Estimating the length of the optimal TSP tour: An empirical study using regression and neural networks

Over the last 35 years or so, researchers have proposed a variety of ways to estimate the length of an optimal traveling salesman tour. Some of the estimators are asymptotic in nature, while others are equations that relate tour length to various independent variables such as the number of points in a problem, size of a problemʹs service area, and density of points. In this paper, we develop simple, empirically based estimators of the optimal tour length using regression and neural network models and show that these models can produce reasonably good estimates easily.