Using Alias to model bidirectional constraints in GAMS - optimization

Question

I'm working on a big optimization problem on GAMS so it's impossible for me to put the entire code here but I hope you could help me with where I am stuck at. I have 4 power nodes in my model that are connected by 2 bidirectional transmission lines (r) like this.
where r_a, r_b are the current transmission line capacities. Power can flow both directions and I'm tracking power going from A to A' and B to B' as well as from A' to A and B' to B. So there are 4 power flows (f) in 2 transmission lines (r). My decision variables are how much capacity upgrade (c(f)) I need to build in each of these lines to satisfy more power flow needs. So in GAMS, I minimized the cost of upgrading as:
investment_cost.. cap_cost =e= sum(f,c(f)*capCost(f));
here capCost(f) is the capital cost of upgrading the transmission line capacity to be able to flow 1 extra GW her hour.
My constraint: In each time period (t), the total power flow p(f,t) must be less than or equal to the existing line capacity + newly upgraded capacity:
line_cap(f,t).. old_line_cap(l)+c(f) =g= p(f,t);
However, my solution looks something like this:
fAA': 6.7 (built 6.7 GW more of capacity in line from A to A')
fA'A: 5.0 (built 5.0 GW more of capacity in line from A' to A)
fBB': 5.5 (built 5.5 GW more of capacity in line from B to B')
fB'B: 8.1 (built 8.1 GW more of capacity in line from B' to B)
But this is not right because if I upgrade line AA' by 6.7 GW, I don't need to upgrade line A'A, since they are the same line. Basically, I pay twice to upgrade the same line.
So I fix this, I'm trying to use Alias such as this:
Alias(f,ff)
line_cap(f,t).. old_line_cap(f)+c(f)+ sum((f,ff)$[line_source(f)=line_sink(ff) and line_source(ff)=line_sink(f)],c(ff)) =g= p(f,t);
But that still does not fix my problem.
I'd appreciate any help! Thank you!

Answer 1

If you want to stick with your 4 fs, let's call them your virtual lines (since a pair of two of these virtual lines actually form one physical lines). Now, let's introduce a new set of physical lines (fPhys) and a mapping between the virtual and the physical lines (fMap):
Set fPhys / fAA, fBB /
fMap(f, fPhys) / ("fA'A", "fAA'").fAA
("fB'B", "fBB'").fBB /;
Now, you can stick with using the set f for your flows, and use fPhys for the investment decision, like this:
investment_cost.. cap_cost =e= sum(fPhys,c(fPhys)*capCost(fPhys));
line_cap(f,t).. sum(fMap(f,fPhys), old_line_cap(fPhys)+c(fPhys)) =g= p(f,t);