Learning Active Constraints to Efficiently Solve Bilevel Problems.

Bilevel programming can be used to formulate many engineering and economics problems. However, solving such problems is hard, which impedes their implementation in real-life. In this paper, we propose to address this tractability challenge using machine learning classification techniques to learn the active constraints of the lower-level problem, in order to reduce it to those constraints only. Unlike in the commonly used reformulation of bilevel programs with the Karush-Kuhn-Tucker conditions as a mixed-integer linear problem, our approach avoids introducing binaries and big-M constants. The application of machine learning reduces the online solving time, and is particularly necessary when the same problem has to be solved multiple times. In particular, it is very adapted to power systems problems, and especially to market applications in which the same problem is solved many times for different loads. Three methods are developed and applied to the problem of a strategic generator, with a DCOPF in the lower-level. We show that for networks of varying sizes, the computational burden is significantly reduced with a good probability of retrieving the optimal solution. We manage to find solutions for problems that were previously intractable.