Multi-Objective Optimization for Traveling Salesman Problem: A Deep Reinforcement Learning Algorithm via Transfer Learning

A wide range of real applications can be modelled as the multi-objective traveling salesman problem (MOTSP), one of typical combinatorial optimization problems. Meta-heuristics can be used to address MOTSP. However, due to involving iteratively searching large solution space, they often entail significant computation time. Recently, deep reinforcement learning (DRL) algorithms have been employed in generating approximate optimal solutions to the single objective traveling salesman problems, as well as MOTSPs. This study proposes a multi-objective optimization algorithm based on DRL, called multi-objective Pointer Network (MOPN), where the input structure of the Pointer Network is re-designed to be applied to MOTSP. Furthermore, a training strategy utilizing a representative model and transfer learning is introduced to enhance the performance of MOPN. The proposed MOPN is insensitive to problem scale, meaning that a trained MOPN can address MOTSPs with different scales. Compared to meta-heuristics, MOPN takes much less time on forward propagation to obtain the Pareto front. To verify the performance of our model, extensive experiments are conducted on three different MOTSPs to compare the MOPN with two state-of-the-art DRL models and two multi-objective meta-heuristics. Experimental results demonstrate that the proposed MOPN obtains the best solution with the least training time among all the compared DRL methods.