Too Big, so Fail? -- Enabling Neural Construction Methods to Solve
  Large-Scale Routing Problems
Jonas K. Falkner Lars Schmidt-Thieme
In recent years new deep learning approaches to solve combinatorial
optimization problems, in particular NP-hard Vehicle Routing Problems (VRP),
have been proposed. The most impactful of these methods are sequential neural
construction approaches which are usually trained via reinforcement learning.
Due to the high training costs of these models, they usually are trained on
limited instance sizes (e.g. serving 100 customers) and later applied to vastly
larger instance size (e.g. 2000 customers). By means of a systematic scale-up
study we show that even state-of-the-art neural construction methods are
outperformed by simple heuristics, failing to generalize to larger problem
instances. We propose to use the ruin recreate principle that alternates
between completely destroying a localized part of the solution and then
recreating an improved variant. In this way, neural construction methods like
POMO are never applied to the global problem but just in the reconstruction
step, which only involves partial problems much closer in size to their
original training instances. In thorough experiments on four datasets of
varying distributions and modalities we show that our neural ruin recreate
approach outperforms alternative forms of improving construction methods such
as sampling and beam search and in several experiments also advanced local
search approaches.