Quality of GUROBI solutions compared to CBC

[Bernd Welter]

As you know: you can use PTV xCluster Server2 with two different mathematical solvers:

• CBC solver (default shipping, no additional costs on top of the PTV xServer)
• The commercial GUROBI solver

GUROBI is much faster. Some features of xCluster require GUROBI (overnight stays, workload planning).

Another question came up: is the quality of GUROBI's output the same as with CBC? Here's the statement from DEV (Frank R.):

The results do not have to be equal. It is also not simple to determine "the better result". Both solvers try to solve the same mathematical problem by finding a solution as close to the perfect optimum as possible. But for us as PTV these solvers are a blackbox: we do not know how they determine their results. Considering the mathematical constraints both solvers return compareable results (*). Which one is the best? That depends on the perspective of the viewer.

(*) if they return results: for large problems the CBC could fail (no result) while GUROBI returns a proper result.
And Nithin mentions:

For medium and larg sized instances the quality of GUROBI is better: it's solutions are closer to the optimal solution (check "approximationTolerance" below profile). SOme examples: a medium size instance with 5% tolerance: CBC requires about 30min while GUROBI is done within 3mins. If the tolerance is set to 2% CBD requires 45mins. GUROBI: 6mins.

Bernd