Added instance generator for KEP #224
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| # ensure that all pairs have at least one in edge and one out edge | ||
| indexes = [(i,j) for i = 1:nb_nodes for j = 1:nb_nodes] | ||
| permutation = shuffle([i for i=1:nb_nodes]) # permutation[i] = j => x[i, j] is branchable | ||
| flat_index_required_branchable = [permutation[i] + (i-1)*nb_nodes for i in 1:nb_nodes] |
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can you briefly explain this ?
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That transform the permutation [2, 1, 3] such that : [2, 1, 3] -> [2, 4, 6]
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alright got it, that's because indexes[i+nb_nodes*j]= (i,j) ? or the contrary ?
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Your last message is right! The idea is that in first place we assign one branchable variable in each line of the matrix with a different column index each time. permutation ensures that each column index is different each time. In that way we ensure that all pairs have at least one incoming arc and one outgoing arc.
| ### Variables ### | ||
| x = Matrix{SeaPearl.AbstractIntVar}(undef, nb_nodes, nb_nodes) | ||
| minus_x = Matrix{SeaPearl.AbstractIntVar}(undef, nb_nodes, nb_nodes) | ||
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| for i = 1:nb_nodes | ||
| for j = 1:nb_nodes | ||
| if (i,j) in index_branchable | ||
| x[i, j] = SeaPearl.IntVar(0, 1, "x_"*string(i)*"_"*string(j), model.trailer) | ||
| SeaPearl.addVariable!(model, x[i, j]; branchable=true) | ||
| minus_x[i, j] = SeaPearl.IntVarViewOpposite(x[i, j], "-x_"*string(i)*"_"*string(j)) | ||
| else | ||
| x[i, j] = SeaPearl.IntVar(0, 0, "x_"*string(i)*"_"*string(j), model.trailer) | ||
| SeaPearl.addVariable!(model, x[i, j]; branchable=false) | ||
| minus_x[i, j] = SeaPearl.IntVarViewOpposite(x[i, j], "-x_"*string(i)*"_"*string(j)) | ||
| end | ||
| end | ||
| end | ||
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| ### Constraints ### | ||
| for i = 1:nb_nodes | ||
| #Check that any pair receives more than 1 kidney | ||
| SeaPearl.addConstraint!(model, SeaPearl.SumLessThan(x[i, :], 1, model.trailer)) | ||
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| #Check that any pair gives more than 1 kidney | ||
| SeaPearl.addConstraint!(model, SeaPearl.SumLessThan(x[:, i], 1, model.trailer)) | ||
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| #Check that for each pair: give a kidney <=> receive a kidney | ||
| SeaPearl.addConstraint!(model, SeaPearl.SumToZero(hcat(x[:, i], minus_x[i, :]), model.trailer)) | ||
| end | ||
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| ### Objective ### | ||
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| #SeaPearl's solver minimize the objective variable, so we use minusNumberOfExchanges in order to maximize the number of exchanges | ||
| minusNumberOfExchanges = SeaPearl.IntVar(-nb_nodes, 0, "minusNumberOfExchanges", model.trailer) | ||
| SeaPearl.addVariable!(model, minusNumberOfExchanges; branchable=false) | ||
| vars = SeaPearl.AbstractIntVar[] | ||
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| #Concatenate all values of x and minusNumberOfExchanges | ||
| for i in 1:nb_nodes | ||
| vars = cat(vars, x[i, :]; dims=1) | ||
| end | ||
| push!(vars, minusNumberOfExchanges) | ||
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| #minusNumberOfExchanges will take the necessary value to compensate the occurences of "1" in x | ||
| objective = SeaPearl.SumToZero(vars, model.trailer) | ||
| SeaPearl.addConstraint!(model, objective) | ||
| SeaPearl.addObjective!(model, minusNumberOfExchanges) | ||
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| nothing |
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I trust you on the model definition as long as is doesn't differ from what has been previously done !
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I have used the same model
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| # the remaining edges are assigned randomly between the non-asssigned elements of the decision matrix | ||
| nb_unassigned_edges = total_edges - nb_nodes | ||
| append!(index_branchable, sample(indexes, nb_unassigned_edges)) |
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very elegant syntax! The fact that splice! removes the value at index i from the array ensures that you cannot append twice the same edge.
Fill a CPModel with the variables and constraints generated. We fill it directly instead of
creating temporary files for efficiency purpose!
The decision matrix
xis the adjacent matrix of the graph (i.e. the instance).x[i, j] is branchable => pair i can receive a kidney from pair j
x[i, j] is not branchable => pair i can not receive a kidney from pair j
The generator ensure that all pairs have at least one in edge and one out edge (i.e. one branchable variable per row and column).
For this we first place one branchable variable in each line of the matrix with a different column index each time.
Then, the remaining edges are assigned randomly between the non-asssigned elements of the decision matrix.