I am trying to solve an optimisation problem and come up with two Integer Linear Programming models. For each model, I am able to find a function that calculate the number of possibilities based on different variables, e.g. problem sizes.
I cannot directly conclude that one model has a smaller search space than the other. Instead, I develop an application that compares the actual numbers of possibilities between 2 models based on different values of the variables.
My application tries millions of different variables and shows that the number of possibilities of one model is less than the other 99% of the time. Is it enough to conclude that it is likely for one model to have the smaller search space, and to be solved faster than the other?