I have a domain problem formulation in MathProg, where the cost function uses geometrical distances. The data sets contain only X,Y coordinates and not the actual distances. Right now, my formulation calculates the distances directly:
minimize total: sum{(f, c) in S} x[f, c] * sqrt(((facilityXs[f] - customerXs[c])**2) + ((facilityYs[f] - customerYs[c])**2));
And I want to know, whether the MathProg compiler is smart enough to see that the expression inside sqrt is constant and thus the whole thing can be precomputed, or whether it recalculates the expression every time, and how can I write it in a more elegant way.
Yes the MathProg 'compiler' is smart enough. It will precompute all equations containing solely parameters (and then create a computation matrix containing just one numeric value per cell). If you put variables in non linear functions like sqrt() the precomputation will fail.
A more elegant way is to keep your core set of equations linear. I often use separate parameters calculated by 'prequations', to keep the main formulations clean and simple.
param distance{(f,c) in S} := sqrt(((facilityXs[f] - customerXs[c])**2) + ((facilityYs[f] - customerYs[c])**2);
minimize total: sum{(f, c) in S} x[f, c] * distance[f,c]);