Min-Cost Flow Problem

[torressa]

Description

Implements min-cost flow from #11.

Checklist

• Implementation:
  • Implementation of the Mod in the gurobi_optimods installable package
  • Tests for the Mod implementation in tests/
  • Docstrings for public API, correctly linked using sphinx-autodoc
• Documentation page:
  • Problem specification with description tab and optimisation model tab
  • Example of the input data format (use gurobi_optimods.datasets for loading data)
  • Runnable code example
  • Presentation of solutions

Have a nice day!

[torressa]

@stevedwards, @simonbowly I've found that we can use networkx.convert_matrix.to_scipy_sparse_array to get multiple edge attributes out (as independent matrices):

>>> import networkx as nx
>>> G = nx.DiGraph()
>>> G.add_edge(0, 1, weight=1.0, capacity=2.0)
>>> G.add_edge(1, 2, weight=3.0, capacity=4.0)
>>> print(nx.to_scipy_sparse_array(G, weight="weight"))
  (0, 1)        1.0
  (1, 2)        3.0
>>> print(nx.to_scipy_sparse_array(G, weight="capacity"))
  (0, 1)        2.0
  (1, 2)        4.0

Alternatively, we can add networkx directly (or use pandas), I don't mind, but it would be good to have an agreement between optiflowmods.

[torressa]

Hey @simonbowly could you please check if the idea of d994dd4 is OK?
I'm thinking of separating all of the mods that were initially in my network_flow file out into separate files (including docs).
I started with the weirdest one min_cost_flow. Following our discussion from #47 I think for this case it makes sense to keep functions separate (as the inputs are different for each case: pandas, scipy and networkx) and the users should be the ones taking care here. But as you said #47 (comment), this looks a bit weird so just want to be sure.

The other ones I will write in the same vein as your matching problem (a single entry point with hidden functions for different interfaces).

[simonbowly]

This looks good to me. In the docs for min cost flow, the networkx example is very cluttered. You could make this a bit easier to read by:

• Loading a networkx graph directly from datasets. There's no need to show the user how to convert from pandas to networkx if the mod will handle either case equally easily.
• Remove the pos attributes from the graph, since they aren't required to solve the mod. Just include them when plotting.

It also might make sense to change the doc structure a bit. You don't have to stick to specification -> code -> solution exactly. In this case it might make more sense to have separate sections for each input format, or you could use synced tabs to switch all examples/output to be relevant to the input format the user wants.

[simonbowly]

@torressa this is looking great! I added a few specific comments. Overall I think the documentation looks a little sparse - do you think it needs a bit more detail?

[torressa]

I think I've addressed all the comments (not sure if marking them as resolved is what one does?).

I've fleshed out the formulation explanation a bit more. Would you like to see more content in the min-cost-flow.rst? I'm not sure I can say much more, maybe on a more inspired day.

[simonbowly]

Nice one, thanks for the great work! Yeah I know the feeling, let's merge this and wait to see if inspiration strikes later :-)