The Optimal Elastic Net: Finding Solutions to the Travelling Salesman Problem

Abstract

We introduce the optimal elastic net (OEN) method for finding solutions to the travelling salesman problem (TSP). The OEN method is related to the elastic net (EN) method[1]. The EN method is analogous to laying a circular loop of elastic on a plane containing a number of cities, and allowing each city to exert an attractive force on the loop; the EN method models this loop as a finite set of points, or units. The EN method encourages each city to become associated with at least one unit, and requires a large number of units in order to ensure that each city is matched to a unit at convergence. In contrast, the OEN method encourages each city to become associated with at least one unit, and each unit to become associated with at least one city. One consequence of this is that the OEN method requires fewer units than the EN method.