  Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often
solve large real-world problems within minutes. This success can partially be
attributed to heuristics. Since their behavior is highly instance-dependent,
relying on hard-coded rules derived from empirical testing on a large
heterogeneous corpora of benchmark instances might lead to sub-optimal
performance. In this work, we propose an online learning approach that adapts
the application of heuristics towards the single instance at hand. We replace
the commonly used static heuristic handling with an adaptive framework
exploiting past observations about the heuristic's behavior to make future
decisions. In particular, we model the problem of controlling Large
Neighborhood Search and Diving - two broad and complex classes of heuristics -
as a multi-armed bandit problem. Going beyond existing work in the literature,
we control two different classes of heuristics simultaneously by a single
learning agent. We verify our approach numerically and show consistent node
reductions over the MIPLIB 2017 Benchmark set. For harder instances that take
at least 1000 seconds to solve, we observe a speedup of 4%.
