Summary of the fuzzy Hopfield-Tank TSP model

This paper discusses recent results concerning the dynamics of the Hopfield-Tank travelling salesman problem (TSP) model (Euclidean). Ayier´s subspace approach is used to ensure feasible solutions. A fuzzy approach to “reading” the state of the system is introduced. This consists of computing, at each iteration, the center of mass of the positive activations in each row of the neural array and sorting them to obtain a “fuzzy” tour at each iteration. The fuzzy approach exposes the inner workings of the system in a unique and surprising way. The system goes through three phases: centroid, monotonic, and nearest-city. These phases are directly related to city position statistics, such as the centroid and principal axis of the city coordinates. We provide a 50 city example