Originally posted by: DeyeTao

I wrote a model which is a little complex. It  has about x*k*580 variables where x presents the traffic number which I hope it can vary from 1 to 10 more or less, and k denotes the number of paths which can equal to 2 or 3.

The problem is that when I choose k=2 and x =4, the ILP model can be optimized while when I increase the x or k, the answer cannot be found in reasonable time.

The model cannot be changed but I think I can change some constraint forms.

So I wonder what is the relation between elapsed time of ILP model and the variables or number of constraints? In which way I can simplify my codes?Or how to set certain parameters to solve the problems efficiently?

I wanna to further describe my model. It aims to solve the routing and spectrum allocation problem in a network. Given a network graph with N nodes and E edges, as well as some traffic demand with respective bandwidth demand and certain destination. Now we need to compute the path to the destination node and allocate the spectrum to each path to satisfy the requirement. Of course, my model includes some more complex conditions, but the crucial point is that I wrote above. So on each link, we should allocate some spectrum for each traffic, which should subject to spectrum continuity meaning spectrum allocated continuous,  for example 1..3. To compute the path from source node to destination node, the nodes should subject to flow constraint meaning for each node, the input flow must equal to the output flow except for the source node and destination node. There are also some other constraints and I just not list each of them here.

I do not know whether I describe the question well. I wonder whether the running time of the software is relative to the number of variables and number of constraints? And if I use more constraints to limit the variables, the time would be decreased or increased? I mean which is better, the constraints is strict or loose?

The relationship between run time and problem dimensions in MILP models is very inconsistent. Some large problems solve quickly (some don't), and some small problems take a long time (some don't). Adding seemingly redundant constraints to a MILP model sometimes make it faster (by reducing the feasible region of the LP relaxation) and sometimes make it slower (slowing down the presolver, or adding "drag" during simplex solves). Adding variables to a model can make it slower (by expanding the solution space) or faster (for the same reason, if the solver was struggling to find an initial feasible solution).

Sorry, but I don't think you will receive an answer to your question that will do you any good.

Originally posted by: DeyeTao

Thanks for your patient explaining. Now I think I should try to decrease the number of variables.