  Vehicle routing problem (VRP) is a typical discrete combinatorial
optimization problem, and many models and algorithms have been proposed to
solve the VRP and its variants. Although existing approaches have contributed a
lot to the development of this field, these approaches either are limited in
problem size or need manual intervening in choosing parameters. To solve these
difficulties, many studies have considered the learning-based optimization
(LBO) algorithms to solve the VRP. This paper reviews recent advances in this
field and divides relevant approaches into end-to-end approaches and
step-by-step approaches. We performed a statistical analysis of the reviewed
articles from various aspects and designed three experiments to evaluate the
performance of four representative LBO algorithms. Finally, we conclude the
applicable types of problems for different LBO algorithms and suggest
directions in which researchers can improve LBO algorithms.
