I've been working with the football pool problem, which is a problem that presents symmetry.
Using the different options of the symmetry parameter that Gurobi has, I have found that these do not cause any change. That is, the same number of nodes are explored with all the options and the execution times are similar, regardless of how aggresive we are with symmetry detection.
I don't understand the reason of this behavior, as I was expecting that detecting symmetries would improve the performance of the branch and bound algorithm.
Given the posibility that this behavior only occurred with the football pool problem, I have also verified what happens with the graph coloring problem, which is a problem that presents symmetry too.
The results obteined with different instances used are again analogous to those obteined with the football pool problem.
I attach two tables with the results for two of the instances:
Could someone tell me why this happens?
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