Modeling network flow problem in Python

[ron-at-swgy]

Hello,

I'm implementing a network flow problem using pywraplp. The constraints that allow "picking a path" require that the sum of all selected routes out of the start minus all selected routes into the start must be 1. The sum of all selected routes out of the goal minus all selected routes into of the goal must be -1. Lastly, the sum of all edges selected into and out of nodes other than the start and the end muse be zero (flow balance).

My question is about expressing this in the Constraint class. How can I say "sum this set of decision variables and subtract this set of decision variables and that must be 1"?

Now we start definining the constraints. First, constraint from equations 4, 5, and 6 to ensure the selected route is contiguous:

s and q above represent the start and goal nodes, respectively.

Equation (4) above requires that exactly one more route must flow out of the starting point than into it. Equation (5) requires that exactly one more selected route must flow into the end point than flow out of it. Finally, equation (6) indicates the outward and inward flow between two nodes must be balanced for all nodes other than the start and the finish.

[ron-at-swgy]

I think this should work similarly to the way I implemented the objective functions:

c4 = solver.Constraint(1)
for f in range(modesz):
  for j in range(nodesz):
    c4.SetCoefficient(get_x(s, j, f), 1)
for f in range(modesz):
  for j in range(nodesz):
    c4.SetCoefficient(get_x(j, s, f), -1)

This should capture the intent of equation (4) above.