I have a set of U users and a set of S servers. I want to maximize the number of users allocated to a server while minimizing the number of servers used (this means that I have two objective functions).
Each user has some requirements w and each server has a total capacity of C.
The solver variables are the following:
# x[i,j] = True if user u[j] is allocated to server s[i]
# x[i,j] = False otherwise
# y[i] = True if server s[i] is used to serve users
# y[i] = False otherwise
As mentioned before, I want to maximize x[i,j] while minimizing y[i]
The constraints are the following:
- Capacity constraint: Since each server i has a certain capacity, the allocation of j users must not exceed that capacity
- Proximity constraint: Only users located within the range of the server can be allocated to it. A user can be located in the overlapping range of multiple servers
- Constraint family: Ensures every user is allocated to at most one server.
Using this library
from ortools.sat.python import cp_model
So far I've done:
- Create the solver variables (they are boolean)
- Create the constraints
- Maximize the x[i,j] variable
- Obtain the objective function
For instance, if I have 10 users and 4 servers all the 10 users are allocated among the 4 servers
What I need but haven't been able to accomplish:
- Maximize the
x[i,j]variable AND Minimize they[i]variable
For the same 10 users and the same 4 servers above, all the 10 users can be allocated among just 2 servers and not 4
I have tried the solution given in this post but it is not working since I got that the problem does not have an optimal solution
