Speeding up my MIP

[Parisa Keshavarz]

Hello, I am trying to solve a mixed integer problem and it takes so long. I searched a bit and came across something called 'numerically unstable' problems that happen when there are continuous variables in the MIP.

Is there a way to figure out if my model has this issue? I am using Gurobi solver in Matlab.

Also, I noticed something else, the staring gap in my problem is around 1500% which is odd. Is there anyway that some limitations can be imposed on the gap? For example to start from some where or to finish at a specific gap. I ask this because I found some suggestions to solve the speed problems for CPLEX but I could not found a way to implement any of them in Yalmip. I have attached the link below.

I appreciate your help.

https://www.ibm.com/support/pages/cplex-performance-tuning-mixed-integer-programs

[Johan Löfberg]

Tuning module is not accessible via YALMIP

Some MILPs (actually essentially all in theory) take intractable amount of time so there is really no surprise

https://yalmip.github.io/slowmilp

There is nothing strange with a massive gap when you start. The gap is even infinite until you find a feasible solution.

[Parisa Keshavarz]

Thank you for your answer. Is it possible to get faster solver time if I move to CPLEX or other solvers? Because they use different algorithms and also cplex has tuning features.

Also, I have another question. Overall, is there a way to find out if my model is numerically unstable? and what can I do if it is?

[Johan Löfberg]

Possible of course. Sometimes problems are solved in 1s using cplex and 1 day using gurobi, and sometimes they take 1s in gurobi and 1 day in cplex. Same with mosek, and any other solver. MILPs are unpredictable by nature, an epsilon change can change the behavior completely

If the model is numerically unstable, most solvers would warn about various such indicators when running