Online Learning for Scheduling MIP Heuristics

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 highly instance-dependent, relying on hard-coded rules derived from empirical testing a heterogeneous corpora of benchmark instances might lead sub-optimal performance. In this work, we propose an online learning approach that adapts the application heuristics towards single instance at hand. We replace commonly used static heuristic handling with adaptive framework exploiting past observations about heuristic’s make future decisions. particular, model problem controlling Large Neighborhood Search Diving – two broad complex classes as multi-armed bandit problem. Going beyond existing work in literature, control different simultaneously by agent. verify our numerically show consistent node reductions over MIPLIB 2017 Benchmark set. For harder take least 1000 s solve, observe speedup $$4\%$$ .