  In the new wave of artificial intelligence, deep learning is impacting
various industries. As a closely related area, optimization algorithms greatly
contribute to the development of deep learning. But the reverse applications
are still insufficient. Is there any efficient way to solve certain
optimization problem through deep learning? The key is to convert the
optimization to a representation suitable for deep learning. In this paper, a
traveling salesman problem (TSP) is studied. Considering that deep learning is
good at image processing, an image representation method is proposed to
transfer a TSP to an image. Based on samples of a 10 city TSP, a fully
convolutional network (FCN) is used to learn the mapping from a feasible region
to an optimal solution. The training process is analyzed and interpreted
through stages. A visualization method is presented to show how a FCN can
understand the training task of a TSP. Once the training is completed, no
significant effort is required to solve a new TSP and the prediction is
obtained on the scale of milliseconds. The results show good performance in
finding the global optimal solution. Moreover, the developed FCN model has been
demonstrated on TSP's with different city numbers, proving excellent
generalization performance.
