I'm solving the mixed-integer quadratic problem with CPLEX. The objective, constraints, and decision variable sizes are following:
Objective matrix: $Q \in R^{312 \times 312}$
Ineqality matrix: $A_{ineq} \in R^{480 \times 312}$
Eqaulity matrix: $A_{eq} \in R^{96 \times 312}$
The number of variables is 312. However, when deciding 24 variables among them, other 288 variables are calculated with equality constraints and inequality constraints. And the range of key 24 variables are integer with lower bound 0 and upper bound 5.
I think this problem is not that complex, but solving this problem needs more than an hour with CPLEX default configurations. My computer's cpu is Ryzen 5 3600, and memory is 32gb that I think sufficient spec to solving the problem. So my questions are
- Is it usual to costs more than an hour to solve this size of the problem?
- If not, how can I reduce the solving time? I altered several CPLEX configurations, but the performance doesn't change drastically.
- The real decision variables in my case are 24, and other variables are used to calculate the objective with multiple steps. Should I change the optimization configuration to improve the optimization performance?
