector of strings is better in your case. Then the mines to ports map could be a dictionary, like so:

regions = ["china", "ghana", "ee+ussr", "s-leone"]
ports = ["accra", "freetown", "leningrad", "shanghai"]
links = Dict("china"  => "shanghai",
             "ghana" => "accra",
             "ee+ussr" => "leningrad",
             "s-leone" => "freetown")

I teach an introductory course in energy system LP modeling. The first assignment is to build (or rather modify) a very simple model of a district heating system. The model was originally written in GAMS but I recently converted it to Julia/JuMP - you might find it useful to see how things can translate. Both versions (and the assignment itself) are available here:

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#3

When I index it in a constraint, I obtain a key error.

Is it not better to have it as a vector of symbols?

#4

It’s very hard to say without seeing the error in context, but key error means you’re trying to look up an element in the dictionary that doesn’t exist. Wild guess: are you doing something like links[x] where x is an integer?

julia> links["china"]
"shanghai"

julia> links[23]
ERROR: KeyError: key 23 not found
#5 
julia> using JuMP

julia> regions = ["china", "ghana", "ee+ussr", "s-leone"]
4-element Array{String,1}:
 "china"
 "ghana"
 "ee+ussr"
 "s-leone"

julia> ports = ["accra", "freetown", "leningrad", "shanghai"]
4-element Array{String,1}:
 "accra"
 "freetown"
 "leningrad"
 "shanghai"

julia> links = [
           "china"  => "shanghai",
           "ghana" => "accra",
           "ee+ussr" => "leningrad",
           "s-leone" => "freetown"
       ]
4-element Array{Pair{String,String},1}:
   "china" => "shanghai"
   "ghana" => "accra"
 "ee+ussr" => "leningrad"
 "s-leone" => "freetown"

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, arcs[r=regions, p=ports; (r => p) in links])
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{String,String}} with 4 entries:
  [s-leone, freetown ]  =  arcs[s-leone,freetown]
  [china, shanghai   ]  =  arcs[china,shanghai]
  [ee+ussr, leningrad]  =  arcs[ee+ussr,leningrad]
  [ghana, accra      ]  =  arcs[ghana,accra]

julia> arcs["s-leone", "freetown"]
arcs[s-leone,freetown]
#6

See also this implementation in JuMP of the classical transport problem in GAMS:

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