  Model-free deep-reinforcement-based learning algorithms have been applied to
a range of
COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}.
However, these approaches suffer from two key challenges when applied to
combinatorial problems: insufficient exploration and the requirement of many
training examples of the search space to achieve reasonable performance.
Combinatorial optimisation can be complex, characterised by search spaces with
many optimas and large spaces to search and learn. Therefore, a new method is
needed to find good solutions that are more efficient by being more sample
efficient. This paper presents a new reinforcement learning approach that is
based on entropy. In addition, we design an off-policy-based reinforcement
learning technique that maximises the expected return and improves the sample
efficiency to achieve faster learning during training time. We systematically
evaluate our approach on a range of route optimisation tasks typically used to
evaluate learning-based optimisation, such as the such as the Travelling
Salesman problems (TSP), Capacitated Vehicle Routing Problem (CVRP). In this
paper, we show that our model can generalise to various route problems, such as
the split-delivery VRP (SDVRP), and compare the performance of our method with
that of current state-of-the-art approaches. The Empirical results show that
the proposed method can improve on state-of-the-art methods in terms of
solution quality and computation time and generalise to problems of different
sizes.
