Recently, Deep reinforcement learning (DRL) models have shown promising
results in solving routing problems. However, most DRL solvers are commonly
proposed to solve node routing problems, such as the Traveling Salesman Problem
(TSP). Meanwhile, there has been limited research on applying neural methods to
arc routing problems, such as the Chinese Postman Problem (CPP), since they
often feature irregular and complex solution spaces compared to TSP. To fill
these gaps, this paper proposes a novel DRL framework to address the CPP with
load-dependent costs (CPP-LC) (Corberan et al., 2018), which is a complex arc
routing problem with load constraints. The novelty of our method is two-fold.
First, we formulate the CPP-LC as a Markov Decision Process (MDP) sequential
model. Subsequently, we introduce an autoregressive model based on DRL, namely
Arc-DRL, consisting of an encoder and decoder to address the CPP-LC challenge
effectively. Such a framework allows the DRL model to work efficiently and
scalably to arc routing problems. Furthermore, we propose a new bio-inspired
meta-heuristic solution based on Evolutionary Algorithm (EA) for CPP-LC.
Extensive experiments show that Arc-DRL outperforms existing meta-heuristic
methods such as Iterative Local Search (ILS) and Variable Neighborhood Search
(VNS) proposed by (Corberan et al., 2018) on large benchmark datasets for
CPP-LC regarding both solution quality and running time; while the EA gives the
best solution quality with much more running time. We release our C++
implementations for metaheuristics such as EA, ILS and VNS along with the code
for data generation and our generated data at
https://github.com/HySonLab/Chinese_Postman_Proble