Hello,
I am solving a MIP (minimization problem) using GLPK. I am running the code in MATLAB using YALMIP.
I have roughly 3000 integer variables in my code. I use --mipgap to get an approximate solution in a reasonable time. From the particular instance of my problem, I can pre-calculate a lower bound of my problem. Can I provide this lower bound as an input to GLPK?
An example:
Let's assume that the optimal solution of my minimization problem cannot be lower than a value of L.
In an usual setting, GLPK continuously updates the lower bounds {L1, L2, ...} through linear relaxation and the upper bounds {U1, U2, ... } and checks if the lower bound & upper bound becomes closer than the --mipgap value. Can I do any of the following two options?
1. I want GLPK to use max{L, L1} ; max{L, L2}, max{L, L3} as the lower bounds. In other words, if my provided lower bound L is greater than the currently found lower bound Li of GLPK, I want GLPK to use that value. This will narrow the gap between the lower bound and upper bound of GLPK and save execution time..
2. I want GLPK to use L as the constant lower bound. In that case, GLPK does not need to solve any linear relaxation. It can just find the feasible solution and check with the lower bound that I provided.
Thanks,
Nazmul