[FlopCpp] Better way of modeling a graph problem

[Arman Boyacı]

Hello,

I am dealing with a multi-commodity flow problem and I am trying to solve a
relatively big instance: *800,000* variables and* 25,000 *constraints.
In order to be able to control solver options, I first write the model into
an MPS file. However it takes more than *2* hours only the model.attach()
process.

I am aware that the instance size is not small and it will take time to
solve it. But the modeling process time should be shorter, the current
situation does not make sense to me.
In the multi-commodity flow problem model, the only important set of
constraints is the flow conservation constraints:

FlowConservation(V,Z) = SUM(A, Incidence(V,A)*Flow(A,Z) ) == Demand(V,Z)

A: arcs
V: vertices
Z: requests
Incidence matrix contains the graph structure

I am suspecting that this multiplication (incidence*flow) causes the
problem.
Is there a better way of doing this (with conditional for example)?

Otherwise what can be other reasons for this problem? Any idea?

Thanks in advance.

*- Arman*
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