Tips for speeding up large-scale mixed integer linear programming

[Ming Jin]

I've been working on a MILP modeling of power systems. The problem is to find out the optimal technology installation and operation strategies for a year (12 months, 30 days, 24 hours, so in total 8640 time steps). The resulting program involves about 70K discrete variables, 30 K continuous variables, 110K equality constraints, and 355K inequality constraints. Most of the variables can be decoupled and only affect the objective for a single day operation, such as the use of electric boiler to meet the heating demands; however, there are variables that affect more than a day, like the dispatch of battery which might have some remaining energy at the end of each day to be used later. This means that we cannot simply treat the whole year as separate problems for each single day.

I used Gurobi MILP in python, with MIPGap to be 0.01, num_thread 1, method as Barrier (2). For this problem, it usually takes more than 12 hours in the presolving steps and even longer to see the actual convergence (i.e., the MIP gap has an actual value, like 50%). In most of the cases, the MIP gap shows a dash line (-) even after 12 hours, which is too long for the application. 

I'm wondering if there are anything I can do to help speed up the case? We've tried the suggestions https://www.gurobi.com/documentation/6.5/refman/mip_models.html but  it still doesn't improve. much thankful for your inputs!

[Kostja Siefen]

Hi Ming,

12 hours of presolve sounds a lot. Please post a log. 

Kostja