Deep reinforcement learning for multi-objective combinatorial optimization: A case study on multi-objective traveling salesman problem

Multi-objective combinatorial optimization problems (MOCOPs) widely exist in real applications, and most of them are computationally difficult or NP-hard. How to solve MOCOPs efficiently has been a challenging issue. The heuristic algorithms have achieved good results on MOCOPs, while they require careful hand-crafted heuristics and iterative computing for the solutions. Recently, deep reinforcement learning (DRL) has been employed to solve combinatorial optimization problems, and many DRL-based algorithms have been proposed with promising results. However, it is difficult for these existing algorithms to obtain diverse solutions efficiently for MOCOPs. In this paper, we propose an algorithm named MOMDAM to solve MOCOPs. In MOMDAM, the attention model (AM) is used and can simply modify the encoder to facilitate the construction of solutions with any weight vector, as well as the multiple decoders (MD) are employed to obtain diverse policies to further improve the diversity and convergence of the solutions. Experimental results on the bi-objective traveling salesman problem show that, MOMDAM significantly outperforms some state-of-the-art algorithms in terms of solution quality and running time.