Suppose you are writing a paper about a certain new problem class. You have certain problem instances of different size (real-world as well as random) given. You developed different integer programming problem formulations for this problem and want to compare the performance of these models in the paper. (I would also be interested if something changes if we compare different algorithms, i.e. Benders Decomposition vs naive MIP formulation)
Now you want to present statistics to compare the performance of the different models.
An incomplete list of some things come to my mind are:
- Value of LP Relaxation
- Time to first solution
- Gap of first solution to optimal solution
- when is the optimal solution found
- Time to solve the model
- Number of solved models
- Performance profiles
- Number of branch and bound nodes
- Primal/Dual integral
and there are many more, but what are the most important statistics which you want to display (and in what form) to give a convincing picture of the performance of the different models without overloading it with too much statistic.