LiMIP: Lifelong learning to solve mixed integer programs

Sahil Manchanda, Sayan Ranu

Abstract:

Mixed Integer programs (MIPs) are typically solved by the
Branch-and-Bound algorithm. Recently, Learning to imitate
fast approximations of the expert strong branching heuristic
has gained attention due to its success in reducing the running
time for solving MIPs. However, existing learning-to-branch
methods assume that the entire training data is available in a
single session of training. This assumption is often not true,
and if the training data is supplied in continual fashion over
time, existing techniques suffer from catastrophic forgetting.
In this work, we study the hitherto unexplored paradigm of
Lifelong Learning to Branch on Mixed Integer Programs. To
mitigate catastrophic forgetting, we propose LIMIP, which is
powered by the idea of modeling an MIP instance in the form
of a bipartite graph, which we map to an embedding space
using a bipartite Graph Attention Network. This rich embed-
ding space avoids catastrophic forgetting through the appli-
cation of knowledge distillation and elastic weight consolida-
tion, wherein we learn the parameters key towards retaining
efficacy and are therefore protected from significant drift. We
evaluate LIMIP on a series of NP-hard problems and estab-
lish that in comparison to existing baselines, LIMIP is up to
50% better when confronted with lifelong learning