  Recently, several studies have explored the use of neural network to solve
different routing problems, which is an auspicious direction. These studies
usually design an encoder-decoder based framework that uses encoder embeddings
of nodes and the problem-specific context to produce node sequence(path), and
further optimize the produced result on top by beam search. However, existing
models can only support node coordinates as input, ignore the self-referential
property of the studied routing problems, and lack the consideration about the
low reliability in the initial stage of node selection, thus are hard to be
applied in real-world.
  In this paper, we take the orienteering problem as an example to tackle these
limitations. We propose a novel combination of a variant beam search algorithm
and a learned heuristic for solving the general orienteering problem. We
acquire the heuristic with an attention network that takes the distances among
nodes as input, and learn it via a reinforcement learning framework. The
empirical studies show that our method can surpass a wide range of baselines
and achieve results close to the optimal or highly specialized approach. Also,
our proposed framework can be easily applied to other routing problems. Our
code is publicly available.
