TSP Combination Optimization with Semi-local Attention Mechanism

The Traveling Salesman Problem (TSP) is a canonical NP-hard combinatorial optimization problem. The attention mechanism has shown promising performances in natural language processing (NLP) and computer vision (CV). But on the TSP combinatorial optimization problems, the attention mechanism has not achieved satisfactory performance. Therefore, this paper proposes a new attention mechanism, termed a semi-local attention mechanism, to solve combinatorial optimization problems such as the TSP road network graph problem. This paper trains a Long Short-Term Memory (LSTM) network to predict a distribution over different city permutations with the input of a set of city node coordinates, uses negative tour length as the reward, and optimizes the parameters of the LSTM network with Adam optimizer and utilizes a stochastic gradient descent and a policy gradient method to train the model. The extensive experiments demonstrate that the semi-local attention mechanism achieves more close to optimum solutions than the local attention and globe attentional mechanism on 2D TSP combinatorial optimization problem graphs with 200 nodes.