Deep Reinforcement Learning Algorithm Based on Graph Weight Multi-Pointer Network for Solving Multiobjective Traveling Salesman Problem

Abstract

The multiobjective traveling salesman problem (MOTSP) is a class of classical multiobjective combinatorial optimization problems (MOCOPs), attracting significant interest across various disciplines. Due to the NP-Hard nature, traditional algorithms struggle to find feasible solutions in a short period of time. To this end, this paper proposes a deep reinforcement learning algorithm based on graph weight multi-pointer network (GWMPN), which only needs to perform forward propagation on the GWMPN model to obtain the solution of MOTSP, thus significantly improving the solution efficiency. Specifically, we encode the problem instance and weight vector by means of the graph weight encoder of the GWMPN model to construct the overall encoded feature with enhanced representation capabilities. Subsequently, the encoded feature as the context vector is fed into the multi-pointer decoder to construct solutions through diversity interactions. Experimental results demonstrate that our algorithm solves the MOTSP more rapidly than classical heuristic algorithms and exhibits superior performance and generalization compared with learning-based algorithms within a reasonable time frame.

Keywords

• Combinatorial optimization problem
• multiobjective traveling salesman problem
• deep reinforcement learning
• graph neural network
• pointer network