Solving multiple travelling salesman problem through deep convolutional neural network

The multiple travelling salesman problem (mTSP) is a classical optimisation problem that is widely applied in various fields. Although the mTSP was solved using both classical algorithms and artificial neural networks, reiteration is inevitable for these methods when presented with new samples. To meet the online and high-speed logistics requirements deploying new information technology, the iterative algorithm may not be reliable and timely. In this study, a deep convolutional neural network (DCNN)-based solution method for mTSP is proposed, which can establish the mapping between the parameters and the optimal solutions directly and avoid the use of iterations. To facilitate the DCNN in establishing a mapping, an image representation that can transfer the mTSP from an optimisation problem into a computer vision problem is presented. While maintaining the excellent quality of the results, the efficiency of the solution achieved by the proposed method is much higher than that of the traditional optimisation method after training. Meanwhile, the method can be applied to solve the mTSP under different constraints after transfer learning.