  This study proposes an end-to-end framework for solving multi-objective
optimization problems (MOPs) using Deep Reinforcement Learning (DRL), that we
call DRL-MOA. The idea of decomposition is adopted to decompose the MOP into a
set of scalar optimization subproblems. Then each subproblem is modelled as a
neural network. Model parameters of all the subproblems are optimized
collaboratively according to a neighborhood-based parameter-transfer strategy
and the DRL training algorithm. Pareto optimal solutions can be directly
obtained through the trained neural network models. In specific, the
multi-objective travelling salesman problem (MOTSP) is solved in this work
using the DRL-MOA method by modelling the subproblem as a Pointer Network.
Extensive experiments have been conducted to study the DRL-MOA and various
benchmark methods are compared with it. It is found that, once the trained
model is available, it can scale to newly encountered problems with no need of
re-training the model. The solutions can be directly obtained by a simple
forward calculation of the neural network; thereby, no iteration is required
and the MOP can be always solved in a reasonable time. The proposed method
provides a new way of solving the MOP by means of DRL. It has shown a set of
new characteristics, e.g., strong generalization ability and fast solving speed
in comparison with the existing methods for multi-objective optimizations.
Experimental results show the effectiveness and competitiveness of the proposed
method in terms of model performance and running time.
