On Distributional Dependent Performance of Classical and Neural Routing Solvers

TL;DR

This paper investigates how the distribution of problem instances affects the performance of neural and classical routing solvers, showing that neural methods improve when trained on sub-samples from a fixed distribution.

Contribution

It introduces a novel approach to generate and utilize problem instance distributions for training neural combinatorial optimization methods in routing problems.

Findings

Neural routing solvers perform closer to meta-heuristics when trained on sub-samples.

Performance gap decreases with distribution-aware training.

Large problem instance distributions can improve neural solver generalization.

Abstract

Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far neural methods struggle to outperform highly engineered problem specific meta-heuristics, this work explores a novel approach to formulate the distribution of problem instances to learn from and, more importantly, plant a structure in the sampled problem instances. In application to routing problems, we generate large problem instances that represent custom base problem instance distributions from which training instances are sampled. The test instances to evaluate the methods on the routing task consist of unseen problems sampled from the underlying large problem instance. We evaluate representative NCO methods and specialized Operation Research meta heuristics on this novel task and demonstrate that the performance gap between neural routing solvers and highly specialized meta-heuristics decreases when learning from sub-samples drawn from a fixed base node distribution.