  Multi-objective orienteering problems (MO-OPs) are classical multi-objective
routing problems and have received a lot of attention in the past decades. This
study seeks to solve MO-OPs through a problem-decomposition framework, that is,
a MO-OP is decomposed into a multi-objective knapsack problem (MOKP) and a
travelling salesman problem (TSP). The MOKP and TSP are then solved by a
multi-objective evolutionary algorithm (MOEA) and a deep reinforcement learning
(DRL) method, respectively. While the MOEA module is for selecting cities, the
DRL module is for planning a Hamiltonian path for these cities. An iterative
use of these two modules drives the population towards the Pareto front of
MO-OPs. The effectiveness of the proposed method is compared against NSGA-II
and NSGA-III on various types of MO-OP instances. Experimental results show
that our method exhibits the best performance on almost all the test instances,
and has shown strong generalization ability.
